BNL 52079 UC-34-D (Physics-Particles and Fields — TIC-4500)
BNL—52079 012506 Proceedings of the NL Neutrino Workshop
Opportunities for Neutrino Physics at BNL
February 5-7, 1987 Editor: Michael J. Murtagh
Organizing Committee: A.S. Carroll, Chairman, BNL W. Lee, Columbia University W.J. Marciano, BNL M.J. Murtagh, BNL T. Romanowski, Ohio State University F. Vannucci, LPNHE, Paris/Boston U.
BROOKHAVEN NATIONAL LABORATORY ASSOCIATED UNIVERSITIES, INC.
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ThiB report waB prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, nor any of their contractors, subcontractors, or their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use woyld not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise, does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency, contractor or subcontractor thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency, contractor or subcontractor thereof.
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NTIS price codes: Printed Copy: A12; Microfiche Copy: A01 FOREWORD A three day workshop on neutrino physics was held from February 5-7, 1987 at Brcokhaven National Laboratory during an unusual stretch of fine Long Island winter weather. The workshop was organized by the AGS Users Group and was sponsored by Brookhaven National Laboratory with additional support from Associated Universities, Inc. The completion of three AGS neutrino experiments in the Spring of 1986 provided the motivation for holding this workshop. Two of the experiments reported preliminary positive results for neutrino oscillations, while the other reported results on the elastic scattering of neutrinos on electrons and protons and on a variety of other topics. In the informal setting of the Workshop, an international group of 75 physicists discussed these new results in relation to already published data. There was considerable discussion of the relevance of low energy results in the standard model theory of weak interactions and of the formalism for neutrino oscillations in the presence of matter and for three neutrino mixing. A number of new ideas for the next generation of neutrino experi- ments at the AGS were discussed. The enthusiastic encouragement of the BNL Directorate is gratefully acknowledged. The organizing committee of Wonyong Lee, William Marciano, Michael Murtagh, Tom Romanowski and Francois Vannucci are to be commended for attracting a large and diverse group of speakers and participants in a remarkably short period of time. Michael Murtagh deserves special thanks for filling in for missing speakers and editing these proceedings. We also wish to acknowledge the untiring efforts of Mrs. Kathy Einfeldt and the other members of the Brookhaven staff to ensure that the conference ran smoothly. Finally many thanks to all the speakers and participants at the workshop for preparing talks and generously sharing their knowledge.
Alan S. Carroll, Chairman Organizing Committee
DISCLAIMER
This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United Stales Government nor any agency ihereor, nor any of their •;mpioyeas, makes any warranty, express or implied, or assumes any legal liability or'responsi- h,lit> for the accuracy, completeness, or usefulness of any information, apparatus product or
process disclosed, or represents that ;lS use would nnt infringe privately owned rights Refer- ence herein to any specific commercial product, process, or service by trade name trademark manufacturer, or otherwise does not necessarily constitute or imply its endorsement recom- mendation, or favoring by the United States fiovernment or any agency thereof The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof. TABLE OF CONTENTS
Page No.
Introduction
Neutnno Physics - A Theoretical Perspective - W.J. Marciano, BNL
Neutrino Oscillation Experiments
Neutrino Oscillations at Accelerators - Past results, future prospects - F. Vannucci, LPNHE/Boston 15
Search for Neutrino Oscillations - AGS Experiment 816 - P. Astier, LPNHE 25
Search for Neutnno Oscillations at the AGS with the Narrow Band Beam - G. Tzanakos, Columbia 39
A Search for i>M—ve Oscillations Using the E734 Detector - M J. Murtagh, BNL 59
Neutrino Oscillations in BEBC - M. Baldo-Ceolin, U. of Padova 67
Searches for Neutrino Oscillations - The CHARM Collaboration - V. Zacek, CERN 77
Future Long Baseline v^—i'e Oscillation Searches at Accelerators - M.J. Murtagh, BML 81
Theory of Neutrino Oscillations
Effects of the Third Generation on Neutnno Oscillations in Vacuum and Matter - C.W. Kim, Johns Hopkins 89
Resonant Solar Neutrino Oscillation Versus Laboratory Neutrino Oscillation Experiments - C.S. Lim, BNL 111
Matter Oscillations: Neutrino Transformation and Regeneration in the Earth - A. Baltz and J. Weneser, BNL 121
- v - Beams and Detectors
Design ar,d Status of the AG3 Booster Accelerator - E.B. Forsyth, BNL 139
Focussing Horn Upgrades - A.S. Carroll, BNL 145
Neutrino Flux Calculations for the AGS Narrow Band Beam - N. Kondakis. Columbia 151
The Liquid Argon Time Projection Chamber - G. Buhler, U. of CA., In/me 161
Physics Calibration of the SOUDAN II Nucleon Decay Experiment Using BNL Neutrinos - W.A. Mann, Tufts 169
The Sudbury Neutrino Observatory
- P.J. Doe, U. of CA., Irvine 177
The Standard Model and Beyond
Elastic Scattering of Muon Neutrinos at BNL - LS. Durkin, Ohio State 1B7 The Effect of Extra Neutral Gauge Bosons on Neutrino-Electron Scattering - G. Godfrey and W.J. Marciano, BNL 195
The Weak Neutral Current - P. Langacker, U. of Penn 205
Second Class Current Effects in Tau Lepton Decay? - M. Derrick, ANL 221
Summary and Conclusions - F.S. Merritt, U. of Chicago 233
List of Participants 248
- vi - BROOKHAVEN NATIONAL LABORATORY
NEUTRINO PHYSICS - A THEORETICAL PERSPECTIVE
W.J. Marciano Physics Department Brookhaven National Laboratory Upton, NY 11973
ABSTRACT Experimental measurements of sin2 9w are surveyed. They are shown to test electroweak unification at the quantum loop level and constrain new physics beyond the standard model. Neutrino oscillations are also examined in the framework of 3 generation mixing. Searches for vu —> vT oscillation at accelerator facilities are advocated.
INTRODUCTION Neutrino experiments at accelerator facilities generally fall into two categories: 1) preci- sion measurements of sin2 6\y, and 2) searches for neutrino oscillations. The first is part of a broader program made up of many diverse neutral current measurements which along with determinations of mw and mz aim to test the standard SU (2)L x U (l) model. They have now reached a high enough level of precision to actually probe the structure of its O (a) electroweak radiative corrections and constrain new physics appendages. Neu- trino oscillation experiments are more in the way of longshots. The standard model does not predict oscillations, but they can be easily accommodated by giving neutrinos small masses and mixing them. So far we have no compelling evidence that oscillations occur, but there may be hints of such phenomena in solar neutrino flux measurements, reactor experiments and even in some of the BNL data discussed at this Workshop. The clear observation of neutrino oscillation would of course have profound implications.
In this introductory talk, I would like to survey several aspects of neutrino physics. In particular, I will focus on measurements that I find interesting. The topics that I have cho- sen to discuss are: Precision measurements of sin 9w and their implications and neutrino oscillations in 3 generation scenarios. Regarding the first topic, T will be rather general in my discussion, since P. Langacker1 will present results of a detailed study2 of neutral current phenomenology in his lecture. In addition, S. Godfrey and I will supplement my discussion of physics beyond the standard model in a seperate contribution.3 There we
- 1 - analyze present constraints on additional neutral gauge bosons from v ^ — e scattering and examine the discovery potential of future experiments. Finally, my comments on neutrino oscillations convey a personal bias for the type of mixing and mass differences one should search for. More extensive lectures on that subject will be given in the talks by C.W. Kim4 and C.-S. Lim.5
2 PRECISION MEASUREMENTS OF sin Bw AND NEW PHYSICS
The weak mixing angle 6y/ plays a central role in the SU (2)L x U (l) model. Writing out the electroweak neutral current interaction Lagrangian
Ztl T 2 C-m% = - eA» (x) Y, QfHf - -^T W £ ( 3//L7M/L - sin 8wQfflflf) sin £u\y
e=g2sm9w (1) with T$f = weak isospin and Qj =electric charge, we see that 6\y occurs both at the fermion weak neutral current level and in the normalization of the SU (2)L coupling q
mw — TUZ cos 6w (2) So, one tests the standard model and the underlying concept of electroweak unification by measuring sin Qw in as many different ways as possible. A deviation in the value obtained from one experiment as compared with another would signal new physics.
Of course, radiative corrections must be accounted for in any precise determination of sin2 9\y, so that they will not be confused with new physics. In some cases, electroweak radiative corrections can be quite large. For example, consider the lowest order natural relationship 2 o 2 2 sin B°w = (e /ff2°) = 1 - Kv/r4) (3) where 0 indicates bare (unrenormalized) parameters. In terms of physical measureable quantities, that relationship is modified by finite O (a) loop corrections. The size of those corrections depends on the definitions employed; but for typical definitions they can be quite large. Defining the renormalized weak mixing angle by
2 2 sin 6W = 1 - mlr/m z (4) where mw and mz are physical masses and defining the renormalized charges e and gi via a =e2/47r = 1/137.036 (5a) 2 = 1.16636 x 10-5GeV~2 (56)
- 2 - leads to
— mz cos Ow J.— 37.28lGeV .„. = T (6) sin^w (1 — Ar)5 where2-6 Ar = 0.0713 ±0.0013 (7) for mt ~ 45 GeV and m^gg ~ 100 GeV. The radiative corrections in Ar ~ O (a) are quite large primarily due to vacuum polarization renormalization of e relative to gi- It is, however, in my opinion a mistake to call that effect a QED correction. Fermion loops enter in the photon propagator as well as the W± and Z propagators. So, the relative correction is calculable only because of electroweak unification.
When either mw or mz determinations are used to obtain sin2 Ow via Eq. (6), Ar causes a sizeable ~ 1% shift in the value found. Similarly, neutral current scattering cross sections and interference measurements must be corrected for O [a) quantum loops in extracting sin2 Ow • The effects of such electroweak radiative corrections are illustrated in Table 1 where several determinations of sin2 Ow are summarized. (For a more complete discussion see P. Langacker's talk.1 ) At present, deep-inelastic v^ scattering provides the best determination of sin2 Ow- In fact, much of the uncertainty in that extraction is theoretical in the sense that a model is employed to correct for charm threshold effects. It, therefore, appears that those measurements have been pushed about as far as possible.
Comparing the sin2 0$c- and sin2 Ow columns in Table 1, it is clear that the uncorrected value obtained from deep-inelastic v^ — N scattering differs from the mw and mz values, but the corrected sin2 Ow are in good agreement. So, the standard model has been tested at the level of its O (a) radiative corrections (at about the 3cr level). That test also limits new physics appendages to the standard model and provides the top quark mass bound2
mt £ 180GeV (8) That bound also applies to fourth generation quarks
mv - mhi ^ 180GeV. (9)
The present world average of all data 2 sin 0W = 0.230 ± 0.004 (10) now carries a rather small uncertainty. Comparing with the minimal SU(5) model pre- diction (for A.^L - 150+il° MeV)
2 sin 0w = 0.216±£o§4 (Minimal SU (5)) (11)
- 3 - Table 1: Values of sin2 $w = 1 — "^/m^ before and after electroweak radiative correc- tions are included. The values mj ~ 45GeV and mjj ~ lOOGeV were employed in the radiative correction.
Experiment sin2 0$?c- Radiative Correction sin2 0w Cs Atomic P.V. 0.221 ± 0.027 +0.008 0.229 ± 0.027 (Paris7- Boulder8) eD Asymmetry 0.224 ± 0.020 -0.005 0.219 ± 0.020 (Yale - SLAC9) (-) 0.212 ± 0.023 + 0.002 0.214 ± 0.023 (BNL10- CHARM11) (-) „ 0.220 ± 0.016 + 0.002 0.222 ± 0.016 (BNL12) +0.023 +0.023 -0.031 -0.031 i/fj.N deep-inel. 0.241 ± 0.006 -0.009 0.232 ± 0.006 (CDES,13 CHARM,14) (CCFRR,15 FMM16)
rnw = 80.9 ± 1.4GeV 0.212 ± 0.008 +0.017 0.229 ± 0.008 (UA117- UA21P)
mz = 91.9 ± 1.8GeV 0.208 ± 0.011 +0.022 0.230 ± 0.011 (UA117- UA218) World Average 0.230 ± 0.004
we see that they disagree by about 3cr. New physics beyond the W and Z mass scale (such as supersyrnmetry) can easily bring GUTS into accord with the higher sin 6w value in Eq. (10). However, it is clear that sin2 0w provides an important constraint on model building and one of the few windows to very high energy, i.e. near unification.
Experimentalists should continue to strive to measure sin2 Byy as precisely as possible. Fortunately, mz will be measured to better than ±50 MeV at SLC and LEP and that will determine sin3 9w to ± 0.00025 via Eq. (6) (after mt is pinpointed). Given such high precision, what role can other experiments play? To test the standard model or look for hints of new physics, one must compare distinct measurements. So, high precision measurements of sin2 Bw should be undertaken in as many processes as possible. As an illustration of that point, I will consider u ^e and v ^P scattering. 2 Averaging all experimental data on v^e —>• u^e and fMe —> u^e scattering, one finds
2 sin 6w = 0.223 ± 0.019 I f Me scattering j (12) which is in good accord with the world average. One can use that good agreement to obtain bounds on additional neutral gauge bosons (see the contribution by Godfrey and Marciano3 ) or look for more exotic effects such as compositeness and anomalous neutrino moments. One way that composite structure could show up is as an effective neutrino charge radius, acR. (It could be large if neutrinos are made of charged constituents.) Defining acR via the electric charge form factor (F (0) = 0)
4 + O (9 ) (13)
2 2 one finds that at low q it leads to a difference between sin 9w measuremeasu d in v Me and sin2 6w measured in non-neutrino reactions. That difference is given by
(the sign is model dependent). From present data, one finds (approximately)
16 CCR £ 1.5 x 10~ cm (15)
Improving sin2 Qw determinations from u ^e by an order of magnitude would probe com- positeness at the level of ~ 5 x 10~17cm.
In the case of anomalous neutrino moments, one can use the good agreement between theory and experiment to bound neutrino magnetic, electric and transition moments. Any such moment of magnitude ne/2me would increase the u^e and P^e neutral current differential cross sections by19
A ((-' da u ,.e dy m\ \y
y = (E^ - me) jEv. (16)
Since there is no evidence for such an effect, one finds (approximately)
9 \nVl\ < 1 x HT . (17)
I note that in the standard model with neutrino mass, one finds |K| ~ 3 x 10~19mi,/leV which is unobservably small. However, it is worth pushing the searches for re as far as possible, since a positive result would undoubtedly point to new physics.
- 5 - How far can v'^e scattering experiments be pushed? An ongoing CHARM II experiment at CERN plans to obtain several thousand events and thus lower the statistical uncertainty on sin2 6w to ± 0.005 from measurements of R
R = o {Ufj,e which in the standard model is given by
2 2 s = si^ 9W
Unfortunately, systematic uncertainties may be larger. A proposed LAMPF experiment20 aims to overcome the systematic normalization problem by stopping TT+ mesons and mea- suring from the decay product neutrinos
R S (
which in the standard model is given by
4 V 1 + 2s2 + 8s4 j K '
The proposed 1.7% measurement of R' would determine sin2 0w to within ± 0.002 and provide a powerful probe of new physics. Besides being sensitive to electroweak radiative corrections, it would constrain (or find hints of) additional neutral gauge bosons as heavy as ~ 800 GeV. Such a measurement is also indirectly sensitive to v^ +-+ vt oscillations. I will comment on that point in the next section.
In the case of elastic v MP scattering, an ongoing analysis of existing data by the E734 collaboration at BNL should reduce the statistical error on sin2 9w to ± 0.005. The challenge is to reduce systematic uncertainties. There is also a theoretical problem or attraction (depending on ones perspective) that comes into play. The standard model has no axial-isoscalar neutral current; but one is induced by loop effects and sea quark contri- butions. Collins, Wilczek and Zee21 have estimated that the two loop triangle diagram induces an axial-isoscalar neutral current amplitude that is about 10% of the tree level isovector amplitude. Of course, such an effect renders a precise determination of sin2 6w
unlikely. However, one can change the goals of u MP elastic scattering measurements. Using sin20w measured precisely from say mz as input, one can extract the q2 depen- dence of the induced axial-isoscalar amplitude from the differential cross section. In that way one may directly observe a two loop effect and study two gluon exchange physics.
- o - NEUTRINO OSCILLATIONS If neutrinos have mass, it is quite likely that they mix and that oscillations between different flavors can occur. In the case of very small masses, oscillation experiments may be the only probe of neutrino masses. Therefore, it is extremely important to search for oscillations wherever possible.
To get a feel for the mass and mixing parameters, probed by different oscillation ex- periments, consider the simplifying case of 2 generation mixing. (Three generations will be discussed subsequently.) The weak interaction states ue and Vy, produced in particle decays are related to the mass eigenstates v\ and vi via cos 9 sin 9 -sin9 cos9 So if at i = 0, a v^ is produced, the probability that at distance R it is still a v^ is given by
= 1 - sin' 20 star ^ R
2 Am2; = m\-m\ (21)
while the probability of it being observed as a ue is [^.Rl (22)
(Those formulas also apply to ue —»• u^ oscillations with Up. *-+ i/e interchanged.) Two 2 fundamental parameters 6 and Am2i enter into those expressions, whereas R and Ev are determined by experimental conditions. Disappearance experiments such as Pe —• Dp. (or Vr) at reactors are subject to flux normalization uncertainties; so they generally probe mixing angles for which sin2 29 ^ 0.1. On the other hand, appearance experiments such as U/j, —> fe at accelerator facilities actually detect the ue via vt + N —+ e + N'. They are mainly background limited by fake events and ve beam contamination which is typically, 1%. Those effects can be subtracted out or controlled by employing two detectors at different distances. Therefore, appearance measurements can easily extend the mixing domain explored to sin 29 *S 0.01. The same comments generally apply to ve or v^ —> vT. So, as a rule, appearance experiments are much better for small mixing scenarios.
The second oscillation parameter Am2i2 dictates the oscillation length. If Arn2i2 is very 2 small compared to RjEv, then the conversion probability is proportional to (R/Eu) . Therefore, one strives to have R large and Ev small. Of course, the fact that neutrino cross sections are proportional to Ev (at high energies) and the effective flux falls with increasing R must be folded in. So, one finds that reactor oscillation experiments where 2 2 Ev ~ 5-10 MeV is small, are very good for exploring small Am2/ £ 10~ eV ; but are
- 7 - limited to disappearance and thus large angles. On the other hand, accelerator oscillation experiments, such as those at the AGS where (Ev) a lGeV, can explore small mixing 2 2 2 via Vp —»• ue appearance and can be made sensitive to Am2i as small as 10~ eV by going out to 10 km distances. Very high energy facilities such as at Fermilab and CERN must go to much farther distances to probe Am2i* ^ 10~2eV2 and the flux falloff due to beam spread then makes such an undertaking very difficult, even though the neutrino cross section is larger. Therefore, in my opinion the AGS offers the best available means for extending the search for neutrino oscillations. Given an increase in the neutrino flux due to the construction of a booster and other likely upgrades, long distance experiments 2 2 2 2 (=* 10 km) should be able to completely explore the sin 29 £ 0.01 and Am2i £ 10~ eV region. I believe that both v^ —> ve and v^ —>• vr should be searched for; but I most strongly advocate the latter. The primary aim of this section is to strengthen the case for Ujj. —> uT searches at accelerator facilities.
Although theory does not specify neutrino masses and mixings, we have formed some prejudices. Based on our experience with the quark sector, we tend to expect relatively small mixing sin2 20 £ 0.2. In addition, the popular see-saw mechanism for majorana mass generation which naturally occurs in many GUTS leads us to expect a hierarchial mass relationship m\ » m\ » ml (23)
More specifically, in some scenarios
m\ : m2 : m2 :: ml : m\ : m\ * (24)
while in others ml : m2 : m| :: m2 : m\ : m\ (25) (In some cases, lepton masses replace the quark masses.) From those relationships one anticipates ml : m\ : m\ :: 1 : 1010 : 1016 (26a) or ml : m\ : m\ :: 1 : 105 : 108 (266) In either case, the hierarchy of masses implies that even with complicated 3 generation mixing, the oscillation problem reduces to an "effective" 2 neutrino problem. (I give an example later, also see C.-S. Lira's talk5 for more details.)
Eqs. (25) and (26) provide useful estimates for plausible mass ratios, but what sets the overall scale? Usually, some large unification mass, M, enters reciprocally e.g. m\ -~ m\/M. There is, of course, much uncertainty regarding M; so, experimentalists would be well advised to ignore any specific value and keep an open mind. Nevertheless, I would like to invoke here the popular idea that matter enhancement of ue —* v^ oscillations (the MSW effect22 ) is responsible for the apparent discrepancy between the predicted and 2 7 4 2 observed &olar neutrino ve flux. That elegant scenario occurs for Am2i ^ 10~ — 10~ eV .
- 8 - (See the talks by Kim4 and Lim5 for other possibiities.) As an alternative one could 2 7 4 2 23 have A7713] ~ 10~ — 10~ eV which would lead to ve —* uT in the sun. In that case (assuming Am2i2 2 7 4 2 Given a Am2i in the 10~ — 10~ eV range, Up —• ue oscillations would be unobservable at accelerators in a 2 generation mixing scenario; but they are still possible in the 3 generation case. In addition, Vp —> uT and vt —> uT may also be observable either in disappearance or appearance experiments. The point is that using that mass difference range in conjunction with Eq. (26) suggests 2 2 4 4 2 Am32 =* Am31 ~ 1CT - 10 eV (27) 2 2 2 which would control oscillations at reactor and accelerator facilities. For Am3i ^ 10~ eV , one should be able to observe such effects at the AGS or at reactors if the mixing angles are not too small, as we shall see. To illustrate the above points, consider the case of general 3 generation mixing Ve\ ( C1C3 SiCZ (28) — C\S2 — S1C2S3&" C2C3 / \ U$ cx = cos Of, i = 1,2,3 where a particularly convenient parametrization has been employed for analyzing oscil- 24 25 2 7 4 2 lations. ' Assuming Am2i =i 10~ - 10~ eV as appropriate for th*e MSW effect and; Arri3i2 ~ Amz22 — 10~2 ~ 102eV2 as expected in many hierarchy sceno.rios, one finds for laboratory energies and distances 2 2 2 Fv^Ve c sin 62 sin 203 sin f^^1 (29) 2 4 2 Vr =* sin 262 cos 6Z sin [^^1 (30) ^] (31) 2 2 2 Pu^ur /Pu^ue ^ cos 02 cos 03/ sin 03 (32) Note that the conversion probabilities are similar to the 2 generation case, because one 2 2 can effectively set Am2i to zero and Am3i ~ What implications follow from Eqs. (29)-(32)? For small mixing angles 02 and 03, one finds 2 PVti->VT ~ Pv^ve/ sin 63. Hence, searches for v^ —> vT are particularly well motivated. - 9 - In addition, it is apparent that PVvL-*Ue experiments at accelerators are not equivalent to reactor measurements of Pyc-*ve, even though constraints from both are generally plotted together. The reactor bounds are actually more restrictive. To further illustrate the above points, I consider some examples. As a first example, 2 2 2 2 2 assume Am3i ~ Am32 ^ 0.6eV , sin 203 c± 0.1 and sin 82 =± 0.3. That would lead to P^-n/e — 0.01 for the AGS neutrino beam at R ~ lkm. At that same distance -Pfji-n/r — 0-25 which is already close to being ruled out by v^ disappearance experiments. Those parameters also lead to a ut —* Qz at reactors that is potentially observable. 2 2 2 2 As a second example, cjsume Am31 ~ Am32 ^ 0.2eV , sin 203 ~ 0.15 and leave sin 6% arbitrary. Those parameters are consistent with the positive results found at the Bugey reactor26 and do not contradict bounds from other reactors. They imply that 2 2 at R ~ lkm, PVll-+Ve ^ 0.006sin 02 and PVII-*VT =: 0.04sin 202- In that case, for small V #2 \L —»• vt oscillations are probably too small to observe, but uu. —* uT may be observable particularly if one goes to longer distances, i.e. 10km. The bottom line is that u^ —»• vT appearance and disappearance experiments should be pushed as far as possible. As a final comment on oscillations, I want to make note of the changes in R and R' (see Eq. (18)) if oscillations occur. From the results in Eq. (29) one finds (for fixed energy 2 4 2 2 2 2 5 r 1 - 4s + f s + 8s sin' 02 sin 203 sin fe- 1 R = ?>{ \ v—±\ (33) 2 4 2 2 2 2 11 - 4s 4- 16s + 8s sin 92 sin 203 sin [^#^ > 2 Unfortunately, such an indirect detection of oscillations does not probe a very small Am3i because Ev is generally quite large in v ^e experiments. The proposed R' measurements at LAMPF are potentially a better probe of oscillations because the neutrino energies are lower EUll = 30MeV (EUe) ^ {E^) ^ 35MeV. Unfortunately the propagation distance is small. A careful analysis would integrate over the ve and Uy, energy spectrum and include the event distance from the target. Rather than doing that I will just note that the main effect is to increase R' by increasing the numerator and (in a three generation scenario) decreasing the denominator. In my opinion, such a measurement provides a consistency check on oscillations rather than a real search. CONCLUSION Neutrino physics has reached a rather mature phase. Using existing measurements of sin 8w, the standard electroweak model has been well tested and new physics appendages such as additional neutral gauge bosons have been constrained. Future measurements of sin $w in v e and u P scattering should strive for uncertainties ^ ±0.005 in order to complement other determinations from mz, asymmetries etc. - 10 - Neutrino oscillation experiments still have tremendous potential. A large part of the possible neutrino mixing and mass parameter space remains unexplored, particularly in the full 3 generation scenario. Given GUT prejudices regarding mass hierarchies, Uy. —»• uT at accelerators and ue —+ i>T at reactors appear to be the "best bets." At the AGS one can certainly do i/y, —> vT disappearance experiments, particularly if two detectors at very different distances are employed. It would, however, be nice to search for vT appearance by actually observing r's. Unfortunately, only about 10% of the AGS fM spectrum is above T production threshold energy and detection of r's appears to be difficult. One might try to increase the high energy neutrino flux by lengthening the parent meson decay path or upgrading the AGS to higher energies. The latter would of course be a major project. In any case t>M —> uT oscillation experiments are well enough motivated and the payoff from a positive result is high enough to warrant careful consideration of the feasibility of such experiments at the AGS. Of course, the detection of real neutrino oscillations in any single experiment would lead to many additional measurements and instill new vigorous life into neutrino physics. ACKNOWLEDGMENT This work supported under Contract DE-AC02-76CH00016 with the U.S. Department of Energy. REFERENCES 1. P. Langacker in these Proceedings. 2. U. Amaldi et al., preprint (1987). 3. S. Godfrey and W.J. Marciano in these Proceedings. 4. C.W. Kim in these Proceedings. 5. C.-S. Lim in these Proceedings. 6. W.J. Marciano and A. Sirlin, Phys. Rev.D29, 945 (1984); Erratum Phys. Rev. D31, 213 (1985). 7. C. Bouchiat and C.A. Piketty, LPTENS preprint (1986); M.A. Bouchiat, J. Guema and L. Pottier, J. Phys. 46, 1897 (1985). 8. S. Gilbert, M. Noecker, R. Watts and C. Wieman, Phys. Revl Lett. 55, 2680 (1985). 9. C.Y. Prescott et al., Phys. Lett.77B, 347 (1978); 84B, 524 (1979). 10. L.A. Ahrens et al., Phys. Rev. Lett. 54, 18 (1985). 11. F. Bergsma et al., Phys. Lett. 147, 481 (1984). 12. K. Abe et al., Phys. Rev. Lett. 56, 1107 (1986). 13. H. Abramowicz et al., Phys. Rev. Lett. 57, 298 (1986). 14. J. Allaby et al., CERN preprint (1986). 15. P. Reutens et al., Phys. Lett. 152B, 404 (1985). 16. D. Bogert et al., Phys. Rev. Lett. 55, 1969 (1985). 17. S. Geer, in Proc. of the 1986 Conf. on High Energy Physics, Berkeley. 18. A. Roussarie, in Proc. of the 1986 Conf. on High Energy Physics, Berkeley. - 11 - 19. W. Marciano and Z. Parsa, Ann. Rev. Nucl. Part. Sci. 36, 171 (1986). 20. D.H. White et al., LAMPF Cherenkov Detector Proposal #1015, Jan. (1986). 21. J. Collins, F. Wilczek and A. Zee, Phys. Rev. D18, 242 (1978). 22. S.P. Mikheyev and A.Yu. Smirnov, Nuovo Cimento 9C, 17 (1986); L. Wolfenstein, Phys. Rev. D17, 2369 (1978). 23. P. Langacker, S. Petcov, G. Steigman, and S. Toshev, to be published in Nucl. Phys. B. 24. C.-S. Lim and W.J. Marciano, to be published. 25. The paraiaetrization is often called the Maiani parametrization, see; L. Maiani, Proc. International Symposium on Lepton and Photon Interactions, p. 877, Hamburg, (1977). 26. J.F. Cavaignac et al., Phys. Lett. 148B. 387 (1984). - 12 - REPRODUCED FROM BEST AVAILABLE COPY Neutrino Oscillation Experiments NEUTRINO OSCILLATIONS AT ACCELERATORS Past results, future prospects - 15 - NEUTRINO OSCILLATIONS AT ACCELERATORS PAST RESULTS, FUTURE PROSPECTS F. Vannuccl LPNHE, University Paris VI et Vil Are neutrinos massive ? This is one of the most fundamental questions still facing physicists, which does not necessitate a new jump In energy. This answer is probably within reach of present machine. Among the various manifestations of massive neutrinos, oscillations are the most sensitive. They already test masses below the 1 eV level. Presents results are summarized and future prospects outlined. What are oscillations ? Oscillations are direct transitions between different flavours of neutrinos . This comes about when the weak eigenstates v , v , M do not coTncide with the mass eigenstatea \i,, vz, v3. Having no compelling evidence of oscillations we may limit ourselves to a binary system. In this case weak eigenstates and mass eigei;.3tates are related by : r e's rcosC sinO'i r ' i vv v-sin9 cos8 v, U The probability of the oscillation v <—> v is : P = sinz26 sin2 no- where R is the distance over which the oscillation is measured and L is the oscillation length 2.5 (Km) Am2(ev2) - 16 - with Am2 = ml - m2 n^ and m2 being the masses of v, and v2. With 3 neutrinos the situation gets more complicated. It is interesting to note that in this case an oscillation v <-> v may be induced by a large v3 (2) e V mass . Oscillations may !",-ppen if two conditions are fullfilled - mixing between generations, just as among quarks - Am2 * 0, at least one massive neutrino. When the oscillation starts to develop It is of interest to use large distances or small energies when Am2 is small. Present limits To look for oscillations one takes a neutrino of a given flavour (v ) and follows it along its propagation. If the oscillation occurs some v will be changed into v ,v or v1 . This u e T allows two experimental procedures : - the disappearance method compares fluxes of a given neutrino flavour at different distances from the source. This is better done with two detectors running simultaneously (CDHS, CHARM and FNAL 701 3) are examples of this technique) or with one detector which position changes along the beam (Goesgen and Bugey ). The disappearance method has the advantage of integrating over the different open channels without an a priori choice. - the appearance method is complementary ; it tries to detect a new flavour in the original beam. It is a more sensitive method since a few events are in principle sufficient to prove the effect. The disappearance method on the contrary must rely on the comparison - 17 - between two large numbers. But practically the appearance method is limited by the contamination in the beam of the new flavour searched for : typically 1} of v in a v beam. BEBC and BNL E731* give e \i stringent limits in the channel v •* v . The search for oscillation U e into v i3 a clean appearance search, since in that case there is no contamination at the level of present searches. This explains why the emulsion experiment FNAL E531 can give a very good limit on v + v with a small statistics. u t Fig. 1 gives the present best limits in the three physical channels existing between know neutrinos. They include the limits obtained in accelerator searches and with reactors. The curves reject the right upperside of the plane. The channel best know is v <—> v . For maximum mixing oscillations test neutrino masses v, e down to 0.1 eV, and for Am2 > 10 eV2 mixing must be smaller than a few 10 . Two experiments appear as favored regions. One, the Bugey search, claims evidence for oscillations in the disapperance of v . The PS191 sees an excess of electron events. If this excess is interpreted as an oscillation the parameters fall in the shown region. Possible developments a) experimental recipes A disappearance experiment relies on the subtraction between two large numbers. The result is limited by a statistical error of order 1//t>T, N being the number of reference events (v u interactions). For large Am2 the limit on the mixing goes as : sinz28 < — For maximum mixing (sin22e = 1) the limit on Am2 goes as : - 18 - Am2 < i -!-_ Increasing the statistics has little influence on the Am2 limit, which is essentially fixed by the choice of distance and energy, the further one goes the better. On the contrary statistics is the dominant factor to improve the limit on mixing. On top of the statistical error, one has to add systematics due to flux calculations or mismatch of the two detectors. These errors are at best at the level of 2-3 %. For an appearance experiment, assuming no candidate found the 90 % confidence level on oscillation probability is given by 2.3/N. This means a limit on mixing sin228 < I and on Am2 Am2 < TT The statistics become even more important than in the disappearance method. The realistic ] i.mit comes from the uncertainty in the contamination level, which enters at the 1? level in v •*• v . u e Among the present limits obtained at accelerators the appearance search has given the best limits, except for the large mixing part of the v •* v oscillation. b) limitations of present searches Even for an appearance search a two detector experiment allows a search where most of the systematics cancel. Still there remain two limitations : the poor knowledge of the contamination gives an uncertainty of at best 10 ; the neutrino source is unknown, and one takes as the origin of the neutrino production - 19 - point the middle of the decay tunnel. This means a - 20 % error in present set-ups. These limitations would be overcome in a tagged neutrino search. A tagged neutrino experiment a) The experiment is again done with two detectors, keeping the advantages discussed earlier. But now we have a usual neutrino detector, supplemented by a first detector, in the decay tunnel, that we call a tagger. The tagger detects and measures the particles produced with the neutrino. In such an ideal situation the neutrino flavour is known event by event : a neutrino produced together with a y is a v by definition. The flavour is known directly at the point of production, this is important for large Am2. Furthermore it is possible to reconstruct the point of meson decay thus the source of each neutrino. This is important to determine the oscillation parameters in case they are found. b) detection One can consider two tagging situations : . the initial beam is a narrow band beam coming from IT and K decays. It is sufficient to detect the y produced with the neutrino. A magnetised iron spectrometer can do it. The neutrino beam is pure v , without contamination, with an energy known at the source. . the initial beam is K obtained by sweeping all charged particles away. One has now to detect both a charged v. and a charged lepton. This gives a better constraint on the v production, but the main advantage is to give a neutrino beam with the four components - 20 - v v v v In almost equal quantities. This is an essential feature in s \xe u -1-1 an oscillation search since it allows for many cross-checks. A proposal Clearly the tagger has to 3tand a huge flux of particles. This is only possible to envisage in a slow extracted mode. With an extraction lasting Is one can tolerate 109 particles on a tagger implemented with fast electronic devices. A slow extraction means a large cosmic background in the detector. Although an existing detector can be used for the present proposal, it has to be complemented by a cosmic veto, and it has to have good timing (1 ns) on interactions. Now back to the tagger. One can imagine several versions of it. The more complete requires a mosaic of small scintillators for timing followed by a spectrometer composed of a large aperture magnet, proportionnal chambers, a calorimeter and a muon filter. The scintillators must be fast (500 ps). In the case of the K beam, they record coincidences between IT and £,. Then the v detector gives a trigger also with good timing (- 10 ns). This allows to only keep the pairs IT, I in coincidence with the v interaction. In average - 20 pairs will fulfill this condition. Finally one must select the unique pair produced with the interacting v by applying kinematical constraints (P_ balance, K T L mass, K momentum). The price to pay is a diminished statistics. L Still with a large acceptance tagger it seems possible to accumulate a few 10 000 v interactions with the full information of flavour, energy and spatial origin. Tagged neutrino physics seems a logical prospect in neutrino studies after the "discovery" experiments and the large statistics experiments. Although it would be limited in number of events, it - 21 - could improve very much the quality of oscillation searches, and more generally of lepton number violation processes. It could also refine other aspects of neutrino physics like the extraction of structure functions. - 22 - References 1) V. Flaminio & B. Saltta, INFN PI/AE 85-6 2) K. Lira Proceedings of this workshop 3) F. Dydak et al, Phys. Lett. 13MB, 281 (1984) F. Bergsraa et al, Phys. Lett. 142B, 103 (1984) 4) K. Gabathuler et al, Phys. Lett. 138B, 449 (1984) J.F. Cavaignac et al, Phys. Lett. 148B, 387 (1984) 5) L.A. Ahrens et al, Phys. Rev. D31 (1985) 2732. C. Angelini et al, Phys. Lett., 179B (1986) 307 Figure Captton Limits on oscillation given by present experiments in the three channels v <-> v . v <—> v . v <-> v . e vi e x v x - 23 - I III 11 I I I {III 11 I I o o i 11 i i I iii lin I.I i I I LUJ.II i-i—i 'inn i ,,L i. CD c O I/) d ill 1 I I Illl II I I o o o •' ' ' ' ' '"III I I I lull I I l_l Illlll I i l linn i i , o o (NJ m o o I I o o a (2A ) SEARCH FOR NEUTRINO OSCILLATIONS Presented by P. Astler, LPNHE, 4 place Jussieu 75230 PARIS Cedex, FRANCE E 816 collaboration"1" : BNL, Boston University, Cern, Paris University. The present paper reports on preliminary results from the E 816 experiment at Brookhaven National Laboratory. E 816 is the continuation of a 1984 experiment ( '3 191) which was devoted to a neutrino decay search in the CERN PS neutrino beam. No candidate was seen (ref 1), but a study of neutrino interactions in the calorimeter indicated an anomalous electron production (ref 2). The statistics was too low and the experiment has been rerun in spring 86 at BNL to look specifically, with an improved detector for v arising from a low energy v beam. The results presented here are preliminary for at least two reasons : first the collaboration is presently running a calibration test which results are not Included here; second, only 1/3 of the neutrino data is used, and no mention will be made to antineutrino data for which the analysis is still going on. The physics of neutrino oscillations has been extensively justified and described in previous talks (see e.g. Marciano's and Vannucci1 s contributions). This report will directly start with a description of our apparatus, followed by the data analysis. Few question marks are raised at the end concerning possible Interpretations of our results. t E 816 collaboration : P. Astier, G. Bernardi, G. Carrugno, T. Chrysicopoulou, J. Chauveau, J. Dumarchez, M. Ferro-luzzi, F. Kovacs, A. Letessier, J.M. Levy, M.J. Murtagh, J.M. Perreau, Y. Pons, J.L. Stone, A.M. Touchard, F. Vannucci, P. Wanderer, D.H. White. - 25 - APPARATUS Beam The *GS (Alternate Gradient Synchrotron) produces every 1.2 s about 1013 protons at 28.3 Gev/c. For the neutrino facility they are dumped on a 45 cm titanium target. The outgoing charged particles, mainly pions and kaons, are focused by a pulsed magnetic horn operating at 285 KAmps. The 90 m decay tunnel ends with a 30 m iron-concrete shielding which stops the muons and remaining hadrons. As mainly pions are produced at the target, the beam is 99% v . The muon flux and profile in the shielding are used to monitor the neutrino beam. We also used the signal from a scintillator counter placed in this shielding as a time reference for the experiment. The short extraction time (2.5 us) and the fine time structure (30 ns buckets separated by 224 ns, fig 1-a) allow good cosmics and noise rejection. As the horn does not make a momentum selection on the mesons, the intensity is high, but the neutrino energy is not well defined as always in a Wide Band Beam (fig 3). The mean energy of the beam is around 1.5 Gev according to the beam line simulation described below. Our apparatus is located 175 m away from the target and 130 m from the middle of the decay tunnel: L/E, the relevant oscillation parameter'*' is therefore of the order of 0.1. That sets the 6m2 region we can explore around 10 ev2 as in PS 191. Detector We use a fine grained calorimeter, made of sandwiches of 3mm thick iron plates and flash-tube chambers. The tubes are 5 by 5 mm2 in cross section and 6 m long ; they only give the vertical coordinate. The 13% of a conversion length between 2 sensitive planes allow a good Y/e separation, as we will see further. The front dimension of the detector is 3*6 mz, while it is only 3-3 m long, and thus has a large angular acceptance. Placed downstream of a liquid scintillator veto counter, 22 out of the 49 sensitive plane3 constitute the fiducial volume (10 tons, 2.5 Xo, less than 1 interaction length), followed by 2 plastic scintillator The standard oscillation formula connecting E, L, 5m2 is derived in ref 3 and discussed in many papers of these proceedings. - 26 - hodoscopes for trigger purposes. To get a good shower containment the remaining 27 planes have been sandwiched with lead plates (added to the iron) to achieve 15 radiation lengths from the middle of the "target" (fig 1). 3 30 m __ 81 iron ! 5 mm tune 5 by 5 mm by 6 m i \ L fig 1-3 Beam bucket structure as measured Dy trigger time (in units of 224 ns). A Trigger -CB.V 3 counter / -target - plastic hodoscopes fig 1 : Detector side view. The energy of a shower is estimated by simply counting the number of hit tubes. Altough the electron test is still in progress, we already have a preliminary calibration curve (fig 2) showing a rough linear relation between energy and number of hits.The actual energy resolution is presently being refined. We are also calibrating the detector with pion data, but since it has not been analysed so far, we only quote here PS 191 result (ref 2) : less than \% of charged pions fake an electromagnetic shower. We triggered within the beam gate on non-vetoed coincidences of the two hodoscopes, the veto being the liquid scintillator counter at the front of the detector. All scintillators threshold were set slightly below the minimum ionizing particle energy loss. As the two hodoscopes are divided - 27 - aECTRON ENERCY (GBV) fig 2: On this calibration curve, the error bars are plotted for the resolution and come from MC. NEUTRINO SPEC:TRA 10 10 — 4 i a. - —I 10 " h 9 "210 - 0 - - NEUTRIN O 8 0 ~" > ^ T 1 1 7 J 10 1 -1 _ _ ~ 1 ( 1 1 1 2 3 6 7 NEUTRINO ENERCY (G<»•) 13 2 fig 3- The v^and ve spectra as computed by Nubeam for 10 protons on target, in neutrino /6ev.m . - 28 - in 20 vertical slabs they give an indication on the horizontal position of the vertex. They especially allow to reject events due to particles coming from the side walls. Besides the hit pattern, we record the time and height (measured by TDC s and ADC's) of the signals of one of the plastic hodoscopes, and the hit phototube pattern for the two other hodoscopes. Because of a flash chamber recovery time of 0.6 s we can only take one trigger per burst. We actually trigger once every 4 bursts when running neutrinos, loosing 1/8 of the beam. Add-'*ig the vetoed buckets the dead time amounts to 14$. Half of the triggers are due to neutrons and entering by side particles from neutrino interactions in the concrete walls and ceiling. DATA ANALYSIS Data sample We have collected 1.1 1019 protons on the target (p.o.t.) and 500,000 triggers in neutrino beam, and 1.3 1019 p.o.t. and 120,000 triggers in antineutrino (i.e. with reversed horn polarity). After processing the tapes through a filter program, we are left with half of the triggers. This program was designed to remove the events with zero or one track, and worked with a negligible bias towards the selected v interaction sample as defined below. The remaining events are then visually scanned by physicists, itid part of them twice. The results presented here are based on 1/3 of the v data (3.64 1018 p.o.t.). Strategy As an oscillation experiment of the appearance type we want to measure the v /v ratio, and point out a possible enhancement with respect to its predicted value : if v oscillate into v , even weakly, we would "see" more v than expected. Assuming the same spectrum for both v flavours we get v /v = #(v N -> e" X) / #(\> N -> y~ X). In our detector the simplest X shows up as a single charged track. We thus look for 2 track events and events with one track and one electromagnetic shower (1T1S). We will then compare the ratio of these 2 classes to Its expected value, according to real spectra, cross-sections and acceptances. This method relies on correct evaluations of both initial v contamination and of all e background contributions. - 29 - Thus, we can roughly estimate the IT0 background level as: 0.2 * 0.2 2*0.13 cross section energy cut connection probability ratio efficiency for 2 showers of quasi-elastic v interactions ; this is of the same order of what we expect from v contamination. Scanning pules Since we look for CC reactions, we demand a lepton candidate,!,e.: either a non interacting track crossing more than 10 sensitive planes (3.3 cm of iron) as a muon candidate, or a shower firing more than 50 tubes and connected to the vertex as an electron candidate. Fig *l displays an electron shower from the test beam run: the signature is quite striking and such a cluster of -115 hits (for a 1 Gev electron) seems hard to miss or to misidentify. III II 11 I II11 15 I III 11 I I I I I I fig 4 - 1 Gev electron from test beam. - 30 - Neutrino spectra The v and v spectra are computed by a standard simulation \i e program Nubeam (ref 5), using measured IT and K production cross-sections, together with the horn and tunnel geometry. Secondary v decays are also simulated. The main outputs are the neutrino energy spectra and integrated fluxes at a given distance for a given amount of protons (fig 3). We can check the integrated flux (assuming the spectrum shape) but we are not able with this apparatus to measure its energy dependence; this last measure was done by the E734 experiment (ref 4), which obtained a good agreement with Nubeam. These spectra, corrected for the slightly higher distance are used in our Monte Carlo1". According to them, the v /\> ratio is small :the ratio of integrated fluxes is below 1 %, a standard though somehow uncertain value. Background The big background we have to deal with is the v induced ir° production : v N -> X TT°, TT° -> 27 , since the Y showers can fake an e~. u The cross section is approximately 20 % of the quasielastic one. But as the TT° is mainly produced with a small energy ( the mean value is 500 Mev ) an energy cut is likely to get rid of many of them, whilst keeping most of the v induced events. We actually do not consider showers of less than 50 tubes (i.e. 400 Mev according to the test beam), then cutting 80% of the Tr0|s and less than 10% of the v events, according to our simulation. e Our search would however be hopeless if the remaining ir° events did fake v interactions. But most photons start showering some distance away from the vertex (i.e. at least one sensitive plane) and can therefore be rejected. Our background reduces to 1 track+1 ir°, the ir° being seen as a single shower beginning right at the vertex, that is in the first 13% of a conversion length. t Our Monte Carlo uses a generator we got from BEBC collaboration. It simulates elastic, quasielastic, delta production, 2 and 3 pions, in charged and neutral currents. The reinteractions of hadrons on the way out of the nucleus are also included, as well as the Fermi motion. The detector simulation and shower generation are performed by the Geant package (ref 6). The events are then visually scanned with the same program as the data: this explains that we deal with about the same statistics in data and MC. - 31 - fig 5 a - 2 track event. - fig 5 b - 1 track + 1 connected shower. - 32 - f ig 5 c - 1 track + 1 disconnected shower . fig 5 d ------1 track + 2 showers - 33 - We also require a track accompanying the lepton candidate, which is a hadron candidate. It has to cross at least 4 sensitive planes: this ensures a long enough lever arm and provides a minimum number of points both for scanning and fitting in pattern recognition. It also eliminates most of nuclear fragments from the intranuclear cascade. One such track has to emerge from the vertex on top of the lepton candidate, and is required to be at least 5 degrees away from it. This last cut is expected to have the same efficiency on M and \> , as charged current cross sections only differ e \i by the outgoing lepton mass (which is negligible at our energy). If we remark now that the lepton requirements are not very stringent, we can expect a similar global acceptance for our two basic topologies : 2 tracks from v and 1 track + one shower from v . u e Events with one or two showers are kept even if those do not connect to the vertex (i.e. are not electron candidates) but arise from it: they provide a tool to monitor and substract the IT0 background. At the end, the interaction is required to occur in the fiducial part and to trigger the apparatus. Events satisfying the cuts are shown on fig 5. Results The following table shows the observed and expected number of events for four different topologies, with the cut3 applied. neutrino data Monte Carlo scan (only v interactions) u 2 tracks 3334 3226 3 tracks 707 693 connected 93 - 9 31 -+ 6 1 tr + 1 sh disconnected 64 * 8 64 t 9 1, 2 tr + 2 showers 54 1 7 55 t 8 - 34 - 200 240 200 - 160 - 120 - Si o 80 - 40 - \ n 10 20 30 40 50 10 20 30 40 50 10 20 30 « 50 LENGTH SHORT LENGTH LONG AND SHORT U LENGTH LONG i c o Z -80 -40 0 40 80 -eo -40 o 40 80 '3 80 120 ISO ANCLE LDMG/BEAJ K.KLE SHORT/BENvl ANGLE BETWEEN THE 2 10 20 30 40 50 10 20 30 40 50 '0 10 20 30 40 50 LENGTH LONG LENGTH SHORT LENGTH LONG AND SHORT CO Q -80 -40 ISO ANGLE LONG/BEAU ANGLE SHORT/BEAM ANGLE BETWEEN THE 2 fig 6 - angle and track length distributions for 2 track events (data and MC) - 35 - The 2 and 3 track event sample is used for normalization and Monte Carlo checks. Absolute and relative number of events, angle and track length distributions agree with MC predictions (fig 6), the discrepancy being far below cross-section uncertainties. We should emphasise that MC and data are scanned in exactly the same way to take into account possible scanning systematics. After a 3 pass scan the shower event sample has been separated into two classes : events with 2 showers and 1 or 2 tracks, and events with 1 track and 1 shower. To disentangle gamma and electron showers we are using our fine granularity by considering the vert ex-to-shower distance distributions. We study first the distributions obtained from the v Monte Carlo y scan (fig 7). We observe on the 2-shower histograms that we get (with a poor statistics) the expected exponential decrease. The slopes of the 2 shower plots lie not so far from -1. and -2. as expected, while it turns to be -1.5 for the one track + 1 shower, in between the two other slopes. But the main feature is that no excess appears in the first bin: though our Monte Carlo simulates nuclear interactions and produces a substantial amount of short protons, our scanning does not suffer a bias from faked connections by short tracks. If we now look at the same plots for the data (fig 7), we see that the fitted slopes are similar within the statistics, but the first bin of the 1T1S plot is 3 times higher than in the MC. That is not a real surprise as the v induced events (not included in the MC) are expected there, on top of the IT0 contribution. This contribution can be evaluated by simply extrapolating the distribution without its first bin, as confirmed by the MC histogram. We get 31 - *• tr° induced 1 track + 1 connected shower events, the uncertainty being derived from the fitting procedure. We will call the 93-31 - 62 remaining events 1 track +1 electron events. The next step is to evaluate the number of such events expected from v contamination. e As we expect from our cuts and trigger conditions a similar for v and v interactions, we induce y e # 1T1S from v JdE - 36 - DISCONNECTION O. 0.5 I. 1.5 2. 2.5 3. 3.5 A.FB = -1.27 29.0 10 0. 0.5 1. 1.5 2. 2.5 3. 3.5 0. 0.5 t. 1.5 2. 2.5 3. 3.5 A.FB = -1.54 30.8 A.F3 = -2.31 24.2 10 — 0. 0.5 1. 1.5 2. 2.5 3. 3.5 A.FB = -1.07 26.7 Z_ O (the closest) H 1 =- in"1 0. 0.5 1. 1.5 2. 2.5 3. 3.5 0. 0.5 I. 1.5 2. 2.5 3. 3.5 A,fB = -l.*5 29.3 /k,FB a -1.78 20.4 fig 7 - The disconnection is defined as the number of sensitive planes crossed when going from the vertex to the beginning of the shower. The disconnection is 7 for the event of fig 5-c. On these histograms, the disconnection is converted in radiation length. The numbers written below each histogram are the fitted slope and th« extrapolated content of the first bin. - 37 - because 2 track events are mainly quastelastic and inelastic. This is simple and reliable. We however scanned v MC events and found for this sample 24 i 3 1T 1 connected shower events : this sets the above ratio to 0.7 1 0.1?. We attribute the difference between the 2 expectations to the shower energy cut and the presence of some neutral current events in the MC and experimental 2 track event sample. We will use the first conservative estimate and point out that the most uncertain factor is not the relative acceptances neither cross section shape but the fluxes ratio. Putting a 25% uncertainty on the estimate we expect 333H # 8 * io~3 = 27 t 6.7 1T 1 connected shower from v contamination. To summarize, 93 _ 9.6 - 27 1 6.7 - 31 _ 4 = 35 t 12.J4 events are in excess. We should point out that we depend on a Monte Carlo (i.e. Nubeam) quantitative prediction only for the v contamination calculation. Although the ir° production rate inside our cuts is consistent with our absolute prediction, both for 1 track + 1 disconnected shower and 2 shower classes, we did not use these quantitative predictions in our ir° background substraction. If we extrapolate from now to the whole experiment we should have 100 "unexpected" 1 track + 1 electron events to explain. Oscillations are obviously a tempting interpretation but we will however be unable to strictly prove that we saw oscillations. Furthermore, most of our sensitivity region in the sin2 (29) versus 5m2 plot is excluded by negative results from other experiments, see e.g. E 734 and BEBC in these proceedings. Apart from oscillations at least two features could explain the excess: first a wrong computation of v contamination (by a factor of 2), second an unknown Z dependent effect: our target material is iron, one of the heaviest used for this kind of experiment. References 1) G. Bernard! et al , Physics Letters 166 B (1986) 479. 2) G. Bernard! et al , Physics Letters 181 B (1986) 173. 3) B. Pontecorvo, Physics Reports 41 C (1978) 4) L.A. Ahrens et al, physical Review D 31 D (1985) 2732. 5) C.P.Visser, Nubeam, Doctoral thesis, University of Amsterdam (1978); and description in Cern Hydra application library. 6) Geant 3 : Cern Program Library CERN/DD/EE/84-1 . - 38 - Search for Neutrino Oscillations at the AGS with the Narrow Band Beam* C. Chi, N. Kondakis, W. Lee, B. Rubin, R. Seto, C. Stoughton, G. Tzanakos Physics Department, Columbia University E. O'Brien, T. O'Hal]oran, K. Reardon, S. Salman Physics Department, University of Illinois B. Blumenfeld, L. Chichura, C. Y. Chien, J. Krizmanic, E. Lincke, W. Lyle, L. Lueking, L, Madansky, A. Pevsner Department of Physics and Astronomy, The Johns Hopkins University (Presented by G. Tzanakos) Abstract We have taken neutrino data with the NBB at BNL, in the summer and fall of 1985, and with the WBB in the spring of 198(5. We are in the process of completing the analysis of the NBB data. In this paper we present preliminary results of this analysis. We observe an anomalous appearance of electron neutrinos above the expected background. (+) This paper is based on additional analysis done since the workshop. - 39 - 1. Introduction If neutrinos have a non-zero mass and if the flavor lepton numbers are not independently conserved, then neutrinos can oscillate from one flavor to another, provided that at least two of the masses are different. Assume, for simplicity, two neutrino flavors, u and v . The probability for the transition u •* v is: 2 P = sin22a.sin2(1.27 Ag ' L), (1) where v a = the flavor mixing angle; L = distance from the neutrino source in km; E = neutrino energy in GeV; Am2 = |m 2-m 2| in eV2; m ,m = the masses of the mass eigenstates. We built a neutrino experiment at L = 1 km from the neutrino source of a narrow band beam of mean energy E = 1.27 GeV and spread NBB run 3 x 1019 POT Summer,Fall 1985 WBB run 3 x 1019 POT spring 1986 TEST (Calibration) Summer 1986 A brief description of the detector and the narrow band beam follows. We will also describe the data taking, data reduction, and analysis of u and v events, including a discussion of the backgrounds. Finally, very preliminary results from this analysis will be presented. - 40 - 2. The Detector The detector1 is located at 1 Km from the target along the neutrino line as shown in Fig. 1. it is composed of two sections, the front 'electron detector', which is a finely segmented EM calorimeter, followed by a toroidal magnetic muon spectrometer> A schematic of the detector along with some details is shown in Fig. 2. The Electron detector is made up of nine sections. Each section is made of 10 planes of proportional drift tubes (PDT), interleaved with absorber planes made of 1" conciete. The last «0O 0 100 • • ' • ' concrete plane in every section FEET Fig. l. Location of the E776 is replaced by a scintillator detector in the AGS v line. plane, used for timing and cosmic ray triggering. Sequential PD1] Fig. 2. E77 6 detector schematic. - 41 - planes are at 90 degrees with respect to each other. Each PDT plane contains sixty-four 18'X3 1/4 "XI 1/2" drift tubes, made of extruded aluminum, with four PDTs per extrusion. The maximum drift distance is 4.1 cm. The sampling interval is 1/3 X , and the weight is 240 metric tons (120 tons fiducial). Each PDT signal is amplified and carried to the input of a 6-bit 22.4 ns flash ADC, connected to a 6x256 bit memory, which allows the 5.7 /is latest history of the wire pulse to be recorded. The muon spectrometer is composed of five iron toroids: there are two planes of PDT's (1X,1Y) between sequential toroids, and six (3X,3Y) PDT planes after the last toroid. The total thickness of the iron is 29" and the magnetic field is about 18 kG, resulting in a P kick of 400 MeV/c. A typical muon neutrino event is shown in Fig. 3a with the mu&n track exiting through the toroid system. The reconstructed muon trajectory is shown in Fig. 3b. The spatial resolution of the detector is a =2 mm, and the angular resolution of the muon tracks at the vertex is approximately 25 mrad. The momentum resolution, a /p, p PUN 3233 a) J-,) EVENT M05 E t t t f • A - • X-VIEW Fig. 3. Typical candidate for quasielastic u interaction, with muon pene- trating the toroid. a) Raw data. b) Reconstructed muon track; p =2,5 GeV/c. - 42 - for muon tracks is on the order of 5% for muons stopping in the electron detector, 10% for muons stopping in the toroids, and 25% for tracks exiting the toroids. The detail of the wire pulses, as digitized by the flash ADC's, is shown in Fig. 5b, for ten sequential planes of x-wires. Fig. 4 shows an electron neutrino quasielastic can- didate. Our criteria for electromagnetic shower development include multiple hits per plane, and missing hits in several planes. The most striking feature is the structure and size of the digitized wire pulses. Fig. 5a shows the wire pulses for ten sequential x-planes. The multiple peaks in the pulses and the dramatically increased Y vie" Fig. 4. Typical candidate for pulse areas reflect the fact quasielestic v interaction. that several shower particles cross each drift tube. A comparison between Figs. 5a and 5b shows a pronounced difference between electrons and muons as seen by the detector. We constructed a small (8 ton) detector and took calibration data in the A2 test beam at the AGS. We exposed this test detector to electrons, stopping muons, stopping pions, and stopping protons of various energies. We measured the e/fi, e/if, and e/p separation in the detector. The electron identification exploits the longitudinal and lateral development characteristics of the shower. (a) :::: a e i t Time > Fig. 5. wire pulses as digitized by the flash ADCs. a) For 10 planes in the x-view of the v candidate (Fig. 4). b) For 10 planes in the x-view of the j/° candidate (Fig. 3). Time > The average longitudinal shower behavior can be described by the equation: a bt N(E) = NQ(E) t e- , (2) where t is the shower depth in radiation lengths, and a+1 NQ(E) = 5.51 E VZ b /r(a+l); a = 1.77 + 0.52 In E; (3) b = 0.634 - 0.0021 Z. The shower maximum occurs at depth t = a/b. Fig. 6 shows the longitudinal energy deposition profile for the test detector along with the curve given by Eq. (2). The agreement demonstrates clearly that the shower development in our detector is what we expect. - 44 - The shower development, Longitudinal dE/dx pr however, fluctuates from this average behavior on an event by- event basis. We exploit these fluctuations in order to separate electrons from other particles. We also calculated the energy calibration constant for electron showers in the neu- trino detector with the data Fig. G. Longitudinal shower energy from the test detector. The profile for 1 GeV electrons. The curve is given by Eq. 2 in the text. measured pulse areas were corrected for gain variations due to changes in temperature, pressure, and gas composition, which were monitored by- studying cosmic ray tracks taken between AGS spills. Fig. 7 shows a plot of the electron energy as measured by the detector versus the energy of the beam, for electrons entering the detector at 6 = 0°, and 6 = 30°. It is clear that the response of the calorimeter is linear with energy and independent of the direction of the shower. The same Measured vs. Incident Energy Energy Resolution For 0° Doto Incident Enorqy (GaV) Fig. 7. EH calorimeter (test detector) response vs. true electron energy. Fig. 8. EM calorimeter energy resolution vs. 1/v/E. - 45 - figure also shows the simulated response of the calorimeter to electrons generated with the EGS42 electron shower generator program. We measured the energy resolution a /E using the A2 test beam data, which is plotted against 1/VE in Fig. 8. The energy resolution is consistent with 20%/>/E. In conclusion, the results obtained from this test data demonstrate that we understand the behavior of the detector. 3. The Narrow Band Neutrino Beam We use a narrow band beam in this experiment for the following reasons: (i) The energy spectrum of the v 's from oscillation is 6 given by the narrow band spectrum of the parent v'&i modified by Eq. (1). In contrast, the v component of the beam has a wide band energy spectrum. (ii) The high energy part of the spectrum, which gives rise to high topology deep inelastic scattering events, is reduced in the narrow band beam. The AGS neutrino beamline consists of the proton beam transport, the target, and the magnetic focusing horns, followed by 80 meters of decay space in the beam tunnel, and the muon shield (30 m of iron). The focused beam intensity profile is measured by two sets of planar segmented ionization chambers (pion monitors) at 40 m and 60 m from the second horn. The details of the magnetic horn calculations, as well as the corresponding beam measurements, are presented in another paper3 given in this workshop. Here we summarize these results. Fig. 9 shows the calculated v energy - 46 - spectrum. The narrow band Total vu ond v. Fluxes For I - 240 ' 1 ' ' ' ' 1 ' ' ' I " ' ' pion and kaon decay con- 10° -' A ' TOTAL », tributions are shown sit- J\ TOTAL », ting on a falling wideband background due to decays 103 ~——___ of the non-focused part of 10* the beam. On the same figure the v beam back- ... 1 © E,IGiV) Fig. 9. HBB v energy spectrum from n* and K+ decays. ground is also plotted The WBB background contribution is included. The total v background in the beam is shown also for comparison. versus neutrino energy. This background is mainly Electron v Flux For I - 240 1 • •• • 1 due to K decays, muon 10° TOTAL v, Bo decays, K° decays, and n decays, which are shown in Fig. 10. The total v /v ratio of the beam was calculated to be at the 8 3 x 10" level with an 2 4 o e E,IGiVI Fig. 10. Energy Bpectra of the most dominant estimated error of 30%. contributions to the v background in the beam. The energy spread of the narrow band beam is a£/E = 15%, and the angular spread of the charged beam is 4 mrad. In order to verify the beam calculation, we compared its predictions with the measurements of (i) the total charged particle flux and beam profile in the decay tunnel (measured with the pion monitors) and (ii) the v energy spectrum and rates in the detector. We used the v flux given by the beam calculation and known cross sections to generate Monte Carlo u events. With the muon neutrino analysis discussed below, in section 5.1, we generated the Monte Carlo spectrum shown in Fig. 12, which we compare to the observed u spectrum. From these comparisons, we conclude: i) The measured flux of charged particles in the beam tunnel and the measured neutrino rates at the detector are - 47 - both 30% higher than the prediction from the beam calculation. This prediction is based on the model of Sanford and Wang, as discussed in the paper on the neutrino flux calculation. ii) The measured beam profiles, shown in Fig. 11, agree with the calculated beam shape, once the absolute beam flux normalization is taken into account. iii) The measured u spectrum, shown in Fig. 12, agrees with the spectrum of Monte Carlo generated v events. In this figure, the number of events in the Monte Carlo is normalized to the number of events in the data below 2 GeV. The spectra peak at 1.3 GeV, as expected for Iun_M = 240 kA, HORN and the widths are both ~ 2 3%. iv) The measured spectrum has ~ two times as many events above 2 GeV as the Monte Carlo spectrum. We are currently investigating sources of this excess. a) Additional channels in the event generation, such as multi-pion production or deep inelastic scattering, contribute additional events in the high energy tail of the Monte Carlo spectrum. Although we attempt to select quasielastic interactions, these additional channels contribute to the observed spectrum. b) The reconstruction of high energy rauon tracks, which exit the toroid system, has non-gaussian errors. This contributes to the observed number of events in the high energy tail. This excess appears to be within the limits of the beam calculation and event reconstruction uncertainties,. However, we are also investigating additional contributions to the WBB background, through the development of a more sophisticated beam flux calculation. We do not expect the v v J i. ratio to change appreciably. - 48 - vu Data and MC Spectra Por I - 240 B OBSERVED DATA } UOKTt CAflU) *— —i—i—i—i—|—i—i—i—i—I—i—i—i—r I 1 4 71 too DATA E * * 1 Ik 2 a L 80 o MC •° . . 1 , . . 1 ....!. 2.5 5 7.5 10 12.5 PIOH UOHfTOR PAP HUUBES 60 S OBSERVED DATA g t - MOHTZ ZARLO A -I \ * + 40 "E + 4 - £ 20 s 2 — * 5 2.5 5 7.5 10 12.5 i lif. I m A.\-t P1QH UDHrrOH PAD HUMflER 0 1 2 . 3 4 5 6 Neutrino Energy (GeV) Fig. 11. Charged beam profile, as measured with the pion monitors in the decay Fig. 12. The measured v energy spectrum from tunnel. The calculated beam profile guasielastic neutrino events compared with the is shown for comparison, a) Downstream energy spectrum from Monted Carlo generated events. monitor, b) Upstream monitor 4. The NBB Run We collected data during the Summer and Fall of 1985 at two neutrino energies: 1.3 GeV (I = 240 KA) and 1.5 GeV horn ' (Ihopn = 280 KA), accumulating 3x10 POT (protons on target). Three different types of records were written on tape: "beam", "free", and "cosmic" triggers. The beam trigger covered the 2.4 /isec beam spill; this trigger contains the neutrino induced events. The naximum drift time in the PDT's is about 2 ps. Thus, the flash ADC time range of 5.7 (is covered the beam spill very conveniently. The "free" trigger read out the detector between spills for a time interval equal to the beam trigger, to monitor the accidental background from cosmic rays. The "cosmic" trigger, generated by a programmable processor using the scintillation detectors, was used to monitor and calibrate the detector. - 49 - 4.1 Data Reduction We collected 2.6X108 beam triggers, 2.6X108 free triggers, and 1.5X10 cosmic triggers during the NBB run. The data tapes were reduced by a series of software filters designed to progressively select the neutrino candidates. Filter 1 separated the cosmic triggers to a separate tape and reduced the beam and free triggers by keeping events with clusters of three or more hits. Filter 2 selected only the neutrino-like events, namely, events with a vertex in the detector. Filter 3 selected those events with at least one contained track and, in the case of showers, a minimum shower energy of 300 MeV. Filter 4 essentially made fiducial and minimum energy cuts and selected fully contained events, for which one can, in principle, calculate the neutrino energy. This filter accepted an event as either an electron candidate (Filter 4e) or as a muon candidate (Filter 4/t). Table I shows the event reduction through these filters. Table I Raw events 2.6 M Beam triggers 2.6 M Free triggers Filter 1 454 K Filter 2 38.3 K Filter 3 12.8 K Filter 4/4 2388 v candidates Filter 4e 1653 v candidates e 5. Analysis After the filtering process we were left with 2388 uA candidates and 1653 v candidates. The analysis started - 50 - with this event sample. Each neutrino candidate was scanned and in each event we assigned hits to 'tracks' with the help of an interactive computer program. Complex events were not used in this analysis. Each track was identified as e, 7, /x, hadron, or "unknown". These tracks were matched in both views. The next step in the analysis was to calculate the kinematical variables for each track, as discussed below. Once the lepton energy and direction were known the neutrino energy was calculated, under the assumption that the interaction was quasielastic, on a stationary neutron. The event time, as measured by the scintillation counters and the beam Cerenkov counters, was used to separate the neutrino events from out-of-time background. Fig. 13 shows the time structure of raw neutrino events. The twelve buckets, 224 ns apart, reflect the rf structure of the beam. Fig. 13. Raw neutrino event time as measured with the scintillator. The twelve-bucket structure reflects the RF structure of the proton beam. \ Ml 5.1 Muon Neutrino Analysis The muon energy measurement was possible if the track stopped in either the electron detector or the toroids, or if it exited the toroids. For a stopping track, the energy was calculated from its range, whereas for exiting tracks - 51 - we fit the track through the toroid magnetic field and calculated its momentum. In both cases we developed an algorithm that resolved L-R ambiguities and reconstructed the track by x techniques, taking into account measurement errors and multiple Coulomb scattering. To determine the muon angle, we used approximately the first one-third of the hits in order to optimize the angular resolution. In order to obtain the final v energy spectrum we applied several cuts: beam quality, beam time, event containment, vertex fiducial containment, muon angle, and event multiplicity. After these cuts we were left with 682 va events» The v energy distribution is shown in Fig. 14. The cosmic ray background contamination of this sample was calculated by using the free triggers and found to be 8 events. Thus, we are left with a final sample of 674 v events. Of 10,000 Monte Carlo generated v interactions, 1207 were accepted through this analysis, giving the v acceptance of 12%. Observed v Spectrum For I = 240, 280 n—r~ i i - —i—r~-|—i— —i—i—i—i—|—i—i—i—i—r—i—i—i- I-T i i -i i : 300- 200-— — - 100 - • rrr^-r-l , , , ," 0 1 2 3 4 5 Neutrino Enerqy (GeV) Fig. 14. Measured u energy spectrum from quasielastic neutrino events, for^data taken with IH0RN = 240 and 280. - 52 - 5.2 Electron Neutrino Analysis (present status) The electron neutrino analysis involves the following steps: i) electron pattern recognition, ii) separation of electrons from 7r°'s, iii) estimation of the 7r° background in the electron sample, and iv) estimation of the beam electron neutrino background in the final neutrino sample. The sample of 1653 v candidates from the data reduction (filter 4e) was further reduced by a series of scans performed by physicists. The first of these scans simply selected events with any shower activity in either view, based on a set of selection rules that were tested with Monte Carlo generated events. If either of the two scanners accepted an event, it was retained. In all of the events, hits were assigned to tracks in the way discussed previously. Non-measurable events were not analyzed. A final scan was performed in order to classify the showers into the following types: "no shower", "electron"-, and "7r°"-like showers. Thus, in the final analysis each event was assigned to one of the following categories: i) "7T°", a 7T°-like shower and no muon track; ii) "/i7i"°", a 7r°-like shower and a muon track; iii) "e", an electron-like shower and no muon track; iv) "fie", an electron-like shower and a muon track. The number of events in each of these categories is given in Table II. This table summarizes the results of the final scan of the data sample. The energy distribution of the showers are shown in Fig. 15 for each of the four classes of events. - 53 - Table II e fie Data 28 21 23 4 -"•-I 1 , . 1 1 ' 1 c 1 2 I 4 5 0 8 /JTT° S 4 - 2 . . 1 . . —! .... 1 .... 1 .... C 1 2 3 4 5 6 8 e" 6 4 i 2 - n .. i.. - .... i .... i .... i .... 2 3 4 Shovir Ensrqy (G»V) Fig. 15. Shower energy distribution for '»«', 'e', and '/ie' events. To understand the significance of the number of v e candidates we observe, two backgrounds must be considered: background from v induced events, which is dominated by 7T* production, and the v component of the beam. - 54 - a. 7T° Background. The TT° background arises from muon neutrino induced interactions v +N •*• (i~ + 7T° ( + X ) (4) and •+ v + 7T° ( + X ) . (5) These can appear as ly-N - fi~ + e ( + X ) (6) •+ Vp + e ( + X ) (7) whenever one of the gammas is not seen, due to very low energy, or when the two gammas are on top of each other, making the TT° appear as an electron in the detector. It should be noted that the reactions (5) and (7) include CC events in which the muon is not seen, in addition to the NC events. The 7r° background is calculated from the number of CC events in the data where a ir° was identified as an electron. The channel "fie" contains events where a muon was clearly identified, and th; shower from a TT° produced in the interaction was identified as an electron. The ratio, then, of the number of "fie" events to the number of "fiir°" events is a measure of the probability that a TTO shower is misidentified as an electron shower. From the neutrino data, this ratio is 4/21. The ratio of the number of "/*7r°" events to the number of "7r°" events is 21/28, which is consistent with the Monte Carlo prediction. From Table II, the number of background TT°'S in the sample of 23 electron events is: (4/21)X28 = 5.3 ± 3.8 events. - 55 - b. Beam Background. To calculate the background due to the v contamination in the beam, we use the observed number of e _3 v interactions, the calculated v /u ratio f = 8 x 10 from the beam calculation, and the relative acceptance of v and v events. The number of u from the beam is (i o e The error in thNe =rati N o xf f isx estimate(A /A ).d to be 3~tf%. (9Fro) m the B v analysis, we saw that 674 events were observed, with an acceptance of 12%. Of 500 Monte Carlo generated u interactions, 76 were accepted, giving an acceptance for v of 15%. Thus, the acceptance ratio A /A =1.3, with an error of 10%. For 674 v events we can calculate the beam v background in the sample of 23 events to be 7.8 ± 3.8 © events. 6. Preliminary Results The calculated neutrino energy distribution of the electron candidates is shown in Fig. 16, along with the spectra for u induced 7r° events measured in the data, and the beam v energy spectra. These background spectra have been normalized, for E > 0.5 GeV, to the calculated number of background events in each channel. The energy of the neutrino for the ir° events was calculated assuming a TT° to be an electron. It is clearly shown that the observed u spectrum and the background spectra are quite different. In addition, a linear combination of the two background sources gives a spectrum which is different from the v spectrum. 6 The total number of electron candidates is 23. The number of v interactions faking u interactions, due to -n° production, is 5.3 ± 3.8. The number of u interations due to the v contamination in the beam is 7.8 i 3.8. So we e expect to observe 13.1 ± 5.4 events due to the beam and %° backgrounds. - 56 - Observed z/e and Background Spectra 10 Obs. j/e 23 Events 8 - TT° Background Beam Background o0 2 3 4 6 Neutrino Energy (GeV) Fig. 16. Measured u energy spectrum for quasielastic events. The background spectra are normalized to contain the expected number of events above 0.5 GeV. If we limit our analysis to those events between the neutrino energy of 0.6 and 2.3 GeV, the results have more significance. The number of background and observed events in the entire spectrum, and in the peak of the beam spectrum, are summarized in Table III. - 57 - Table III Low Energy Cut 0.5 GeV 0. 6 GeV High Energy Cut 10. 0 GeV 2. 3 GeV Observed u 2:J 20 e 7T° Background 5 3 ± 3.8 3.4 ± 2.7 Beam vjv 9.3X10-3 30% 6.6X 10"3 ± 30% ± Observed ZA. 674 579 Beam Background 7 .8 ± 3.8 4.5 ± 2.6 Total Background 13 .1 ± 5.4 7.9 ± 3.7 Excess v Events 9 .9 12.1 The beam v «/v ft ratio i6 the acceptance-corrected value, and 30% is the systematic error from the beam calculation. The errors in the backgrounds are the errors in calculating the backgrounds combined with the statistical error in the background. At this stage of the analysis, we want to study the systematic errors in the beam calculation, our event selection, and event reconstruction before we make any conclusions. We would like to thank the members of the AGS staff for much valuable support, and in particular Dr. A. Carroll, for his perseverance with the horn system. This work was supported by NSF Grants PHY86-10898, and PHY86-19556, and by the U. S. Department of Energy, under contract DE-AC02- 76ERO1195. References 1) "Major Detectors in Elementary Particle Physics", LBL-91 supplement. 2) W. R. Nelson, H. Hirayama, and W. O. Rogers, "The EGS4 Code System", SLAC-Report-2 65 (19 85). 3) N. Kondakis, contribution to these proceedings. - 58 - A Search for v^ -> ue Oscillations Using the E734 Detector E734 Collaboration1) Presented by Michael J. Murtagh Department of Physics, Brookhaven National Laboratory Upton, New York 11973 USA ABSTRACT No evidence for vM —> vs oscillations is observed in an experiment in the wide band beam at Brookhaven National Laboratory using the E734 neutrino detector. The 90% confidence level limits obtained are sin2 2 1. INTRODUCTION The E734 detector at Brookhaven was constructed by a USA-Japan collaboration1) comprised of physicists from BNL, Brown Univ., KEK, Osaka Univ., Univ. of Pennsylvania and SUNY at Stony Brook. The original proposal for this experiment was to measure the elastic scattering of neutrinos on electrons and protons. Since the emphasis in the design was on electron identification and e/7 separation, it is an excellent detector for a v^ —*• ue oscillation search. The detector is located at the end of the neutrino beam line with a mean distance from the center of the decay tunnel to the center of the detector of 96 meters. Since the wide-band beam peaks at 1 GeV, the L[EV is 0.1. The detector (Fig. 1) is a 175 ton target-calorimeter containing 112 modules followed by a lead-liquid scintillator shower absorber and a magnetic spectrometer. Each module contains a 4m x 4m x 7.5cm plane of liquid scintillator segmented into 16 horizontal cells followed by 4m x 4m x 3.75cm X and Y measuring planes of proportional drift tubes (each plane contains 54 PDT's). The liquid scintillator cells have phototubes on each end and multiple times and a single pulse height can be recorded for each spill. Two times and a - 59 - single pulse height can be recorded for each PDT tube. Each module is wl/4 radiation length and the detector is approximately 90% active. The high segmentation coupled with the timing and pulse height information provides excellent irjp separation, electron identification and photon rejection. In this experiment the ration of ue quasi-elastics [ven —> e~p) to Vy. quasi-elastics [Uf,.n —• n~p) is measured as a function of neutrino energy and compared to the calculated ratio. These events, in the low Q2 region, appear in the detector as single tracks or showers with at most some low energy associated activity at the vertex and are very similar to neutrino elastic scattering events. No excess of electron events was observed2' and the 2 3 2 resultant 90% confidence level limits on u^ —> ue are sin a < 3.4 x 10~ at large Am and Am2 sin2a < OAZeV2 at small Am2. 2. DATA ANALYSIS The data for this analysis comes from an exposure of .9 x 1019 POT corresponding to 1.25 x 106 AGS beam bursts. Electron candidates were obtained by processing all bursts through a coarse computer filter program designed to retain events with an electromagnetic shower within 240 mrad of the neutrino beam direction. After scanning by physicists to remove events with additional hadron tracks or significant disconnected energy, a total of 873 events with 0 < 240 mrad and 0.21 < Ee < 5.1GeV remained. The shower energies have a 40% correction for invisible energy and the energy resolution is AE/E = 0.12/\/E[GeV). The shower angle was determined from a fit to all shower hits in the PDT cells and the angular resolution was A0 = 30 mrad. The major backgrounds in this sample are from uNn neutral currents, inelastic ue scattering (i/eNn) and to a lesser extent u^e —* v^t elastic scattering. Backgrounds with a 7r+ in the final state were measured by observing the delayed signal from n —* y. —*• e decay. The shower energy distribution for the events remaining after the TT+ background events were subtracted ia shown in Fig. 2a. During the scanning, events with a single shower associated with an upstream energy deposition were collected and used as a control sample of identified photons. The shower energy distribution of these photons is shown in Fig. 2b. The e~p candidates (Fig. 2a) below 0.9GeV are expected, from calculation and observation, to be mostly photons with a small number of u^e —• u^e and very few low - 60 - energy ven -> e~p because of the 240 mrad restriction. Therefore it is possible to subtract the photon induced events above 0.9GeV in Fig. 2a by normalizing the distributions in Fig. 2a, 2b below Q.9GeV. After subtracting events with observed TT+ decays and correcting for the TT+ decay efficiency (40% of candidates), removing 7r°'s using the observed PT° events (13%) and making small corrections for eiW (3%) and u^e -* u^e (5.8%), a total of 418 e~p events remained. The ue events were normalized to a sample (« 10% of data) of 1370 u^n —»• fi~p quasi-elastic events in which one long track left the detector and the other stopped in the detector and was identified by range and ionization as a proton. The background in this sample after acceptance criteria were applied, consisted of charged current single ?r+ production (13% of the yTp rate) and a small contribution (fa 3%) from TT° and multipion production. 3. RESULTS The neutrino spectra derived from the measured quasi-elastic samples are shown in Fig. 3 together with the calculated spectra3). The agreement between the observed and calculated v^ spectrum in Fig. 3 is a check on the validity of the beam program and of the parameters for n and K production used in it. The agreement between the observed and calculated ue spectrum as a function of energy sets limits on possible Uy. —*• z/e oscillations. To determine the oscillation limits only the ratio of fluxes is required. This ratio is shown in Fig. 4a and the difference between the measured and calculated ratios as a funtion of neutrino energy is shown in Fig. 4b. Clearly there is no evidence for oscillations. The errors on the data points include a systematic uncertainty of 20% (comprised of equal contributions from the flux calculation and the acceptance calculations). Using the data 2 2 in the energy range 900 < Ev(MeV) < 2100, the region in Am — sin 2a space excluded with 30% confidence is shown in Fig. 5. In the large Am2 limit sin2 2a < 3.4 x 10~3 while in the small Am2 limit Am2 sin 2a < 0.43eV2 at the 90% confidence level. 4. CONCLUSION The results from this experiment are compared with other results presented at this workshop in Fig. 5. The high statistics and good e/7 separation in this experiment yield - 61 - 2 the best sin 2a limits for large mass differences while the L/Ev value of 0.1 restricts the Am2 range of the oscillation search to > 0.43eV2. There is no evidence in the E734 data for the excess of electron events reported by the E816 collaboration4) at this meeting and initially reported by the CERN PS1915) experiment. The major advantages of the present analysis compared to that in E816 is the use of the simplest (single track) topologies, the ability to identify jingle photon showers and to measure the incident neutrino fluxes via the observed muon and electron tracks from quasi-elastic events. This work was supported in part by the US Department of Energy and the Japanese Ministry of Science and Culture through the Japan-U.S.A. Cooperative Research Project on High Energy Physics. REFERENCES 1) E734 Collaboration: K. Abe, L.A. Ahrens, K. Amako, S.H. Aronson, E.W. Beier, J.L. Callas, D. Cutts, M. Diwan,L.S. Durkin, B.G. Gibbard, S.M. Heagy, D. Hedin, J.S. Hoftun, M. Hur- ley^. Kabe, Y. Kurihara,R.E. Lanou, A.K. Mann, M.D. Marx, M.J. Murtagh, Y. Nagishima, F.M. Newcomer.T. Shinkawa, E. Stern,Y. Suzuki, S. Terada, D.H.White, H.H.Williams, and Y. Yamaguchi; Brookhaven National Laboratory, Brown University, Hiroshima University, National Laboratory for High Energy Physics (KEK), Osaka University, University of Pennsyl- vania, State University of New York, Stony Brook 2) Ahrens, L.A. et al., Phys. Rev. D 31, 2732 (1985). 3) The beam program used was a CERN wide band beam program (Hydra Applica- tions Library, Nubeam: Neutrino Beam Simulator, C. Visser, CERN, 1979) modified extensively by R. D. Carlini, Los Alamos National Laboratory. The systematics of pion and kaon production used to obtain the curves in Figs. 3 . d 4 were based on + the semiempirical studies cited in reference 4. The two studies g v.: for K /it *" ratio averaged over all meson momenta from 1 to 14 GeV/c 0.083 (GHJxy and 0.089 (SW). The values of the ratio ^(E(ve))/^(E(utl)) at any Eu between 1 and 5 GeV obtained using the two studies differ by less than 10%. Details of this work on neutrino beams at BNL are published in Phys. Rev. D 34, 75 (1986) - 62 - 4) J. R. Sanford and C. L. Wang, BNL 11479, 1967 (unpublished), and H. Grote, R. Hagedorn and J. Ranft, Particle Spectra, GERN, 1979 (unpublished). 5) Angelini, C. etal. Phys. Letts. B179, 307 (1986). 6) Bernardi, G. et al. Phys. Letts. B181, 173 (1986). 7) E816 (A Boston Univ., BNL, CERN, Paris Collaboration) Presented at this workshop by P. Astier, LPNHE, Paris. 8) E778 (A Columbia Univ., Univ. of Illinois, Johns Hopkins Univ. collaboration) Pre- sented at this workshop by G. Tzanakos, Columbia Univ. - 63 - FRONT VIEW GAMMA MUON CATCHER SPECTROMETER MAIN DETECTOR, ELEVATION Fig. 1. The E734 detector - 64 - 1 I i r (a) Fig. 2a. Shower energy distribution for all 40 possible uen —»• e~p candidates; b. Shower 30 energy of photons associated with upstream 20 event vertex; c. The electron energy distri- CD 10 bution after all background subtraction. O 0| (b)H UJ 10 0 20 (cH lOi 0 1 2 3 4 Ee (GeV) T T" 10 (a) 10 6 [h O 4 \ a. Fig. 3a. i/ji flux obtained from v^n —* fi p 't events; b. ue flux obtained from uen —• e~p CM 10 events. The solid lines are the fluxes calcu- lated from a neutrino beam program. =r 2 10' LU > ^K (b) >=+sL-k ^k 10 ^ _L 0 2 3 4 Ev (GeV) - 65 - 1 1 Fig. 4a. Ratio of fe/fM flux as a function of 1— Ev\ b. The difference of the calculated and LL) H\— f measured fe/fM flux ratios as a function of 1 A Ev. LU - io3 \ 1 i i ' 0.02 —< LU UJ —! 1b 0.01 - sin 2a = 1.0x 10-f 1 - O T T 0 —I 01 UJ S "° " -Q-, -0.02 I 1 1 | 3 4 (GeV) 100 — i Fig. 5. Experimental results on r/M —>• fe r BNBNLL 1 CERN PSl rE72.fi \ BEBC! l| oscillations. Limits from BNL 734 (Ref. 2) I 1 and CERN BEBC (Ref. 5). Positive re- 10- •J suits from CERN PS 191 (Ref. 6) which is in agreement with BNL E816 (Ref. 7) re- sults and E776 (Ref. 8). The E776 region j is indicative of the allowed region but does not represent a confidence level contour. 0.1 - E 0.01, ,.001 0.01 0.1 1.0 - 66 - NEUTRINO OSCILLATIONS IN BEBC M. BALDO-CEOLIN Dipartimento di Fisfca dell'Universitk, Padova, Italy and Istituto JVazionaie di Fisica Nucleare, Sezione di Padova, Padova, Italy In the following I present and discuss the new experimental limits on i/M -*• i/e oscillations which have been reached in BEBC - the heavy liquid bubble chamber - by the Athens-Padova-Pisa-Wisconsin Collaboration*1*. In the discussion, for sake of simplicity, I will assume the hypothesis of mixing be- 3 tween Pp and ve only; the oscillation probability is then^ ) 2 2 2 Pfa. -+ ?'e) = oin {20)sin {1.276m L/E) (1) 2 2 2 3 where 5m =|mj — TWJ||, in eV , and 9 is the Vp — ve mixing angle. 6m and sin (29) are the parameters that determine the oscillation probability. L is the neutrino propagation length in meters emd E the neutrino energy in MeV. As eq.(l) illustrates, in the v oscillation hypothesis, a ue component is expected to originate in a Vp beam and the sensitivity to small 8m2 values increases in proportion to L/E. A measurement of small Sm2 thus requires a large distance between the neutrino source and the detector and a low energy neutrino beam. Moreover, in this type of experiment the miisidentification of events could be a real source of errors so that a good measurement needs: 1) a clear, unambiguous identification of the Up and ve events; 2) the ve background to be small and well known; 3) a good neutrino energy determination; 4) detailed knowledge of the ue and v^ relative detection efficiency. In the following I will discuss these points in some details. - 67 - THE EXPERIMENT The present experiment was performed at CERN PS with the aim of exploring the small 8m2 region. The low energy neutrino beam was generated by 19.2 GeV/c proton . The u^ flux was enhanced by focussing TT+'S and if*"'s with a pulsed magnetic horn. The horn was followed by a 45 m decay tunnel and a concrete-iron shielding. The most probable v^ energy was 1.1 GeV, the average being 1.5 GeV. 3 The background ue flux was estimated from existing measurements^ ) of the z and K production rates at this energy and from the known geometry of the beam and found to be 0.4% of the v^ flux*4*. The energy dependence of this background is shown in Fig. 1, together with the v^ spectrum. Due to its high resolution, the BEBG bubble chamber was chosen as the v detector. It was located 825 m from the target so that L/E resulted 2.6 < L/E < 0.16, and 3 was filled with a 73% Ne/H2 molar mixture (p = 0.68 g/cm , XO=43 cm). The filling liquid mixture was chosen according to the resulting quality on particle identification and neutrino energy evaluation. The energy determination resulted on average a AE/E = 0.03 for p's and AE/E = 0.20 for electrons at 1 GeV. The short radiation length of the liquid assured an excellent identification of the electrons through the observation of the characteristic elet tromagnetic processes which constituted the signature. The fiducial volume was chosen to provide a mean potential path length of about 150 cm for the ft particles produced in the v interactions, allowing a reliable separation of the muons from hadrons (hadron interaction length of about 100 cm). Furthermore, the BEBC high magnetic field (3.5 T) was able to trap a fraction (more than 25%) of the muons which were then identified through their spiralization and eventual decay, while about half of the leaving muons were identified through a cyfindricairy-symmetric set of proportional wire chambers (the Internal Picket Fence - IPF), placed outside the chamber body which provided timing and spatial information. A total of 794,000 pictures, corresponding to 0.9-1019 protons on target, were taken. All the pictures were visually scanned for nuclear irvents induced by neutrals, with - 68 - the exception of bare one-prong events; isolated gammas or electrons, with momentum larger than 120 MeV/c were also recorded. Approximately 60% of the pictures were scanned twice and, in addition, a special scan was performed on the frames flagged by a track that gave a hit in the IPF during the 2.2 psec beam-gate. The average scanning efficiency was c = 0.90. 4017 interactions and 589 isolated gammas or electrons were found and measured. Negative, non-interacting tracks that left the chamber after a track length of at least 20 cm, or those that came to rest with or without visible decay with a range compatible with that of a muon, were considered candidate muons. To allow a good n/p discrim- ination and to ensure the background being negligible, muons stopping without visible decay were required to have a momentum greater than 150 MeV/c. 880 events had a track satisfying these criteria. To be accepted as an electron a track was required to show two or more of the following signatures: a) visible Bremsstrahlung (Pe+e- > 20 MeV/c), or Gompton electron (Pe- > 20 MeV/c) pointing tangentially to the track; b) £-ray, carrying at least 20% of the initial energy; c) trident (e+e~ pair lying on the track); d) spiralization and a range longer than that of a muon. The probability, for an electron track, of producing at least two of the above signa- tures, was evaluated as a function of energy by two independent Montecarlo programs. For instance, a 1 GeV/c electron produces an average of 6 signatures and has an iden- tification probability of 95%. The possibility of misidentifying a 7 or a JT,/* track as an electron is completely negligible. EVENT SELECTION The following conditions characterizing the v interaction were considered as partic- ularly suitable in order to disantangle GO v interactions from background events: 1) EUIB = Pt,l8; - 69 - 3)(P,,,,)x=0 p bein th where Evia = £E; and PtnS=£P», ®i and i S Energy and Momentum of the i track; (Pvf»)// and (PU!0)x are xiv. Pvis projections respect to the v direction. Accordingly, taking into account the experimental resolution, the following selection criteria have been applied to the candidates: 1) Evia -FviB where 6 k the angle between Pvi8 and the neutrino direction, and A is the angle between Pvis and the horizontal (beam) plane. According to Montecarlo studies, these selection criteria give an acceptance of 93.5% for genuine OG events; they led to the selection of 470 i/^ GG events, as illustrated in Table I. Table I Gut Events cos* < 0.8 co80 > 0.8 Total none 403 477 880 Evia-Pvis < 1 GeV 297 473 770 cosh. > 0.8 91 473 564 coeO > 0.8 - 473 473 (Pvi*)// > 200 MeV/c - 470 470 In Fig. 2 the cosO distribution is shown for all the 2626 events with at least one negative track, the dotted area represents the selected events. The black area (scale twice larger) represents the IPF events and nicely confirmes that the requirement: cosB > 0.8 optimizes the signal to background ratio. vt GG events were carefully searched for as possible evidence for i/p -» ue oscillations: 4 events with negative and 1 with positive electron were found: they satisfied all the above selection criteria. - 70 - Table II gives the numbers of Vp CO events, according to the p~ track type, weighted for scanning efficiency . The corresponding Montecarlo predictions are also given in the same Table. The agreement is satisfactory. The background - in the sample of 470 Vp OC candidates - were determined by several methods 24 ± 5 events. It is well consistent with being mostly due to v~ - produced is NC or cosmic ray events - which leave the chamber without showing any interaction. Energies and topologies of i/e events are given in Table HI. Table II t/p 00 Events ft leaving with ft leaving without p decay+stop IPF hit IPF hit Experiment 194 207 120 Montecarlo 193 193 135 The possibility of background due to Vp events mimicking i/e interactions was con- sidered in great detail. This would happen under some rare conditions when a 7 at the interaction vertex wotild appear to be a single electron along with the absence of an identified muon. The background was evaluated using the 7 asymmetry and Oompton probabilities, the vertex resolution, and the known energy dependence of 7 multiplicities in both charged and neutral current events: it resulted entirely negligible. Table III Electron GO Events Charge of Electron Event Energy Electron Energy (Roll/Frame) GeV GeV 1158/850 negative 2.5 1.50 1280/428 negative 5.9 3.40 1287/1241 negative 2.8 2.00 1306/1047 negative 1.4 0.86 1310/2542 positive 2.2 1.67 - 71 - EVENT ENERGY DETEBMINATION Knowledge of the GO event energy is critically important for the determination of the interesting parameters Sm2 and »tn2(20), as well as for a correct subtraction of the background contribution. Although thr mrrgy of the events in this experiment is determined rather well, some incertitude may be due to a possible ambiguity between JT+ and p at relatively large momenta , thus in order to better determine the v interaction energy the variable: (2) was used; here N is the number of visible particles in the final state, pi// is the longitudinal momentum of the ith particle and Ei its energy or, if identified as a baryon, its kinetic energy. Neglecting Fermi momentum, fj would be zero for v interactions if all the tracks were visible and their masses correctly assigned. The loss of neutrons would smear the t] distribution and slightly shift its average to positive values, the misidentification of protons as pions would shift tj to higher positive values. Thus the ambiguity between ff+ and p was solved for each event by matching the total visible energy and longitudinal momentum P//. The resulting i\ distribution is shown in Fig. 3a. The average energy lost in gammas and neutrons was estimated as a function of the event energy and found to be ~ 5%. In the final analysis discussed below, a correction factor for this loss was applied in a proper, energy dependent, way. The energy spectrum of the v^ events is shown in Fig. 3b; the fi~ momentum spectrum is shown in Fig. 3c. In all figures the solid lines are obtained by a Montecarlo simulation normalized to the total number of events. The agreement corroborates both particle identification and the scanning and measuring procedure. OQNGLUSIONS AND ANALYSIS In Fig. 4 the relative acceptance for electron and muon event as a function of v energy is shown in the present experimental conditions, as evaluated by the Montecarlo program. - 72 - Montecarlo studies indicates that from 470 v^ CC events a background of 3 ve OC events is expected, which is compatible with what is observed. The observed e+ event is also compatible with the background estimates (~0.2 events). It is to be noted that the energies of the vt events are somewhat higher than those of the t/ft events, as expected from the ve contamination in the beam. Thus, the conclusion is that in the present data there is no evidence for v^ —* ve oscillations. To set limits on the oscillation parameters, a two neutrino (i/p —» ve) oscillation scheme was assumed. The likelihood ratio h=L/L0 was computed as a function of the parameters, using the function: L(«m2, sin2 {29)) = J[ P?{ (1 - Pi)1""* where n^ = 1(0) if the event is an electron (muon) event, and P,- is given by: with a, = nna(20)mn3(1.27 • L • 8m2/{Ei)), where Ei is the visible energy (in MeV) of event i, corrected for the undetected fraction of energy carried away by neutrals, $ is the expected ratio of background i/e to v^ in the beam at energy E\ ft is the detection efficiency for electrons relative to that of muons, including the ratio of Up to i/e cross sections at energy 2%, and f is the fraction of background events in the muon sample. Lo is the likelihood function corresponding to the hypothesis of no oscillations. The resulting confidence region is shown by the solid line in Fig. 5. The lowest value of the oscillation parameters that are excluded at the 90% confidence level by the present experiment are: 6m2 = 0.09 eV* (for sin2{29) = 1) and sin2 {29) = 0.013 (for Sm2 = 2.2 eV2). The result on 6m2 - gin2{29) is essentially unchanged when the parameters 23,-,$,$ and f in eq. (3) arc allowed to vary within their uncertainties. - 73 - A comparison of the present data with the most recent results is made in Fig. 5. It can be seen that the results obtained in the present experiment are by far the most 5 stringent limits on the transition i/^ -* i/e in the small Sin? region* ^. This is mainly due to the ability of the detector in providing a clear and unambiguous electron identification and to its good energy resolution. REFERENCES (1) C. Angelini, A. Apostolakis, A. Baldini, M. Baldo-Ceolin, L. Bertanza, F. Bobisut, E. Calimani, U. Camerini, S. Oiampolillo, R. Fantechi, V. Flaminio, W.J. Fry, H. Huzita, P. Ioannou, S. Katsanevas, C. Kourkoumelis, J. Koutentakis, M. Loreti, R. Loveless, G. Miari, R. Pazzi, P. Pramantiotis, M. Procario, G. Puglierin, DJD. Reeder, R.K. Resvanis, B. Saitta, M. Vassiliou, Phys. Lett. 179Jg, n. 3, 307 (1986). (2) B. Pontecorvo, JETP 34, 247 (1958), JETP 7 , 172 (1958); Zh. Eksp. Teor. Fiz. 5_£, 1717 (1967) [JETP 26, 984 (1968)]. S.M. Bilenky and B. Pontecorvo, Phys. Reports 41, 225 (1978). The possibility of neutrino oscillation among flavours had independently been sug- gested in 1962 by Z. Maki, M. Nakazawa and S. Sakata; Progr. Theor. Physics 28, 870 (1962). For recent reviews of the theoretical aspects of lepton non-conservation see G. Costa and F. Zwirner, Rivista del Nuovo Cimento 9, n.3 (1986), and Vergados, Phys. Rep. 133, 1 (1986). (3) J.V. Allaby et al., CERN REPORT 70-12 (1970). H. Grote, R. Hagedorn and J. Ranft, Atlas of Particle Production Spectra, CERN (1970). (4) C. Visser, NUBEAM: Neutrino Beam Simulator, Hydra Application Library, CERN (1979). (5) L.A. Ahrens et al., Phys. Rev. 1331, 2732 (1985). F. Bergsma et al., Phys. Lett. #142. 103 (1984). For a recent review of neutrino oscillation experiments see V. Flaminio and B. Saitta, to be published in the Rivista del Nuovo Cimento. - 74 - i i i i i i i i 1 600- -600 500- 500 400- 400 300 300 200 100 0 0 1 2 3 4 5 6 -1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 Ev(GeV) Cos e Fig. 1 Energy dependence of the v^ and ve fluxes. Fig. 2 Cos0 distribution for the events having at least one negative track, inside the fiducial volume. The dotted area corresponds to the selected events (see text). -i—i—i—i—i—F—i—r V0 20 30 40 SO 00 0.4 08 12 Evl5lGoV| KGeV) Fig. 3 Experimental distributions of some kinematical variables of the v^ CO events com- pared to the corresponding Montecarlo predictions: (a) r\ ; (b) visible energy ; (c) muon momentum. - 75 - 10. v i i I i HI—•CT—i—i i i i in 1 1—i I i i i 1.2 1.0 Jm2(eVJ) „ 0.3 t 1.0 <* a.* 02 This Exp 0.0 O.« 0.8 1.2 I.S 2O 2.4 CJCrt 10" 10" -j i i i i • i 10" 10" 10" 1.0 Sin2 2 9 Fig. 4 Ratio between the ve and v^ events acceptance, as a function of B^. Fig. 5 Correlated limits on the oscillation parameters, at the 90% confidence level, as obtained in this expetiment (solid line) compared with the results (dashed and dotted line) of two other recent experiments (Ref.5). - 76 - SLARCHUS FOR NEUTRINO OSCILLATIONS CHARM Collaboration CERN, Geneva. Switzerland. Two searches for evidence of neutrino oscillation have been performed by the CHARM Collaboration looking foi the the appearance of r in r beams. In the first one two similar detectors were exposed to the low-energy PS neutrino beam. This experiment was sensitive to small differences of the neulrno masses, and a limit of Am2 < 0.19 cV2 was obtained at 90% c.l. in the case of complete inixing. A second search was performed at the high-energy SPS neutrino beam. The higher -'..luslics allowed sensitivity lo mixing angles as low as sin220 = 0.005 (90% c.l.). The CHARM Collaboration performed an expeiimenl at neutrino energy'. As shown in Fig. 1 the detectors were the CERN Prolon-Synchiotron (PS) aimed at searching for located as far as 123 m (close detector) and 903 m (far evidence of neutrino oscillations. Since the fine-grained detector) from the proton target [?]. In the figure the inset deiecor allowed an identification of both •• - and >• -induced shows the computed ••• and P fluxes at the far detector. charged current events |1] two analyses could be performed. The proton energy was chosen as low as 19.2 GeV, yielding The probability of v «-• :'£ (appearance experiment) was an average neutrino energy of about 1 GeV. Data were determined by searching for leading electrons in the final recorded for about 9.8 x 10'8 protons on target. state. The probability of an oscillation of muon-ncutrinos to any kind of neutrino species (disappearf-ncc experiment) was The aim of the appearance analysis was to deduce the rate done by absolute flux measurement comparing the rale in of y -induced events compared to events induced by two detecors exposed to the same v beam. muon-neutrinos, which were the dominating particles (>99.5%) of the original beam. Although the mea-.i The CHARM experiment was the first to search for neutrino energy was much below the range usual for v ~- i Figure 1 10 SUBUMlS FIR OEIECICO 1901ml presented "by V. Zacek - 77 - A new estimator was developed as an outcome of intensive studies of electron and pion test data taken at ITEP using a special CHARM-delector-like lest setup [1). An upper limit of 3 8% (90% c.l.) for the fraction of ^'s which transformed to o s was obtained. For complete mixing (sin*2fl = 1) this corresponds to a limit of am2 < 0.19 eV2. The limits obtained in the plane AmJ-sin22fl arc shown in Fig. 2. In this figure the full line is ihe border of the excluded region obtained by comparing the r£ event rale in the close .^nd far delators (CD - FD). The dotted limit is obtained using only the events measured in the CD. The result wss essentially limited by the low statistics accumulated in the detector. •e*c \ 1 I0" 10'* 10"' Figure 3 y -induced charged-current events The rates of these events measured at both detectors were compared to the expected number, which was calculated by a Monte Carlo program simulating the neutrino beam. No indication for an oscillation of v to vr. or possible heavier neutrino species, was found. For complete mixing the limit in this case was Am* < 0.29 eV2 (90% cl). The limits in the plane Am*-sin228 are shown in Fig. 4 together with those obtained by the CCFR [9] and CDHSW [10] Collaborations. sin!29 Figure 2 A similar analysis, performed on a data sample taken in the high intensity CERN SPS wide-band neutrino beam, did not suffer from this problem.'The distance between the average neutrino creation point and the CHARM detector (= 650 m) and the high mean neutrino energy (= 13 GeV) limited the sensitivity to small mass differences, but the high-statistics data sample provided sensitivity to mixing angles as low as sin22fl = 0.005 (90% c.l.). The limits in the plane &m2-sin22S obtained from this experiment are also shown in Fig. 2 (dashed line). The combination of both results is shown in Fig. 3 together with the limits obtained by the BNL BC [3], BNL E755 [4], and BEBC [5] experiments looking for the appearance of i-.. In the figure are also shown the limits obtained by tti"e Gosgcn experiment [6] looking for the disappearance of i>e. Fhc dashed regions are the allowed regions in the plane Am2-sin220 corresponding to ths indications of neutrino oscillations found by the CERN PS191 [7] and Le Bugey [S] experiments. In the (ijappearance experiment the CHARM Collaboration looked for an unrxpected variation of the i^-flux passing through th: detectors exposed ;o the PS beam 12]. A computer r.u..-rithm was designed to Belcct all - 78 - REFERENCES [6] Gabathuler K. et al., Phys. Lett. 138B. 449 (1984). 17] Bernardi G. ct al., preprint CERN-BP/86-58 [1] Dorcnbosch J. ct al. (CHARM Collab.), preprint (1986), submitted to Physics Letters B. CERN-EP/86-74, submitted to Nuclear [8] Cavaignac J.F. et al., Phys. Lett. 148D, 387 Instruments and Methods. (1984). [2] Bergsma F. et al. (CHARM CoUab.), Phys. Lett. [9] Stockdale I.E. et al., Phys. Rev. Lett. 52, 1384 142B. 103 (1984). (1984). 13) Baker NJ.etal, Phys. Rev. Lett. 47, 1576(1981). [10] Dydak F. et al., Phys. Lett. 134B. 281 (1984). [4] Ahrens L.A. et al.. Phys. Rev. D31, 2732 (1985). 151 Flaminio V. and B. Saitta, Univ. Pisa PI/AE 85/6 (1985), submitted to Riv. Nuovo Cimcnto. - 79 -/-3D- Future Long Baseline v^ —> ve ve Oscillation Searches at Accelerators Presented by Michael J. Murtagh Department of Physics, Brookhaven National Laboratory Upton, New York 11973 USA ABSTRACT The additional neutrino flux available when the Booster at the AGS becomes oper- ational will make possible u^ —> ue oscillation searches at Brookhaven which signifi- cantly extend beyond the present limits. 1. INTRODUCTION Present u^ —* ue oscillation searches at accelerators are limited by their LjEu range (0.1-1) to Am2 > 0.1 eV2 and sin2 2a > 5 x 10~3. It appears possible with the advent of the Booster1) to significantly improve the Am2 range to perhaps Am2 < 0.01 eV2 while maintaining reasonable sin2 2a coverage. However for a reasonable amount of Booster running (« 1020 POT) with a modest detector (1 Kton fiducial volume), it will be difficult with distances greater than 10 Km to retain acceptable sin2 lot coverage. 2. NEUTRINO RATES The analysis for most low energy i>M —»• ue oscillation, searches at accelerators focusses on quasi-elastic events. There are a number of reasons for this. They constitute a sig- nificant fraction of the total cross section at these energies ((un —> i~p)/ all events « 0.6/Eu(GeV)). The topology is very simple, reducting to a single forward track at low Q2, which simplifies the extraction of the signal and the rejection of TT0 backgrounds. In addition, if the lepton energy and angle with respect to the beam are known, the incident neutrino energy is calculable. Consequently, by restricting the analysis to single track - 81 - muon and electron events, one can in principal measure the incident v^ and ue flux as a function of neutrino energy. An oscillation signal would show up as a distortion of the measured energy dependance of the ratio of Ue/v^ fluxes compared to the calculated ratio which had the correct Ev behavior. The rates used for the estimates discussed below are based on the observed event rate in the E734 detector which has been taking data in the wide band neutrino beam at BNL for some time2). The conventional normalization in E734 comes from a measurement of low Q2 Vp,- ^uasi-elastic events which appear in the detector as events with a single forward track consistent with being a muon. Since most of these muons escape the detector it is not possible to reconstruct the incident spectrum from these events. The spectrum shape is determined either from the quasi-elastic events with muons which pass through the 2 2 2 spectrometer {Ev = F(PM,0M)) or high Q [Q > 0.25(GeF/c) ) events in which both the muon and stopping proton are measured [Ev = F(Q(l,Ep)). The energy of quasi-elastic uen —* e~p events, on the other hand, can be reconstructed from the observed forward electromagnetic showers of low Q2 events since the shower is, in this case, contained in the detector {Ev = F(Ee, 0e)). While forward leptons constitute only « 15% of the total cross section at these energies they have many advantages as the basis for a good v^ —* ve oscillation search and provide a reasonable estimate of the number of usable events in the detector. The rate of detected \ir tracks with 0M < 30° and P^ > 350MeV/c from i/^n —• pTp quasi-elastic events in the E734 detector is 4 x 1CT2 /i~/lO13 POT/30 mton. For distances > 1 Km this rate is given by N £ 20 x M/L2 where M is the detector fiducial mass in mton, L is the source to detector distance in Km and N is the observed number of quasi-elastic muons for 1019 POT. This rate assumes a 1/Zr2 beam dependence which is reasonable for L > 0.5 Km. The formula has been explicitly corrected for the measured E734 rate which is at 100m. Recently the AGS has averaged 1.5 x 1013 POT/pulse with a 1.4sec rep. rate during fast extracted beam running. This corresponds to 1019 POT hi less than 3 weeks of running if one assumes 80% operating efficiency. E734 has actually averaged 101D POT per 3 calendar weeks for significant parts of its last two major runs. If the Booster increases - 82 - the rate by a factor of 4, then a run of 1020 POT appears quite reasonable. The observed forward (j,~ quasi-elastic rates for a 1 Kton fiducial volume detector with a 1020 POT run are given in Table 1. the expected e~ quasi-elastic rates for an e\\i ratio of 1% are also listed. TABLE 1 Observed Rates for 1020 POT with 1 Kton Fiducial Volume Detector L(Km) #M-ftt-p) #e~fe-p) 1 2 x 105 2 x 103 10 2 x 103 20 100 20 .2 1000 .2 .002 The rate beyond 10 Km is discouraging. This is unfortunate because one might hope that with sufficient distance matter oscillation effects might become significant. However, even at 1000 Km (Fig. 1) the matter effect is insignificant3) and at this distance the rate 's negligible. Significant enhancements for specific E/Am2 ranges do occur but only for distances in the earth of « 8000Km. 3. RESULTS AND CONCLUSIONS If one assumes that the large detector used in this search has approximately the electron identification and photon rejection capabilities of the E734 detector4), then it is straightforward to calculate the expected oscillation limits (Fig. 2). As is clear from these limits, the lack of statistics beyond 10 Km severely restricts the sin2 2a limit and the increased distance does not substantially aid the Am2 limit. Consequently, even with the added flux of the booster it is unlikely that searches much beyond 10 Km will be effective. On the other hand, there is every possibility of significantly extending the present u^ -> ue oscillation searches. Clearly any experiment which improves v^ -> ue searches should be able to improve on v^ disappearance searches but it is more difficult to estimate the expected limits in this case. This work has been supported by the US Department of Energy under contract US- AC02-76CH00016. - 83 - REFERENCES 1) Booster Design Manual, Accelerator Development Dept., Brookhaven National Lab- oratory, 10/29/86. 2) Elastic Scattering of Muon Neutrinos at BNL, Presented at this workshop by S.L. Durkin. 3) A.J. Baltz, Presented at this workshop. 4) A Search for v^ —»• i/e Oscillations Using the E734 Detector, Presented at this workshop by M.J. Murtagh. - 84 - 10 i i rrnir "rrnrm Fig. 1. Probability for ue events due to oscil- 2 2 0.8 lations as a function of E(MeV)/Am {eV) at 1000 Km taken from a calculation by A. 0.6 Baltz, J. Weneser (Ref. 3). Dashed curved is for vacuum oscillations only while the solid 0.4 curve includes matter enhancement from pas- sage through the earth. iou 100- - BNL IBEBCCERN PS / I 10- Fig. 2. Estimated Uy. —* ve oscillation limits for various source to detector distances (L) for 20 L=lkm a 1 Kton fid. vol. detector and 10 protons on target. L-IOkm—., O.I 0.01 0.001 0.01 O.I 1.0 sin2 2u - 85 - / REPRODUCED FROM BEST AVAILABLE COPY Theory of Neutrino Oscillations Effects of the Third Generation on Neutrino Oscillations in vacuum and matter C.W. Kim Department of Physics and Astronomy The Johns Hopkins University Baltimore, Maryland 21218 Abstract Analysis of neutrino oscillation data is presented with emphasis on the role of the third generation neutrino. Differences between the two and three generation cases are highlighted. The implications of recent results on the solar neutrino problem are also discussed. I. Introduction When neutrinos are mixed as well as massive, they display the phenomenon of neutrino oscillations. Observations or non-observation of the oscillation provides information on the lepton mixing angles, 8., and the mass squared difference, A.. = m^ - nu . This phenomenon has been and is being searched for, but so far no decisive evidence has been seen. In the past, experimental results have, almost always, been presented in the framework of two neutrino flavors, i.e., in terms of an angle 9 and a mass squared difference A. This, of course, is justified when the third neutrino is sufficiently decoupled from the first two. In this report we review how the third neutrino affects .analyses based on the two neutrino assumption. In particular, differences between the two and three generation analyses will be emphasized for v -* v and v -» v oscillations and the solar neutrino problem. First, in Section II, two generation analyses of laboratory oscillation experiments are briefly summarized to establish the notation. Effects of the third generation are discussed in Section III. Recent results on the solar neutrino problem, both in the two and three generation cases, are given in Section IV. In Section V, implications of the present data on the solar and terrestrial neutrino oscillations for future experiments are summarized. II. Two Generation Analysis To establish the notation and to compare later with the three generation case, we briefly review the well known analysis of the neutrino oscillations for two generations. The weak eigenstates v and v i are related to the mass eigenstates v± and v2 by a unitary matrix U as - 89 - cos9 sinGe" (1) -sinBe cosB where 6 is the mixing angle and (5 is the CP phase which can be absorbed into neutrino phases for Dirac neutrinos. For Majorana neutrinos, /3 has physical consequences. For example, the effective mass 12/3, where the upper (lower) signs are for the case of the same (opposite) CP eigenvalues for ut and v2 . P, however, does not appear in neutrino osc illations. When v is produced at t=0 and u_ is detected at the time t(=L), 2 the probability P(u -» uR) is given by P (v a V a up(t)|ui(t) x< (3) ai1 ai1 where we have used E. — E + m./2E. The two generation formula for the i' -» i> oscillation is, from Eq. (3), 2 2 (V v ) = sin (29)sin (1.27 L/E A21), (4) 2 2 where A2i = m2 - mj, and L,E and A2i are in units of meters, MeV and (eV)2, respectively. In the following we set k = 1.27 L/E. First, for the sake of argument, consider an experiment in which no positive signal is seen, with the following upper limit at L/E = 1/1.27 (i.e. k = 1): P2 (v -» v ; 1.27 L/E = 1) < 0.01 (5) 2 In the rap id oscillation limit which neans A21 >> leV , P2 = 1/2 sin (29) < 0.01 so that we conclude sin (28) < 0.02. In the 2 2 case of maximal mixing .which means sin (29) = 1, we have A21 < O.leV . In general, of course, one obtains the familiar allowed (or forbidden) 2 region in the A21 - sin (20) plot. - 90 - With a positive signal of, say, P2(u -» 1.27(L/E) = 1) = 0.01, 2 2 allowed values of 0 and A21 lie on the curve sin (28)sin A2i = 0.01. (In practice, however, experimental errors broaden the above curve into a band.) Of course, observation of oscillations at two or more values of L/E fixes values of 0 and A21 uniquely. Ill Three Generation Analysis In the case of three generations, Eq. (1) becomes V U U U V e el e2 e3 1 V V (6) = 2 V U U U V T ri r2 r3 3 n the Kobayashi-Maskawa representation the unitary matrix in Eq. (6) is given by -s, cne -s, sne -i/3 16 id. i(p-B) U = )e (7) -ip ifi. -i(p —B) )e Ci s2s3-c2c3e where c. = cos9. , s. = sin0. and /3, p, 5 are CP phases. For Dirac neutrinos, only 5 remains unabsorbed (into lepton phases), whereas all three phases remain for Majorana neutrinos. Since there has been no evidence for CP violation in the lepton sector, we restrict our discussions, for simplicity, to the case of Ct invariance and set j3 = 5= p =0 in Eq, (7).( CP eigenvalues of u. do not appear in oscillation formulas.) A. v v Oscillation —e From Eqs. (3) and (7), we obtain the three generation formula4 (8) where a = 2sin (k A,.) b = 2sin2(k A,,) c = 2sin2(k A,.) 5 1 5z. A 2 2 A 2 2 = m2-m2, k = 1.27 L/E &„2,1 = m 2- m1 , A = m -m , According to the prevailing theoretical prejudice which is based on the see-saw mechanism of neutrino mass generation and on the experience - 91 - gained from the quark sector, lepton-mixing angles are expec:-d to be small. In particular if 02 and So are small, Eq. (8) reduces to Eq. (4) and the two generation analysis is justified. This prejudice, however, has not yet been substantiated by experiment so that it is worthwhile exploring the possibility of large mixing angles in the lepton sector. First, we discuss a situation, as in the case of two generations, in which no positive signal is seen in experiment. That is, given Eq. (8) and, say, P (u -» v ; 1.27 (L/E) = 1) < 0.01, we investigate what 3 \x e we can say about A2i and Q^ . 1) Rapid Oscillation (L/E) A^ >> 1 In this case we have a=b=c=l, so that This is not particularly interesting but we know at least that each term in Eq. (9) is less than 0.01. This, however, does not imply that all the mixing angles are small since U2 U2 , for example, can be small even if 82 and 83 are large, as can be seen from Eq. (7). 2) Leading Oscillation (L/E)A..<< 1 If m3>>m2>>m1, Eq. (8) becomes 4 P3 - 4 m 3 if3 l£3 < 0.01 (10) which is not restrictive enough to give any meaningful information since there are four unknown parameters. 3) Maximal Mixings When three neutrinos are maximally mixed, the matrix U is given by,6 1 -I -1 2 2TTi/3 .,,. 1 -X -x u = x = e (11) 2 1 -X -X (In this case CP must be violated but neutrino masses are still arbitrary.) By substituting Eq (11) into 5q. (8), we find - 92 - (12) Recall that the corresponding formula for two generations is 2 P2 = sin (kA21). In the rapid oscillation limit which is applicable to = 1 the solar neutrino case, we have P3 (i^ ~* V- ) ~ (4/Q)(J/2) = —. Similarly, P3(D -* v ) = —, which can explain the solar neutrino problem as can be seen later. When combined with P3(v -» D ) < 0.01, Eq. (12) yields an allowed region in the A31 - A21 plot as shown in Fig. (1). Note that in the case of two generations, one only obtains ,1 . -i r~T~ 4) General Case Now we discuss more general cases. Equation (8), which takes into account oscillations of (i to e through vlt v2 and v3, may be written as 2 2 P3 (u -» u ) = sin (2a)sin (kA) (13) or 2 2 P3 (u -» i) ) = sin (20 )sin (kA ) + "corrections" (14) In Eq. (13), a and A are, respectively, functions of 9. and A... Therefore, when expressed as in Eq. (13), the meanings of a and A become obscure, in particular when 92 and 83 are large. When written as in Eq. (14), the correction term obviously depends on 02 and 03 . It is shown that for most values of B± and A.., the correction term is positive. (It becomes negative for large A2i and small 9±). Therefore, given 2 2 P3(u -> v ) < 0.01, the two generation curve sin (20!)sin (kA21) = 0.01 for a given value of L/E is indeed the same lower bound of a forbidden region even in the three generation case, except in the region where A2i is large and 0t is small However, in the event of positive signal e.g. P3 (u -> u ) = 0.01, allowed values of 0! and A21 do not lie on the curve sin (29t)sin (kA21) = 0.01 anymore. Let us take, for example, A < 2 2 2 P3 (Ufi -• ue) = ^3U 3 = 2(sis3) (c1c2s3+ s2c3) = 0.01 (15) which is satisfied, e.g., by G2 = 93 = 45° and Qt = 5.8°. Clearly, 0j = 2 2 2 2 5.8° and A21 ^ 10" eV do not lie on the curve sin (205)sin (A21) = 0.01 which is the two generation answer. - 93 - 2 The allowed region in the A2i-sin (20! ) plot for three generations with P = 0.01 is, instead, a region below the curve sin (29j)sin (A21) 0.01. This is shown in Fig. (2). Note that any point in the allowed region may be satisfied by more than one set of 92, 63 values. In practice the value of (L/E) is not uniquely given in experiments but instead has some spread., say, A(L/E). Let us take a = A(L/E)/(L/E) to be 0.2. In order to take this spread into account, sin2(1.27(L/E)A..) must be replaced by 3 21 A sin2(1.27 L/E ->TU-e " ° ij cos(2.54 L/E A^)] (16) ^ With this replacement in Eq. (8), one finds various contours for different sets of 92, 03 ana A32. This is shown in Fig. (3). 5) Analysis with Models So far we have treated the parameters Q^ and A., as if they were independent. It is, however, very likely that Q± and A., are, in general, not independent. Different models impose different constraints among them. For example, the maximal mixing model fixes 8. but A., are arbitrary. When the Fritzsch model7 is applied directly to the lepton sector,8 all the lepton mixing angles are determined by lepton mass ratios and phase angles. In order to illustrate how different models yield different 3 constraints, affecting the allowed regions in the AZ1 - sin (20!) plot, we discuss the Fritzsch model. The most general Fritzsch model for leptons is given by the following r.ass matrices for neutrinos and charged leptons. 0 A 0 v 0 ,-1 M = A 0 B M = P (17) i v v AL 0 B C v v E = ei/32, The model is based on the assumption that lighter fermion masses msy be generated by nearest (immediate) neighbor interactions starting with a finite heaviest fermion mass. In this nodel the K-M matrix U is given by -1 T U = P V P V (18) v L where V and V diagonalize the matrices M and M , respectively, i.e. I) Lt V LI diag(M ) = V M V & v v v v 1 diag(ML) = V^ P" M (19) The expressions for V and V in terms of mass ratios are given in Ref. (9). A few elements are presented here: ( rrwnfo (m.^ ~m^>) Vn % ) (ra3-m: nil. (m.T-m .) ? (20) J (ma+ni! )(m3-m1 ) Since (n^ /m2) and (m2/m3) as well as /3. are unknown in this model, the results in Eq. (20) are not very useful. We consider the followiing two extreme cases. a) We assume that (.mj/m2) "/"> (m /m ) and (m2/m3) >> (m /m ). In this case we can take M to be diagonal to begin with. We have Lt Ull U12 U13 (21) u = U21 U22 U23 U31 U32 U33 with aB(B-a) U 21 (22) (P-a) 12 22 where a = i , /? = Substituting Eq. (22) into Eq. (8), we find - 95 - 2ctB(B-a)(B+l) ^Ta-1 0 a-P1 1J In the limit 6 -» a, one recovers the two generation formula 4a identifying 4a/(a + I)2 to be sin2(29!). Equation (23) can be written as 2 ( ,:s\ The other extreme in the Fritzsch model is the case in which {m1/m2) << (m /m ) and (m2/m3) << (m /m ). Here, the mixing angles are completely determined by the ratios (m /m ) and (m /m ), i.e all mixing angles are small. We have, in this case, 2 2 5 2 P3(u -» u ) = 1.7xl0" sin (kA21) - 6.34xl0" sin (kA31) s 2 +6.37xl0" sin (kA32) (26) 2 2 where A21 ^ m2 and A31 ^ A32 — m3. In this case the contributions from the third generation are negligible and the two generation formula is more than sufficient for analysis. For example, P(u -» v ;k = 1) < 0.01 implies, with Eq.(26), 2 A21 oi. m2 < 0.87 eV . B. v -» v _ Oscillation -V- r Wow we briefly discuss v -> v . The probability P-, (u -» v ) for three generations is, from Eqs. (3) and (7), - 96 - P3(U -» v ) = (a+b-c)lf I + (— a+b+c)tr JJ _ (27) (10) The latest experimental upper limit for E(u -» "T) is P (u -» u ) < 0.002 for A small upper limit seems to indicate that 02 and 03 are small. However, this is not the case. From Eq. (7) we find that when 4 2 A21 ~ 10" (eV) , A31 ^ A32 >> A21 and c, = 1, |sin2(02+03)| < 0.063 (29) This is equivalent to 6n + 6O < 2° or 88° < 0O +0. < 92° implying that 92 and 03 can be large. Thus, an apparently small upper limit on P(u -» v ) does not imply small B2 and 93. In the Fritzsch model with (m1/m2) >> (m /m ) and (m2/m3) >> (m /m ), we have v f \ 2op(a-l)(P+l) ; - _ - , . . ^n-, r un u c 3 ^. T.'~/'~,i\/'R_i\/R~\/-n~,iNlR~ n _ . i ••• f V.JU; In the limit a,/3 -» «> with P - a >> 1, Eq. (30) becomes which is the two generation formula. In the other extreme of the Fritzsch model, where the charged lepton masses ratios dominate over the neutrino mass ratios, we have 3 2 3 2 P3(u -» UT) = -1.0xl0" sin (kA21) + 1.Oxl0~ sin (kA31) 2 + 0.209 sin (kA32) (32) The observed limit P (u -» v ; IV Solar Neutrino Problem Another well known method to probe the neutrino mass is the solar neutrino oscillation. Since (L/E) for solar neutrinos is (L/E) ^ 101D. - 97 - this oscillation is sensitive down to A.. < 10 ev . The recent surge of interest in the problem has led to some specific conclusions on the values of A., and 0, (if the v depletion were indeed 21 1 e due to the oscillation in matter). In this section we briefly review the subject. According to the solar model based on the solar constant (1370+0.5W/cra2) and the zero-age main sequence star model, the neutrino flux which is expected to be detected in the Cl experiment (with the reaction i> + 37C1 -> 37A + e") is 2_. = 5.90 + 2.2 SNU where errors are e ineo three standard deviations and SNU is the solar neutrino unit (10~36capture/atom/sec). On the other hand, the observed flux is1 2= 2.1 + 0.3 SNU. The ratio 2^ /2_, =0.36+0.07 (33) Expt Theor being different from unity is the famous solar neutrino problem. There are many explanations available at present. The list includes: 1) Either experiment or the solar model (or both) is wrong. 2) Less neutrinos are produced in the Sun due to slightly lower temperatures in the core than predicted by the standard solar model(dark matter,13...). 3) Something happens to solar neutrinos on the way to the Earth. Possible mechanisms are a) Neutrino oscillation in vacuum. b) Neutrino oscillation in the Sun. c) Unstable neutrinos.14 About two thirds of the neutrinos decay on the way. d) Sun spots.1 Magnetic fields due to the Sun spot activities flip the helicity of neutrinos, making them sterile. The above explanations are all possible (i.e. not yet ruled out) but all of them, with the exception of (3b), require fine tunings of the parameters involved. In the following we briefly discuss neutrino oscillations in the Sun. The equation of motion of the weak eigenstates v , v , and v .denoted by ^ is T w ^ = JL.M g> t M = u M rjT (34) 2E w w ' w D - 98 - 0 0 0 m2 0 0 m2, The above equation leads to well known formulas for oscillations in vacuum. The rratrix M is, for two generations, w j^j y21 M = 1. . -,-r.s 2 2O 2 . 2Q (35) w -A sinU°) m cos 6+m sm 0 As first discussed by Wolfenstein and further elaborated by Mikheyev and Smirnov17 (MSW), the matrix M in Eq. (35) is modified in matter, e w such as in the Sun. The electron neutrinos "see" an additional potential due to the coherent interactions v + e -* v -re r e e The potential is given by V = 2(G A/2)N where G and N are, respectively, Fermi's constant and the electron density in the Sun. The presence of V modifies the M± •, element of M as w Mi (36) where A = 2EV = 2V2EG N , while all the other elements remain £ 6 unchanged. 18 When we diagonalize the new M with the modification in w Eq.(46), the two effective mass squared values are given by 2 1/2 A_lf (Aolcos(29)-A) + (Anisin(29)) 2 2[ 1/2 + I + f|(A cos(2B)-A)i! + (A sin(20)) (37) ol21 21ol" or 2 1/2 = [(A21cos(29)-A) (A21sin(2e)) ] (38) In addition to the changes in the mass values, the mixing angle 0 is also modified in the Sun. Instead of presenting well known formulas for changes of 9 and A21, and arguments for u depletion, we present here a heuristic picture19 of the solar neutrino oscillation in two generations using an analogy to an - 99 - electron spin in a time-dependent magnetic field. In vacuum the two mass eigenstates are represented, as shown in Fig. (5), by two unit vectors ±no = ±(cos(29^e t- sin(26)e ) (39) Z X respectively. Note that the vx- v2 axis is tilted by twice the angle 0, i.e. by 28 from the v - v axis. In this picture the orthogonal v and i> states are 180° apart instead of 90°, as shown in Fig(5). The time evolution of u (i.e. v - v oscillation in vacuum) can be described by A the precession of a unit vector ]io, which is taken to coincide initially A A with e , around the axis n with the frequency w =A2i/2E (Fig(5)). z o o e Upon defining an angle Po as cos2/3o = fJ.o" , the probability that z v remains as v is given by 2 P (u -» v ; vac) = cos /3o = -(1 + fio-e ) . (40) A A A A In a coordinate system in which nf=e' and e =e', we have 2, y y' e = cos(29)e' - sin(20)e' , (41a) z z x ^o = cos(29)ez - sin(29)(cos(wot)e' + sin(wot)e') (41b) Substituting Eq.(41) into Eq.(40), we obtain the familiar result for vacuum oscillations 2 2 P (wo -• v ; vac) = 1 - sin (28)sin (&)ot/2) (42) For v produced in the Sun, the mass eigenstates in matter |p,(t)> = cos a(t)|u > + sin a(t)|u > = -sin a(t)ji) > + cos a(t)|u > (43) are represented by the two instantaneous unit vectors ± n(t) = ± (cos(2a)e + sin(2a)e ) (44) - 100 - The time evolution of u is now described by the precession of j_i around e the instantaneous n(t) axis(see Fig(6a)) with the frequency w(t) = A,. /2E = (A../2E) J(a-cos2G)2+sin22G (45) 21,m 21 N where a = A/A21 (46) A (Its vacuum value is of course uo = A. /2E.) Note that co(t)n is a vector anc sum of uono * -8io0e . Our picture is equivalent to that of the z precession of an electron spin around a fictitious time-dependent A magnetic field B(t) =u(t)n(t). In our picture, the solar neutrino oscillation may be described as A follows. When v is produced in the Sun, the vector p. is precessing A around the axis n as shown in Fig.(6a). By the time when i> leaves the e A A A Sun, n has migrated to noand when this process is adiabatic, \x continues A A to precess around n which eventually becomes no as shown in Fig.(6b). the probability that i> survives as v is given, from Eq.(40), by e e P (u -* v ) = -r(l + i±>e ) (47) s s z, z A A where e and \i are given by Eqs.(41a) and (41b) with 0 in Eq,(41b) z replaced by a. When averaged over time, Eq.(47) leads to the well known . .20 result P (ug -» ug) = jf(l + cos(26)cos(2a)) (48) When u is produced inside the resonance region, a 2: 90° so that Eq.(48) becomes for a ^ 90° P (u -» u ) = -^(1 - cos(26)) = sin26 (49) which explains the depletion of v for small 0. - 101 - When u is produced in the so-called resonance region where wz 45°, e v is an equal mixture of v. and v . As it traverses and leaves the e i z Sun, an equal mixture of v and u emerges. For v& born outside the resonance region, it remains mostly as i)g as it leaves the Sun. One can calculate the neutrino capture rate in Cl using the standard solar neutrino flux and Eq.(48) to yield the allowed regions in 21 the 91-A21 plot. The results are shown in Fig.(7) for two generations. Values of 0t and A21 which lie in the allowed region can solve the solar neutrino problem. An important conclusion of this analysis is that in order to solve the solar neutrino problem the value of A2i must be equal to or smaller than 10~4eV2, at least in the two generation analysis. If this is the case laboratory observation of A21 through the v -» v oscillations seems fj. e impossible. The three generation treatment of the solar neutrino problem is quite involved. The precession picture presented above is impractical for three generations for one cannot draw three orthogonal vectors in the three dimensional space when two orthogonal vectors are 180° apart instead of 90°. This means a higher dimensional picture. This loses the attractiveness of our picture. Direct diagonalization of the 3x3 mass matrix is another alternative. Although the process is physically non-transparent, the diagonalization is actually possible. There have been a number of attempts 3>2 to make some sense out of the three generation analysis. According to Ref.(23), there is no difference between the two- and three-generation cases if d± is no larger than ~ 20°. However, as can be seen in Fig(8), the part of the contours beyond 01=2O° shows a rapid upshifting (from the two generation curve) behaviour as 0Z gets larger, i.e. when there is substantial mixing of the third neutrino with the first two. In essence what would have been line contours in the two generation treatment (doubly solid curve) smears into broad bands towards larger Qt values, when 92 and A32 o are taken into account. Beyond ~30° the two generation results merely serve as the lower bounds for the allowed region in the three generation case. Presently the experimental data on the 3'C1 detector capture rate is 2.1+0.3 SNU. Assuming the adiabatic condition, the region on the @i~A21jO plane compatible with the experimental data within one standard deviation, i.e. at a 68.3% confidence level, is shown in Fig.(9). It can be seen that even at this confidence level the allowed region in the three generation case is markedly more extensive than that predicted by the two generation calculations, which is shown on the same graph together with upper bounds from previous accelerator and reactor neutrino oscillation experiments. - 102 - V. Solar and Terrestrial Connection The neutrino oscillations in the Sun, enhanced by the matter or resonant oscillations (MSW effects), provide a very attractive alternative for explaining the solar neutrino problem. This explanation is quite natural for a wide range of mixing angles. In fact the effect becomes more prominent for small mixing ingles. Whether the MSW effect is indeed the correct answer to ths solar neutrino problem or not can only be answered in future experiments. The most promising at present is the Gallium experiment based on the reaction v +71Ga -»7iGe+e~. The reaction has a threshold energy of 0.233 MeV, which enables one to detect D from the dominant pp chain. The calculated neutrino flux (without depletion) is 122 SNU compared with 5.0 SNU for the Cl experiment. The expected flux 2 is as follows 0.8~0.9 for dark matter 1/20 for neutrino decay 2(Expected)=2 " (Ga) x • 1/3 for vacuum oscillation 0.88 for adiabatic resonant oscillation k lc If the solar v depletion turns out to be due to mechanisms other than the oscil'ations, there are, of course, no restrictions on laboratory u oscillation experiments. If future Ga experiments and others continue to detect only one third of the calculated flux, as in the Cl experiment, it is likely that three generations of neutrinos mix maximally. Without models there will be no restrictions on A... The absence of confirmed oscillations in the laboratory experiments (up to E (u -» v ) < 10 2) implies, in this case, that A..(L/E) < 10"1 and the oscillation may be in the leading oscillation limit. When the resonant oscillation case is confirmed, the allowed region in the A2i-sin (29i) plot is as shown in Fig.(11). For example, the 2 z combination (A21 ^ leV , sin (291) o± 0.1) is ruled out regardless of the values of 92 and A32. This ,however, does not imply that the v -» v e v oscillation is impossible since the oscillation can occur through G2, 63 2 2 2 and A32, A31. The combination (A21 ^ 10~ eV , sin (291) ^ 0.8), on the other hand, is in the allowed region. But this is true only when 92 is reasonably large. That is. the combinations (A21 , 0t ) in Fig.(11) can explain the solar neutrino problem only when 92 and A32 are properly chosen. For example, if 92 is small, the combination (A21 ^ 10"'eV , sin (29j) — 0.8) can not explain the solar neutrino problem. - 103 - A few typical cases are listed in Table 1. In Table 1 "small" (large) angles mean that they are about 5° (30° or larger). "Yes" means that u -» u and v -* i> can be detected at a level of P = 10~2 ~ 10~3 V e P- T for (L/E) ~ (1) and the resonant oscillation can explain the solar neutrino problem, respectively. In conclusion, it is to be emphasized that the confirmation of the resonant oscillation explanation of the solar neutrino problem does not necessarily imply that observation of u -» u and v -* v oscillations in laboratory is impossible at the level of P = 10 ~ 10" . Acknowledgements The author wishes to thank J. Ingham, J. Kim, L. Mr.dansky, and W. K. Sze for discussions. The work is supported in part by the National Science Foundation. References 1) C.W.Kim and H.Nishura, Phys. Rev. D 3_, 1123 (1984). 2) See, for example, S.M.Bilenky and B.Pontecorvo, Phys. Reports 41., 225 (1978). 3) M.Kobayashi and T.Maskawa, Prog. Theor. Phys. 49_, 652 (1973). 4) V.Barger, K.Wisnant, S.Pakvasa, and R.J.N.Phillips Phys. Rev. 22D, 2718 (1980); C.W.Kim, Proceedings of the Fourth Symposium on Theoretical Physics, Sorak, Korea, Aug. 1985, edited by H.S.Song, Kyohak Yunkusa, Seoul, Korea. 5) M.Gell-Mann, P.Ramond, and R.Slansky, in Supergravity, Proceedings of the Stony Brook Workshop, edited by P. van Nieuwenhuizen and D.Z.Freeman (North Holland, Amsterdam, 1979); T.Yanagida, in Proceedings of the Workshop en the Baryon Number of the Universe and Unified Theories, Tsukuba, Japan, 1979, edited by O.Sawada and A.Sugamoto (KEK, Tsukuba, 1979). 6) L.Wolfenstein, Phys. Rev. 18D, 958 (1978). 7) H.Fritzsch, Phys. Lett. 73J3, 317 (1978). 8) See, for example, 6); A.Bottino, C.W.Kim, H.Nishiura, and W.K.Sze, Phys. Rev. 34D, 862 (1986). 9) H.Georgi and D.V.Nanopolous, Nucl. Phys. B155, 521 (1979). 10) N.Ushida, et al, Phys. Rev. Lett. 5_7, 2897 (1986). 11) J.N.Bachall, et al, Rev of Mod Phys. 54, no. 3 (1982). 12) R.Davis, et al, Science Underground AIP Conference Proceeding # 96, AIP, N..Y. 1983. 13) L.M.Krauss, et al, Astrophys. J. 2£9, 1001 (1985). 14) J.N.Bachall,' S.V.Petcov, S.Toshev, and J.W.F.Valle, Phys Lett. B181, 369 (1986). - 104 - 15) A.Cisneros, Astrophysics and Space 10_, 87 (1971); L.B.Okun, M.B.Voloshin, and M.I.Visotski, ITEF 86-20, 86-82 (1986). 16) L.Wolfenstein, Ehys Rev. 17D, 2369 (1978), 20D, 2634 (1979). 17) S.P.Mikheyev and A. Yu. Smirnov, Nuovo Cimento 9_C, 17 (1986) 18) F.J.Botella, C.S.Lim, W.J.Marciano, BNL (86). 19) C.W.Kim, S.Nussinov, and W.K.Sze, to be published. 20) See, for example, S.Parke in Ref.(21). 21) H.A.Bethe, Phys. Rev. Lett. 56., 1305 (1986); S.P.Rosen and J.M.Gelb, Phys. Rev. 34D, 969 (1986); W.C.Haxton, Phys Rev. Lett. 52,1271 (1986); V Barger, R.J.N.Phillips, and K.Wisnant, Phys. Rev. 34JD, 980 (1986); S.J.Parke, Phys. Rev. Lett. 5_7_, 1275 (1986); S.J.Parke and T.P.Walker, FNAL Preprint Fermilab-Pub-86/107-TA, 1986; A.Dar, A.Mann, Y.Melina And D.Zajfman, Technion Preprint Technion-PH-86-bO, 1986. 22) V.Barger, K.Whisnant, S.Pakvasa, and R.J.N.Phillips, Phys.Rev D22..2718 (1980). 23) C.W.Kim and W.K.Sze, Phys. Rev. D, in press. 24) T.K.Kuo and J .Pantaleoie, Phys. Rev. Lett. 5_7, 1805 (1986); PURD-TH-86-20; A.Baklini and G.F.Giudice, IFUP-TH-29/86; S.Toshev, SOFIA 1107 (1986). Table Caption Table 1. v -» v , v -» v and resonant v oscillations for some \± e' j. r e combinations of 9. and A... "Small (large) angles" mean that they are means that v -» v and v -» v can be about 5° (30° or larger). "Yes p. e p. T -2 detected at a level of P = 10~3 10 for (L/E) = (1) and the resonant oscillation can explain the solar neutrino problem, respectively. Figure Captions Fig.(l): Allowed region in three generation A31- A2t plot for maximal mixing case. 2 Fig. (2): Allowed region in three generation A21- sin ^^) plot without constraints on 8. and A... The upper bound is I IJ common for two and three generation cases. Fig.(3): Allowed contours with realistic spread A(L/E). 2 Fig. (4): Allowed region in A-2i sin (2^) plot with constraints imposed by the Fritzsch model. Fig.(5): v oscillation by analogy with an electron spin in a - 105 - magnetic field. v precesses around no with the frequency u. in vacuum. In matter the v direction is u x j m 2 -» -» -» -• eiven by to = to. + u where u & 0 m m is the matter contribution. Fig.(6): Adiabatic rosonant oscillation of v . When u is born in e e A the solar core, Fig. (6a), \x precesses around the ii axis, whereas, when v leaves the sun, u. precesses around e the v axis as shown in Fig.(6b). Fig.(7)- Domain of values of A21 and sin (2d± ) that would solve the solar neutrino problem in two generation case. Fig.(8): 2.1 SNU contour plots for Cl detector on A2i- 9i plot with different values of A32 and 02. The adiabatic condition is assumed. Fig. (9): Allowed region on the A21- 8-L plane consistent with Cl data for three generation (shaded) and two generation (cross-hatched) cases. The adiabatic condition is assumed. - 106 - Table 1 Oscillation Resonant oscillation Parameters y e fj. T in the Sun eit B2, 93 small A ~ 10"4 eV2 No Yes Yes A A ~ e^2 32' 31 9. small 0 , 9 large Yes Yes No A21> A31> A32 =10~1 ~ leV2 large 0 , 03 ssmall Yes Yes No 10"2eV2 91' 92' 93 large A21* A32' A31 YeS Yes Yes = lO"1 ~ leV2 - 107 - )=0.0l Fig. fi) i ^ a-fjfr5"^—' ^ 10 O.E ©.* 05 $8 1.0 fa MO - 108 - (a) (b) 2 A2;o/eV fey1) (2. IO-3 (30°, 0.002) 10 ,-4 «0 10 If* 2 Generations- (25o,0.0l) 10* tf 3(f 8, (2°, I (2O°,O.OI) 1 Fig (f) IOC 20° 30° 40° 50° 0, (a) - 109 - 10 - no - BROOKHAVEN NATIONAL LABORATORY RESONANT SOLAR NEUTRINO OSCILLATION VERSUS LABORATORY NEUTRINO OSCILLATION EXPERIMENTS Chong-Sa Lim Physics Department Brookhaven National Laboratory Upton, NY 11973 ABSTRACT The interplay between resonant solar neutrino oscillations and neutrino oscillations in laboratory experiments is investigated in a 3 generation model. Due to the assumed hierarchy of neutrino masses, together with our choice of a convenient parameterization of the 3 generation mixing matrix, we can derive a simple analytic formula which reduces the solar neutrino problem to an effective 2 g^ aeration problem. The reduction makes it apparent that the allowed range of mixing and mass parameters crucially depend on whether the survival probability of solar neutrinos S satisfies S ^ 1/3 or not. The formulae for probabilities of laboratory neutrino oscillations are also greatly simplified. We argue that a combination of the observed solar neutrino depletion and data obtained from reactor experiments seems to rule out some range of neutrino masses. If a sizeable i/fi —> vt oscillation is observed at accelerators, as sugp-isted at this Workshop, it severely restricts Lhe range of 2 mixing angles. INTRODUCTION The main purpose of this talk is to clarify in the 3 generation model of leptons the inter- play between the probabilities of neutrino "matter oscillations" within the solar interior and neutrino "vacuum oscillations" on the earth, i.e., in accelerator or nuclear reactor experiments. We assume throughout this talk that the resonant enhancement of neutrino oscillations in the presence of matter, advocated by Mikheyev, Smirnov1 and Wolfenstein2 3 is the source of the depletion of solar ue flux. Define a "survival probability" 5 by S = (detected solar neutrino flux) / (prediction of solar model). (l) In contrast to the case of a 2 generation model,M,3,5,6,7 jn a realistic model with 3 gen- erations, as we will see, the survival probability 5 around 1/3 will not necessarily lead to - Ill - very small neutrino mass-squared differences (like Am2 £ 10 4eV2),5 thereby encourag- ing laboratory neutrino oscillation experiments. In the 3 generation model, we at least need to diagonalize a 3 x 3 matrix to analyze the solar neutrino problem. Furthermore, the formulas for probabilities of ua —>• t/p (a, (3 = e, /Li, r) oscillations in laboratory exper- iments, denoted by Pa-*p, are in general complicated functions of neutrino masses and generation mixing angles (including even a CP violating phase), even though the experi- mental bounds on such parameters are usually given as if there are only 2 generations.8 In our analysis, the following very reasonable hierarchical structure of mass scales will be assumed:9 2 2 2 A, Am2i < Am3i a Am32 , (2) where Am^ = m,2 — mf [i,j — 1,2,3) with m; being the mass of V{, a mass eigenstate in the vacuum, and A = 2\f2Gp Ne k (Ne: electron density, k: neutrino momentum) is the famous "matter effect."1'2'5 The hierarchical structure in Eq. (2) will not only simplify the expressions for Pa_/3, but also will enable us to derive a very simple analytic formula, which reduces the solar neutrino problem in 3 generation model to the one in "effective" 2 generation system for arbitrary mixing angles. In this way, existing results in the 2 generation model obtained by sophisticated procedures6'7 can be utilized to analyze the solar neutrino problem in the 3 generation model. We also propose to take advantage of using a parametrization of generation mixing matrix; 10 weak eigenstates ua (a = e, n, r) are related to i/j by va = VQ,^, where C1C3 S1C3 lS 16 V = I -sic2 — ciS2Sse c\c% — siszsse S2C3 | (3) S -C1S2 — SiC2S3elS C2C3 and c,- = cosdj, st- = sin^- (i -— 1,2,3). The reasons why this parametrization is so well suited for our discussion are two-fold; (i) among matrix elements of V, only Vei (i = 1,2,3) 11 12 are responsible for the parameter S. ' This is because only ue —> i/e is relevant for S 13 and the matter effects proportional to A are invariant under any u^ *-*• uT U(2) rotations. 2 2 (ii) Eq. (3) is most convenient to describe Pa-+p. In particular, when Am2i This talk is based upon the work with W.J. Marciano. The details including the argument on the possible generalization to higher generation models, will be reported elsewhere.14 The solar neutrino problem in the 3 generation model has also been discussed by C.W. Kim in this Workshop (see also Refs. 11 and 12), relying mainly on numerical computations. - 112 - SOLAR NEUTRINO PROBLEM First, let us focus our attention on the solar neutrino problem. The key idea here is to consider the (time) evolution of vacuum mass eigenstates i/,-. Note that the relevant "Hamiltonian" matrix, which governs the evolution, is dominated by the (3,3) matrix 2 element Am3i /2fc. Let us emphasize that this statement is true for arbitrary mixing angles, as long as (2) is maintained, since we are working in the base of U{, instead of ua. Thus, the 1/3 state turns out to be decoupled from the remaining two states, linear combinations of v\ and f2. Namely, when Pe_»e is averaged over the detection points and integrated over the neutrino energy spectrum, it yields a relation14 4 4 S = cos 03 • Seff + sin 63, (4) where the second term on the r.h.s. is nothing but the contribution of a "decoupled" 1/3, and the factor cos4 #3 reflects the incompleteness of unitarity in the subspace of V\ and ^2) ie-) Hi=i 2 l^eil2 = cos2 ^3- ^eff is defined as a survival probability in the effective 2 generation system, whose (tune) evolution is governed by ^\ 2 2 77(2) _ J_ Meff - Am2i cos20i Am21 sin20 2 4k \ Am2i sin20i -AeS 2 where Asg = cos 03 • A. Thus, the possible contours in (Am2i", 0i) space can be trans- lated from known 2 generation results. The net effects of the 3rd generation's presence are re-scalings of parameters, S —>• Seg and A —> AeQ. For adiabatic solutions, the change 2 2 2 2 A —* j4e(f is equivalent to Am2i —»• Ameff = Am2i /cos 03, and the contour in a 2 gen- 6 1 eration model, ' corresponding to Ses (not S itself), can be immediately re-interpreted as the contour in the plane of (Ame/, 0i). As for the non-adiabatic case, such a re- interpretation is pot so easy, in general. Howevar, if we assume Ne To get a rough idea, in Figs. 1 and 2 we have shown the iso-5 (survival probability) contours, in 2 generation6 and 3 generation models, respectively. For illustrative purposes, 5 has been calculated for fixed neutrino momentum k and we have taken sin2 03 = 1/3 in Fig. 2. We learn from these figures that a plausible value of 5 around 1/3 has quite different consequences in two kinds of models. Namely, in the 3 generation model the order 2 2 of magnitude of Am2i is very sensitive to S; if S < 1/3, Am2i £ 2/3 • 2y/2kGpNc, where the factor 2/3 is due to the re-scaling of adiabatic solution and Nc is the electron 2 density at the center of the sum, while 5^1/3 allows a solution with large Am2i . This should be compared to the result in the 2 generation model, where S « 1/3 always requires very small Am2.5'6'7 Such a qualitative difference of results in the two kinds of models just reflects the fact that a "large" mass-squared difference means the irrelevance of matter effect and is possible only if vacuum oscillation is by itself capable of explaining - 113 - > O.I - CVJ E 0.01 - 0.001 0.01 0.1 sin 20 Fig. 1: The iso-5 (survival probability) contour plot in the (Am2/2y/2kGpNc, sin 20) plane derived in Ref. 6 (we have added a contour for S = 0.5), in the 2 generation model. NQ is the electron number density at the center of sun, and we have assumed an exponential density distribution, Ne oc exp (—x/Rs), with GpRsNc = 1.7 x 103. the depression of solar neutrino flux. Let us remember that vacuum oscillation implies S > 1/Ng (Ng: the number of generations). To be more quantitative, we take 2.1 SNU15 as the detected solar neutrino flux for 37Cl experiment, and take two typical predictions of solar models: (i)16 S = 2.1/5.9 > 1/3 and (ii)17 S = 2.1/7.5 < l/c. We also rely on the sophisticated procedure by Parke and Walker7 to get possible contours. In accordance with the above argument, we find 2 4 2 2 that in case (ii) we have an upper bound: Am2i £> 1 • 10~ cos 6% eV (5ef ^ 0.39 from Eq. (4)), while in case (i), 5eff can exceed 1/2 (Seff ^ 0.55), and Am2/ can be arbitrarily large provided B\ and Oz satisfy S = 2.1/5.9 = cos4 63 (cos4 $i + sin4 #i) + sin4 #3, which is nothing but the relation describing vacuum oscillations and gives 0.89 ^ sin2 d\, 0.21 ^ 2 sin 203 £ 0.46. - 114 - L. 13 W CVI E 0.01 0.001 0.01 sin 20, Fig. 2: The iso-S contour plot in the (Am2//2\/2kGpNc, sin20i) plane in the 3 gen- eration model. We have taken the same value for GpRsNc as in Fig. 1, and for simplicity sin2 #3 has been fixed to be 1/3. LABORATORY NEUTRINO OSCILLATION EXPERIMENTS (A=0) Now let us turn to a discussion of neutrino oscillations in accelerator or reactor experi- ments. From our study of the solar neutrino problem we have learned that the magnitude of Am2i2 crucially depends on the values of S (and #3). So we will consider two possible scenarios: (a) Am2i2 We will first discuss case (a), which is required in the scenario (ii) solution to the solar neutrino problem. Since v\ and v 2 sin (6) and our parametrization simplifies the expressions, e.g., 2 2 2 2 /Am31 = sin 02 sin 203 sin (7a) - 115 - 2 4 2 = sin 202 cos $3 sin (^jf^*) , (76) 2 2 Pe_e =1 - sin 203sin (^^-x) , (7c) where x is the distance from the neutrino source to the detector. Since only Am3i2 is responsible for the oscillations, ua can oscillate only through their couplings to v%. Therefore, these probabilities behave very differently from corresponding 2 generation results, although Eq. (7) mimics the form of 2 generation results. In fact, in the "2 generation limit", which is realized when Q% and 63 are very small, we find P,«-+e is greatly suppressed; 2 PM_>e c* sin 03 • PM_>T. (8) For illustrative purposes, we take values suggested by quark generation mixings, sin 02 =* 7 0.05, sin 03 o± 0.01, which yield for averaged probabilities Pft-*e — 5 • 10~ and Pp-+T — 3 5 • 10~ . The result implies the relative importance of v^ —> vr experiment. Although the oscillation probabilities in Eq. (7) depend only on 02 and 03, scenario (a) has no immediate contradiction with all existing experimental upper bounds.8 In fact, if Am3i2 is sufficiently small (say £ O.leV2) the bounds on 02 and £3 are not very restrictive. We should also note that bounds on (Am3i2, 02, 03) derived from laboratory experiments will be consistent with the observed solar neutrino depletion, as long as sin4 03 < S is satisfied. Once 03 is fixed, e.g., by reactor vt —»> ve experiments (see (7.c)), an observed S will be easily translated to Seg through (4), which in turn determines the contour in 2 (Am2i , 0i) space. But, whether Seg > 1/2 or not, there always exists a solution with small ( Next, we will study another scenario (b), which can happen only if S ^ 1/3 (as in the case (i)) for some range of 03. In this case the same phenomenon as in solar neutrino oscillation occurs; after the oscillatory terms associated with Am3i2 are averaged (ATO312 "> 1 eV2), the contribution of 1/3 decouples from those of the remaining two neutrinos, i.e., ) ^ (9) 3=1,2 \ ) In particular, the probability of ue —* vt has exactly the same expression as Eq. (4), 4 4 Pe_>e = co3 03Peff + sin 03, (10) where Peff is the probability in an effective 2 generation system, (11) The other oscillation probabilities are rather complicated functions of all angles, including even 6, and Am2i2, e.g., - 116 - 2 2 2 2 2 PM_e = (sin 20J [cos 02 cos 03 - - sin 02 sin 203] + - sin 40i sin 202 cos 03 sin 203 cos 6) sin2 (———x) + - sin 20X sin 202 cos 03 sin 203 sin 6 sin(———i) 2 2 +-sin 02sin 203. (12) It is easily understood that in the "2 generation limit", v^ —»• fe just reproduces the 2 generation result and is the dominant oscillation, in contrast to case (a); iV-r < P^e - (1/2) • sin2 20i. (13) The reason is simply because in this limit ue, u^ sector and uT are almost disconnected. However, this scenario seems to be ruled out, or at least very nearly so, once information from both the solar neutrino depletion and data from reactor ue —>• Qe experiments are taken into account. In scenario (b), since A Finally, let us ask what are the implications of the reported possible excess of i/e events in 20 21 21 the Up -> ue experiments BNL E816 and E776. We will take the suggested values Am2 ~ 0.5eV and sin 20 ~ 0.05, given in the 2 generation assumption. From our formula (7a) we find Am3i2 ~ 0.5eV2 and 2 2 sin 02 sin 203 c* 0.05. (15) Since Am3i2 has been fixed, upper bounds on other processes impose additional con- straints through (7b) and (7c); 2 4 Vp.-^Vr: sin 202 cos 03 < 0.3 Ref. (8), 2 vt -»i/e : sin 203 < 0.1 Ref. (19), (16) which have a consequence, consistent with sin4 63 < S < 0.37, 2 2 0.92 £ sin 02, 0.013 £ sin 93 £ 0.014. (17) We realize that the allowed range is not so wide and is very sensitive to P^ri therefore a dedicated u^ ->• vT experiment will be very desirable to settle the situation. - 117 - SUMMARY We learned that assumed neutrino mass hierarchy Eq. (2), and our choice of parametrization of the mixing matrix Eq. (3) greatly help our qualitative under- standing concerning both the solar neutrino problem and neutrino oscillations in laboratory experiments in the framework of the 3 generation model. Thanks to these key ingredients, the following points were revealed. (i) The solar neutrino problem in the 3 generation model actually reduces to the problem in an "effective" 2 generation system. As a result, possible contours in a (Am2i2, #i) plane is quite easily derived from the existing results in the 2 generation model. (ii) The allowed range of parameters, especially Arn^i2, consistent with the solar neu- trino depletion, crucially depends on whether S ^ 1/3 or not (and also on #3), as is seen in Fig. 2. Thus the settlement of the solar model predictions looks like a very urgent issue. (iii) As for neutrino oscillations at laboratories, Pa_>/j behave very differently in the two possible scenarios examined: (a) Am2i2 (iv) As a matter of fact, scenario (b) appears to be ruled out, once information from the solar neutrino depletion and reactor experiments are combined. (v) The possible excess of ue events, reported in this Workshop, is compatible with all upper bounds from r.ther types of oscillations (so far). However, it was argued that the allowed range is very restricted and is very sensitive to the bound on Pfj..^T- Thus, a dedicated u^ —* vT experiment looks very warranted and is strongly motivated. Finally, our arguments based on two key ingredients Eqs. (2) and (3) can be easily generalized to higher generation models.14 ACKNOWLEDGMENTS I would like to thank W.J. Marciano for the collaboration on which this talk is based, and for improving my manuscript. Work supported under contract DE-AC02-76CH00016 with the U.S. Department of Energy. REFERENCES 1. S.P. Mikheyev and A.Yu. Smirnov, Nuovo Cimento 9C, 17 (1986). 2. L. Wolfenstein, Phys. Rev. D17, 2369 (1978), and D20, 2634 (1979). - 118 - 3. For the review on the present status of solar neutrino puzzle and on neutrino oscilla- tions in the laboratory experiments, see: W.J. Marciano, these Proceedings. For the argument on alternative explanations of solar neutrino depletion, see also Ref. 4. 4. E.W. Beier et al., UPR-0140E, to be published in the Proceedings of the 1986 Summer Study on the Physics of the SSC, Snowmass, Colorado, June 1986. 5. H.A. Bethe, Phys. Rev. Lett. 56, 1305 (1986); S.P. Rosen and J.M. Gelb, Phys. Rev. D34, 969 (1986); V. Barger, R.J.N. Phillips and K. Whisnant, Phys. Rev. D34, 980 (1986). 6. S.J. Parke, Phys. Rev. Lett. 57, 1275 (1986). 7. S.J. Parke and T.P. Walker, Phys. Rev. Lett. 57, 2322 (1986). 8. K. Kldnknecht, Comments Nucl. Part. Phys. 16, 267 (1986). 9. The relation Am2i2 - 119 - - BROOKHAVEN NATIONAL LABORATORY MATTER OSCILLATIONS: NEUTRINO TRANSFORMATION AND REGENERATION IN THE EARTH A.J. Baltz and J. Weneser Physics Department Brookhaven National Laboratory, Upton, NY 11973 ABSTRACT Transformation and regeneration phenomena are calculated to result from transmission through the Earth of neutrinos with E (MeV)/Am2 (eV)2 in the vicinity of 106 to 107. As a result, large time-of-night and seasonal variations are predicted for various solar neutrino experiments in this parameter range. Analagous effects are predicted for terrestrial cosmic ray and accelerator experiments. 1. Introduction The existence of resonant matter-induced neutrino oscillations as a possible resolution of the "solar neutrino puzzle" was originally understood by Mikheyev and Smirnov.1 That is, the effect of the solar medium on neutrinos emitted in the sun's central region may well provide the basis for understanding the unexpectedly low counting rate observed in the BNL37 CI experiment.2 Such an explanation implies a number of characteristic effects that are open to test in other experiments and would serve as clear confirmations of what we will call the MSW (Mikheyev-Smirnov-Wolfenstein) effect. But as we haT/e shown3 there is an analogous effect brought on by the neutrinos' passage through the Earth which also would lead to characteristic effects open to experimental test. In this paper we examine the effect of the Earth's matter on the transformation of neu- trinos from one species to another. As will be seen, the effects are dramatically large for some regions of the ratio of neutrino energy to the neutrino mass difference squared. In the appropriate parameter range such transmission phenomena translate for solar neu- trinos into time-of-night and time-of-year effects that would be observable in real-time experiments. Depending on time resolution and statistics, such effects could appear as well in radio-chemical experiments. Furthermore, our calculations show large effects for neutrinos created at the surface of the Earth and passing through it. - 121 - 10 E/Am* Fig. 1: A recalculation of the Mikheyev-Smirnov solution for the probability that an electron neutrino created in the central solar region will avoid an oscillation transformation and will survive as an electron neutrino in its transit through the solar medium and space to the Earth. Three values of the mixing pa- rameter sin 20 are shown: medium dashes, 0.1; short dashes, 0.2, solid line, 0.4. We begin our presentation in Section 2 with a discussion of the Mikheyev-Smirnov- Wolfenstein effect in the sun and in the Earth In Section 3 we discusB the results of the BNL 37C1 experiment in terms of the constraints put on the neutrino mass and mix- ing angle by it. Seasonal and day-night effects will be considered. Predictions for the MSW effect in the 71Ga solar neutrino experiment are made, including a discussion of its complementarity to the 37G1 experiment and the utility of seasonal and day-night ef- fects. The related phenomenon of matter induced neutrino oscillations in the Earth for accelerator and cosmic ray neutrinos is then treated in Section 4. Next, in Section 5, the proposed detection of spectra of solar neutrinos in a real-time facility such as the Sudbury heavy water detector is investigated with a detailed calculation of the predicted matter effects of the Earth. Finally, in Section 6, some general remarks are made about the effect of the Earth on neutrino oscillations. - 122 - 2. The MSW Effect in the Sun and in the Earth The necessary formalism can be taken directly from Wolfenstein4; we shall here consider only two neutrino mixing. Then, the general state, a mixture of the two-neutrino species, We) and Wx)> is described by the transmission equation (Ce\ = l dtdt{Cx ) (2.1) are The physical combinations \ue), \vx) understood to be the combinations of the mass eigen-states \v\) and |i/2): \ue) =cosO\vi) + s'm6\v2) \Vx) = -sin«|i/i> + cos%2)- (2.2) The transmission equation is governed by the energy differences (for the same momenta) between the two mass components and by the interaction between the electron-neutrino, \ue), and the electrons of the medium, y/2Gne—an interaction not available to the other neutrino species. G is the Fermi coupling constant and rce is the number of electrons per cubic centimeter. The large mixing effects, the basis of the MSW phenomenon, occur at or near the degen- eracy that occurs when the neutrino-electron interaction balances out the mass effects. This equality between the diagonal elements, cos 20 = -y/2Gne. (2.3) requires m2 > m\, which we shall assume to be the case; in familiar units, this optimuum mixing condition is: E(MeV) 7xlO6 „. . , . \, L w —f 1 ^r— cos 20, 2.4) 2 2 3 Am (ev ) p (gm/cm ) ye where p is the density of the matter and ye is the number of electrons per AMU. Since the 5 density of the earth varies from ~ 3 at the surface to ~ 13 at the center and ye ~ 1/2, neutrinos for which E/Am2 lies in the region ~ 106 to ~ 107 should show interesting effects. For the effects on solar neutrinos the fundamental equations must be solved in both the sun and in the Earth. As we have 3hown,3 a narrow energy averaging in detected neutrinos on the Earth is sufficient to justify dropping rapidly oscillating terms related to the Earth-sun separation distance. Figure 1 contains a recalculation of that originally - 123 - y 10 , \v\W--- I iq io IO'IO" io° i (a) Fig. 2: Contours for the 37C1 experiment labeled by SNU values (see text). given by Mikheyev and Smirnov.1 It turns out that for these experimental conditions the calculation of the MSW effect in the sun, such as in Figure 1, may be accurately carried out using the adiabatic and Landau-Zener approximations.6 However for transmission through the Earth, numerical solution of the fundamental Eq. (2.1) appears to be the most satisfactory way to get trustworthy results. The form of the first order coupled differential equations for probabilities as written by Mikheyev and Smirnov,1 are solved using the Bashforth-Adams-Milne predictor-corrector method.7 The physically interesting initial conditions at the surface of the earth differ, however, from those usually considered; instead of limiting the discussion to the familiar one in which the initial neutrino state is pure \ue), two different initial mixtures are included in order to accomodate studies of solar neutrinos, which via their oscillation in transit through the solar medium and in space, arrive in a spectrum of mixtures. One obtains3 an expression for the probability PSE that an electron neutrino emitted within the sun remains an electron neutrino after passing through the sun and through the earth PSE = 1 + 2PSPE1 -Ps~PE1- = (2PS - l) {2PE2 - l) tan26. (2.5) In this expression Ps is the energy averaged (over a part in 100) solution in the sun (Figure 1), PEl is the probability that an electron neutrino emitted at the surface of the earth and passing through it remains an electron neutrino, and PE7, is the probability of finding an electron neutrino after transmission that begins at the Earth's surface with the - 124 - 10 io" r 10 10" vt sin (20)/cos(20) Fig. 3: Night minus day contours for the 37C1 experiment labeled by SNU values (see text). Shaded out is the region consistent with the existing experimental result of 2.1 ± .3 SNU. boundary condition of equal parts of both species of neutrinos and real relative phases. 6 is of course the mixing angle. It is important to note that the oscillation phase must not be averaged for the Earth transmission solutions. Both P^x and PE% aie functions of the trajectory from entry to detector. 3. 37C1 Results and the 71Ga Experiment Since the data in the 37C1 experiment was taken night and day over a number of years, effects of the Earth would affect the count rate only in an average way in the region of the parameters Am2 and sin 20 where an Earth effect occurs. Figure 2a shows contour lines of the expected detected neutrinos by the 37C1 experiment as a function of these parameters. Standard solar model values8 have been used for sources of neutrinos consistent with a predicted flux of 5.8 SNU in the 37C1 experiment. The effect of the Earth has been included in the calculation of the contours by averaging over day and night and seasonal changes for a year. For comparison Figure 2b displays the contours of equal numbers of counts (in SNU) without the effect of the Earth. If one interprets the 37C1 result of 2.1 SNU as due to a reduction from the expected 5.8 SNU because of matter oscillations, then it is evident that the set of points on the plot that are consistent with the experimental result is affected by the proper inclusion of the averaged effect of the Earth. The so called third solution, the near-vertical portion of the contour on the right of the plot, corresponds to - 125 - 10 10 10 10 10 10 10 10'lCf 10"" 10* 10"' 10" 10' sii\ (20)/cos(20) sill (20)/cos(20) (a) Fig. 4: Contours for the 71Ga experiment labeled by SNU values (see text). a large mixing angle, sin 20 of .95, without the effect of the Earth. On the other hand, the average effect of the Earth distorts the contour to sin 20 under .8. For possible development purposes it is also of use to investigate the day-night difference in the number of counts expected in the 37C1 experiment. For simplicity we will present here the results for that part of the year when day and night are approximately equal in length, the six months closest to the two equinoxes. Night and day are each taken to be twelve hours. Figure 3 shows the difference between the number of counts seen at night and the number seen during the daytime. Superimposed is the band corresponding to the solutions valid for the existing data (Figure 2a). For only a small region of the parameter space consistent with the existing data would the taking of data separately night and day show a detectable effect. The predicted response of the 71Ga detector is different from 37C1 mainly because of the lower energy neutrino threshold of the former. This allows 71Ga to detect the neutrinos from the basic p-p burning process in the sun that are inaccessible to 37C1. Figures 4a and 4b show the contours of equal SNUs expected night and day respectively in the 71Ga experiment. The superimposed band of the values consistent with the 37C1 experiment indicates that an experimental result of anywhere from near zero to near the full solar model prediction of about 120 SNUs would still be consistent. - 126 - 10 - ' ""'I 10 1Q" 10"' 10" 10 sin (20)/cos(20) Fig. 5: Night minus day contours for the yiGa experiment labeled by SNU values (see text). The region consistent with the existing 37C1 experimental result of 2.1 ± .3 SNU is shown as shaded. If early results from the 71 Ga experiment show a low number of counts relative to the solar model prediction, then the night-day differences might well be worth measuring. Figure 5 shows the predicted difference in number of counts between night and day for 71Ga. The difference is sizeable where the 71Ga response would be low. Therefore, if the number of counts turns out low, then the observation of a night-day difference (or lack of it) might further constrain the possible values of Am2 and sin 20. In particular, for Am2 of about lO^^and sin 20 greater than about .3, a difference of 20 to 40 SNUs between night and day is predicted. The practical difficulty that stands in the way of such a night-day difference experiment is that presented by background and statistics, which, at low counting rates, would make a meaningful result unlikely with the present arrangements. In short, it seems that the night-day effect could be important for the 71Ga experiment, but only if the counts are low relative to the solar model predictions. However, if the counts are close to the full solar model prediction, indicating a parameter range with little MSW effect in the sun, there can be little MSW effect in the Earth and thus no night-day effect would be expected for the 71Ga experiment. - 127 - 4. Accelerator and Cosmic Ray Neutrinos One of the ingredients of our Equation (2.5) for PS£, the probability that a solar neutrino remains an electron neutrino after passing through the sun and through the Earth, is the probability PEI that an electron neutrino emitted at the surface of the Earth will remain an electron neutrino after passing through it. This is, of course, the physical situation that obtains for a neutrino created at the surface of the Earth either by an accelerator or by a cosmic ray event which then passes through a portion of the Earth to be detected at the far surface. It turns out that for the two-neutrino mixing case, by symmetry, PEI is equally valid as the solution for the probability that a muon neutrino, for example, created at the surface of the Earth will remain a mucn neutrino and not change into an electron neutrino after passing through it. This situation seems experimentally more feasible than the converse. lCf E/Am* Fig. 6a: Probability of a muon neutrino turning into an electron neutrino after passing into the Earth and emerging at a detector 1000km surface distance from the source, sin 20 = .4. The solid line represents the effect of the Earth and the dashed line the replacement of the Earth's matter by vacuum. - 128 - E/Am' E/Am Fig. 6b,c: Same as 6a for a detector 8000km (b,top) and 15000km (c,bottom) surface distance from the source. - 129 - 345 4 3 Fig. 7: Principal density zones of the Earth marked together with the densities (in gm/cm3) at the beginning and ends of these zones. Trajectories through the Earth followed by a solar neutrino to reach a detector located at 43° north latitude at various times of the night at the winter and summer solstices and the spring-fall equinoxes, are also shown. Figures 6a,b,c show the results of calculations for the probability that a muon neutrino will change into an electron neutrino after passing through the Earth. The mixing angle sin 20 was chosen to be .4. Fig. 6a is a calculation for a chord which corresponds to a surface distance of 1000 km around the Earth (i.e. roughly the distance from BNL to the Sudbury detector). Matter oscillations are just beginning to differ significantly from the vacuum solution for the same distance. At shorter distances the matter oscillation solution approaches the vacuum solution. However, at 8000 km around the Earth, seen in Fig. 6b, the efFect of matter is dramatic for E (Mev)/Am2 (ev)2 in the vicinity of 3 x 106. The distance can be further tuned to obtain complete transformation in this region. In contrast to these trajectories which only involve the mantle of the Earth we show in Fig 6c the results of putting a detector 15000 km around the earth where neutrinos would - 130 - go through both mantle and core. The discontinuity at the mantle-core interface (Figure 7) results in the peculiar pattern of oscillations seen in Fig. 6c. Thus matter effects can be quite large for accelerator neutrinos passing through a sufficient length of the Earth. However the number of counts obtained in any conceivable experiment at 1000 km or more is not encouraging (as is pointed out by M. Murtagh in these proceedings). 25.0 20.0- 15.0 CM 6 <3 10.0- 0.0 0.0 0.1 0.2 03 04 05 06 0.7 0.8 0.9 1.0 sin(20) Fig, 8: Probability that muon neutrinos would change into electron neutrinos after passing through the Earth. An average of all events entering the detector from 30° or more below the Earth's horizon is taken. In this illustration the neutrino flux is taken as independent of angle. LoSecco9 has estimated that it is possible to put a rough limit on the value of sin 20 from the lack of up-down asymmetry in already existing data from the Kamiokande experiment. - 131 - 10 10' 10 1Q 10"" 10' 10" 1Q"4 10" 10° 101 siri (20)/cos(20) sin(20)/cos(20) Fig. 9: Number of events per kilotonne year to be detected by the Sudbury heavy water detector as a function of Am2 and sin 20. The daytime rate is on the left and the spring or fall nighttime rate is on the right. We have calculated the fraction of electron neutrinos expected to be detected from events that started as muon neutrinos at the surface of the earth as a function of the mixing angle and mass-energy parameter. Figure 8 shows a contour plot of that fraction for all neutrinos coming from 30° or more below the Earth's horizon (one fourth of the total solid angle). There are two regions where the transformation is large. For large mixing angles (sin 20 greater than about .7) and Am2/E large enough there is a broad region of transformation due partially to the vacuum mixing. But there is an additional island of large transformation at Am2/E of about 3.5 x 10~7 largely due to the Earth's matter. If the detector is sensitive to neutrino energy of about 300 Mev, then for Am2 of about 1CT4 and sin 20 between .25 and ,6, more than half of the muon neutrinos from this lower direction will change to electron neutrinos. In contrast, all the muon neutrinos produced above will travel a relatively short length and presumably remain muon neutrinos. This calculation shows the usefullness of the up-down asymmetry in constraining the neutrino mass and mixing angle in a limited range of these parameters. - 132 - 10" l'cr* i'o"3 lb ib sin (20)/cos(20) Fig. 10: As in Fig 9, but only the high energy daytime events. 5. Detection of Neutrino Spectra: the Sudbury H©avy-Water Detector A large heavy-water Cerenkov detector has been proposed10 that would be sensitive to the solar 8B electron neutrino flux, spectrum, and direction. In addition, the detector might also measure the8 B neutrino flux independent of flavor. We have investigated the effects of the Earth on the expected number of counts for the electron neutrino part of the experiment. The product of the neutrino spectrum and the detector response has been taken from the Sudbury write-up.10 Figure 9 shows the daytime and nighttime number of expected counts as a function of Am2 and sin 20. With a threshold of 5 MeV, the detector will be sensitive only to 8B neutrinos from the sun. Thus the shape of the contours is similar to that for the 37C1 detector, except that the contour for 37C1 (Fig. 2) shows a small bump at Am2 of lO-^indicating the onset of an outward shift of the diagonal contours at lower Am2 corresponding to the contribution of neutrinos between the .81 MeV threshold and 5 MeV. A crucial advantage of the Sudbury experiment is that it is designed to detect the energy of the neutrinos to 15% at 10 MeV and their direction to 25°. This makes possible the determination of distortion of spectrum shape, which is characteristic of an MSW effect. - 133 - 10- 10 10 1Q" 10" sin (20)/cos(20) Fig. 11: Ratio of high energy events to total events seen in the daytime at the Sudbury heavy water detector. Figure 10 shows the expected number of daytime counts for E > 9 MeV. Not only is the number of counts reduced but also the contour shapes are shifted relative to the fuller (E > 5 MeV) spectrum inclusion. Figure 11 exhibits this spectrum distortion effect as the ratio of E > 9 MsV ev-nts (from Fig 10) to E > 5 MeV events (from Fig 9a). Determining such a ratio experimentally might provide a constraint on allowable values of Am2 and sin 26. Of course, since this is a real time experiment, one could use the difference between nighttime and daytime counts (such as is seen in Figure 9) to obtain information on Am and sin 26. In fact a real time experiment allows one to tag events by time of night and date, thus identifying a trajectory length with each event. This would allow the events to be binned most efficiently for isolating effects of the Earth in terms of length of matter traversed rather than some time-of-day or season of year variable which involves an average over a number of trajectories. 6. Conclusions calculations have shown that for values of the two-neutrino mixing angle sin 29 > .1 there is a large transformation effect induced by passage through the Earth. This - 134 - transformation from one species to the other (either ux to ve or vice versa) occurs in the E/Am2 range of about 1 — 7 x 106. Depending on Am2, this transformation effect could turn out to provide a spectacular determination of the neutrino mass and mixing parameters. With different solar neutrino, cosmic ray neutrino, and accelerator neutrino experiments probing different ranges of neutrino energy, one can hope to eventually hit on the sensitive E/Am2 range for transformation in the Earth. ACKNOWLEDGMENT This work was supported by contract number DE-AC02-76CH00016 with the U. S. De- partment of Energy. REFERENCES 1. S.P. Mikheev and A.Yu. Smirnov, Sov. J. Nucl. Phys. 42, 913 (1985)(Eng. Trans.); H.A. Bethe, Phys. Rev. Lett.56, 1305 (1986); S.P. Rosen and J.M. Gelb, Phys. Rev.D34, 969 (1986). 2. J.K. Rowley, B.T. Cleveland, R. Davis, Jr., Conf. Solar Neutrinos and Neutrino Astronomy, Homestake, SD (1984); Am. Inst. Phys. Conf. Proc. 126, 1 (1985). 3. A. J. Baltz and J. Weneser, Phys. Rev.D35. 528 (1987); E.D. Carlson, Phys. Rev.D34, 1454 (1986); J. Bouchez, M. Cribier, W. Hampel, J. Rich, M. Spiro, and D. Vignaud, Z. Phys C 32, 499 (1986). 4. L. Wolfenstein, Phys. Rev.Dl7, 2369 (1978). 5. F.D. Stacy, Physics of the Earth (2nd Ed.), John Wiley & sons, p.171; J.-C. De Bremaecker, Geophysics: The Earth's Interior, John Wiley & Sons, p. 63 (1985). 6. Stephen J. Parke, Phys. Rev. Lett.57, 1275 (1986); Stephen J. Parke and Terry P. Walker, Phys, Rev. Lett.57, 2322 (1986); W. C. Haxton, Phys. Rev. Lett.57, 1271 (1986). 7. J. Mathews and R.L. Walker, Mathematical Methods of Physics, Benjamin, p. 336, () 8. J.N. Bahcall, B.T. Cleveland, R. Davis Jr., and J. K. Rowley, Astrophys. J. 292, L79 (1985). 9. J.M. LoSecco, Phys. Rev. Lett.57, 652 (1986). 10. G. Aardsma et al. (The Sudbury Neutrino Observatory Collaboration), to be pub- lished. - 135 - -- Beams and Detectors DESIGN AND STATUS OF THE AGS BOOSTER ACCELERATOR* E. B. Forsyth Brookhaven National Laboratory^ Associated Universities, Inc. Upton, New York 11973 INTRODUCTION A booster accelerator for the AGS was originally proposed in 1983 as an accu- mulator for polarized protons and shortly after as a means of also increasing the AGS proton intensity.* It was later proposed to also design it for use as a pre-accelerator for heavy ions from the Tandem Van de Graaff so that all ions up to Au (mass 197) could be fully stripped and accelerated in the AGS.^ Without the Booster the maximum mass that can be directly injected into the AGS is sulfur (mass 32).^ The Booster is thus an essential component in the chain which will permit the AGS to act as a heavy ion injector into the pro- posed Relativistic Heavy Ion Collider (RHIC). The diverse requirements for the Booster impose many difficult constraints and compromises on the design. Prior to the start of construction in November, 1985, a preliminary design had emerged for a fast-cycling machine with a circumference one-quarter of the AGS using a separated function FODO lattice.^ DESIGN REQUIREMENT After construction started in late 1985 design groups were formed in several areas to address detailed problems. A panel of international experts review- ed the design in March 1986; their report focused on both problems of detail and the general concept of the accelerator. Further examination of the Booster design at Brookhaven resulted in the publication of a Design Manual in the summer of 1986. This manual is intended to bridge the transition from conceptual to engineering design. Comments on some areas of the design con- sidered in the period leading to the Design Manual are given below. Lattice: Some consideration was given to a choice of one-third rather than one-quarter the AGS circumference. This would have given the options of higher energy, longer straight sections, higher tune and reduced ramping rate. In the end this option was dropped, mainly due to the higher construc- tion cost. Meanwhile, detailed investigation continued on the one-quarter AGS design; chromatic correction was refined0 and such topics as space charge * Supported by the U.S. Department of Energy. tOperated by Associated Universities, Inc., Under Contract to the U.S. De- partment of iiergy. - 139 - limit7, resonances and instabilities^'9, and aperture limitations10 were con- sidered. The structure resonance at the vertical and horizontal tunes of 4.5 was the subject of particular attention as this is the major stopband which will be crossed due to tune depression caused by space charge. The correc- tion system is being designed to minimize the driving term for this res- onance.^1 Other lattices were considered using both separated function and combined function magnets. The latter magnets, possibly used in a hybrid lattice i.e., separate quadrupoles are also used with gradient dipoles, pro- vide longer straight sections - an important engineering consideration for a small accelerator. A summary of some lattice options considered is given in Table 1. Energy and Repetition Rate: An important concern of the review committee was that the 1 GeV injection into the AG5 for protons envisioned in the prelimi- nary design may not provide a sufficient improvement in AGS intensity due to space charge limitations in the larger machine. The factor By was raised by a factor of nearly two by increasing the nominal energy for proton ejection to 1.5 GeV. This was achieved by keeping the same mean rate of change of flux in the magnets and thus decreasing the repetition rate from 10 Hz to 7.5 Hz. The flow of real and imaginary power to and from the main power supply was studied in detail in order to determine the voltage and phase flicker on the feeder to the laboratory. The main dipole power supply has a maximum rating of 13 MVA. Voltage fluctuations on the 69 kV feeder will be below 0.25% and phase flicker will not exceed 0.72° in the proton acceleration mode. Injection: Three methods of injection must be provided for the various spe- cies to be accelerated in the Booster.11 The proposed method of proton injec- tion was investigated in detail because the preliminary design required that the injection beam pipe pass through the return leg of a dipole yoke. In ad- dition the equilibrium orbit perturbation at injection raised the possibility of aperture limitation both vertically and horizontally due to strong cou- pling. The possibility of reducing some of these problems by using an injec- tion region with four fast kicker magnets, similar to that used in SNS1 , was a major motivation in considering lattice choices with longer straight sec- tions. In the end tracking studies indicated that aperture limitation was not severe during injection and the cost and complexity of four kickers greatly outweighed the perceived problems of the preliminary design. The de- sign of the beam injection and ejection transfer lines has reached an advanced stage.^ Radio Frequency System: The design of the RF system is complicated by the need for a wide frequency swing for heavy ion acceleration and effects of beam loading during proton acceleration. Initially, the heavy ion accelera- tion system will be designed for a harmonic number of three and will use two cavity/amplifier combinations to cover the required frequency range, one will cover the low frequency end and the other the high frequency portion of the range. The general characteristics are shown in Table 2. At a later date it will be possible to replace one cavity and amplifier in order to operate with a harmonic number of unity; this option may be necessary to increase the par- - 140 - tides per bunch required when the AGS is serving as an injector into RHIC. A considerable design effort has gone into the conceptual design of the ac- celeration system for protons. In particular, a compromise must be found be- tween the ramp rate, bucket size and maximum RF voltage. The system that evolved maintains a minimum bucket size of 1.0 eV sec (plus safety factor) and uses two cavities simultaneously. With some light-ion species the same cavities may also need to complete acceleration to the specified maximum en- ergy. The details of the system are given in Table 2. Vacuum Chamber: The vacuum system requirements are set by heavy ion accele- ration - changes in the charge state caused by collision with residual gas molecules will cause a loss of accelerated particles. A goal of 3 x 10~^ torr has been set for the maximum pressure^, to achieve this level will re- quire a method of baking each component to 200°C in situ. The vacuum chamber crosssection in the dipole magnets is roughly oval, the sextupole moment of the magnetic field caused by the eddy currents during the maximum ramping rate (proton acceleration) has a magnitude roughly comparable to the natural chromaticity and must be corrected. The random component of the sextupole field caused by variations in the vacuum chamber has been investigated and tolerances set on the chamber dimensions. PRESENT STATUS During the period fiscal years 1986 and 1987 approximately 15% of the esti- mated total construction cost of ^ $29 M was received. This funding profile has, of course, influenced the technical progress. Instead of building the tunnel and conventional civil engineering support facilities, emphasis has been placed on completing detailed design. Three dipole magnet prototypes have been tested ^ and the yoke laminations ordered. R&D is proceeding on the vacuum chamber design and the RF cavities. A start has been made on the conceptual design of the computer control system. It is expected that the Title II phase of conventional construction will be completed by the summer of 1987 and a start can be made on the tunnel in the fall of 1987. A new 20 MVA transformer is on order to upgrade one of the main laboratory substations in anticipation of the increased electrical load of the Booster. A summary of the present design parameters is given in Table 3. ACKNOWLEDGEMENT The design of the Booster is due to contributions from many members of the AGS and Accelerator Development Departments at Brookhaven. - 141 - REFERENCES 1. L. W. Smith, (Editor) "Accumulator Booster Proposal for the AGS," BNL Informal Proposal 32949, 1983. 2. Y. Y. Lee, and L. W. Smith, "Accumulator Booster for the AGS as a Heavy Ion Booster," Private Communication. 3. D. S. Barton, "Heavy Ion Program at BNL: AGS, RHIC," Proc. 1987 Parti- cle Accelerator Conference, Washington, D.C., March, 1987. 4. "Conceptual Design of the Relativistic Heavy Ion Collider," BNL Pub. No. 51932, 1986. 5. Y. Y. Lee, "The AGS Improvement Program," IEEE Trans. Nuc. Sci., Vol. NS-32, No. 5, 1607, 1985. 6. Y. Y. Lee, E. D. Courant, et al "AGS-Booster Lattice," Proc. 1987 Par- ticle Accelerator Conference, Washington, D.C., March, 1987. 7. G. Parzen, "Space Charge Limit in the AGS Booster," Proc. 1987 Parti- cle Accelerator Conference, Washington, D.C., March, 1987. 8. Z. Parsa, "Chromatic Perturbation and Resonance Analysis for the AGS Booster," Proc. 1987 Particle Accelerator Conference, Washington, D.C., March, 1987. 9. S. Y. Lee, and X. F. Zhao, "The Coherent Microwave Instability in AGS and AGS Booster," Proc. 1987 Particle Accelerator Conference, Washing- ton, D.C, March, 1987. 10. Z. Parsa, "Beam Aperture and Emittance Growth in the AGS-Booster," Proc. 1987 Particle Accelerator Conference, Washington, D.C., March, 1987. 11. Y. Y. Lee, "Injection and Accumulation Schemes for the AGS Booster," Proc. 1987 Particle Accelerator Conference, Washington, D.C., March, 1987. 12. G. H. Rees, "Status of the SNS," IEEE Trans. Nuc.Sci., Vol. NS-30, No. 4, 3044, 1983. 13. R. C. Gupta, S. Y. Lee, Y. Y. Lee, and X. F. Zhao, "Beam Transfer Lines for the AGS Booster," Proc. 1987 Particle Accelerator Conference, Wash- ington, D.C., March, 1987. 14. G. Young, (ORNL) Private Communication. 15. G. Danby, J. Jackson, Y. Y. Lee, R. Philips, J. Brodowski, E. Jablon- ski, G. Keohane, B. McDowell, and E. Roger, "AGS Booster Prototype Mag- nets," Proc. 1987 Particle Accelerator Conference, Washington, D.C., March, 1987. - 142 - Table 1 Some Lattice Options Considered for the AGS Booster Systematic No. of Approx. Phase Stopbands Dipole General Super Tune Adv Per Order Length Type Periods Qx, Qy Cell (deg) 2 3 4 m Comment Separated 6 4.8 72 3,6,9 4,6,8 4 •> 6 2.4 Standard lattice in the fn design manual. Separated 8 6.8 102 4,8 5,3,8 4,6,8 2,7 High periodicity, high fn tune and longer straight sections. Disadvantage is high quadrupole gradient. Combined 12 4.8 72 6,12 4,8 3,6 2.9 An attractive design but fn judged to have some problems as a polarized proton accumulator. Table 2 Booster RF Systems Species: P P 5 *4 Au 33 RF Amplitude Injection 90 kV 7.35 kV 0.61 kV 1.6 kV Ejection 90 kV 40 kV 17 kV 17 kV Harmonic Number 3 3 3 3 RF Frequency Injection 2.5 MHz 2.5 MHz 0.446 MHz 0.206 MHz E/A 200 MeV 200 MeV 4.69 MeV 1.07 MeV Ejection 4.11 MHz 4.11 MHz 4.13 MHz 3.06 MHz Phase Space Area/A 21-0 eV-s 0.3 eV-s 0.066 eV-s 0.066 eV-s Intensity It)" 3 x 1011 5 x 109 8 x 109 (per bunch) Total Gap Impedance <24 kfi - - - (frf = 4.1 MHz ) Accelerator Time 62 ms _<0.5 s <0.5 s <_ 0.5 s Maximum Power 156 kW - - - Delivered to Beam Maximum B 9.5 T/s - Binj 1.5 T/s <0.15 T/s <0.15 T/s - 143 - Table 3 Summary of Booster Characteristics Circumference 201.78 m (1/4 AGS) Avg. radius 32.114 m Magnetic bend radius 13.75099 m No. of particles/pulse protons, 1.5 - 3 x 1013 polarized protons, 10^ C S I Au 54 15 6.6 3.2 x 109 ions L.ititice type separated function, FODO No. of superperiods o No. of cells 24 Betatron tune, x, y 4.82, 4.83 Number of magnets 36 dipoles, 48 quady Magnet type iron-dominated, tfater-cooled Cu conductor nipo1j2 length (magnetic/physical) 2.4/2.34 m, excl. coils Quad length (magnetic/physical) 0.50375/0.472 m, excl. coils Vacuun chanber, dimensions 70 x 152 mm, dipoles 152 mm (circular), quads time 62 ms, protons & polarized protons 500 ms (max.) heavy ions Repetition rate 7.5 Hz (4 pulses/AGS pulse), protons 1 Hz (t pulse/AGS pulse), polarized protons 1 Hz (1 pulse/AOS pulse), heavy ions - 144 - FOCUSSING HORN UPGRADES* A. S. Carroll Brookhaven National Laboratory Associated Universities, Inc. Upton, New York 11973 I see that I gave myself the somewhat overly ambitious title of "Focus- sing Horn Upgrades!" A more more accurate heading might have been "Present Status and Suggestions for Possible Upgrades." As you have just beard from Eric Forsyth, the AGS Booster will enable us to gam up to a factor of * or 3 in proton flux. However, since neutrino experiments are interested in neu trino flux rather than just protons on target, improvements in the focussing of pions could also lead improvements in experimental sensitivity. An overall view of the neutrino area is shown in Fig. 1 with the horns, decay space, shielding and detectors. Since the neutrino beam was originally designed for the 7 foot Bubble Chamber and other close in experiments, the decay space was kept relatively short to keep the solid angle of the detectors large For long baseline experiments such as Exp. 776, the neutrino flux increases nearly linearly with the decay length until a majority of the pions have decayed. For the present horn systems the decay space was lengthened from ~50 m to ~ 75 m corresponding to 36% decays for 3GeV/c pions. TARGETu HORNS DECAY REGION Fig. 1 AGS Neutrino Area with horns in present positions with 75m decay space before the iron shield. The detector shown is in the Exp. 734 block house. Figure 2 shows a schematic of the Broad Band Horn system - an assembly about 10 meters long.1 The purpose of this system is to produce, and then form a parallel beam of as many pions as possible in the momentum band from 1 to about lOGeV/c. The target is an integral portion of the first horn. Sur- rounding the target are 300kA pulsed 300kA currents which provide 6T fields to * Work performed under the auspices of the U.S. Dept. of Energy. - 145 - TRAJECTORY \ X>9 Fig. 2. Schematic of Broad Band Horn System. Arrows in the horns show the path of the pulsed current. to trap the pions leaving the tar- get. The horn shape downstream of the target produces a field integral along the particle trajectory roughly proportional to the particle production angle. This configura- tion gives a reasonable approxima- tion to a lens. The dotted lines in Fig. 2 gives the trajectory of a focussed pion. The large diameter second horn recaptures the pions and then bends them into a nearly paral- lel beam pointed down the tunnel. The beam spectrum for the present broad band beam is shown in Fig. 3 as calculated by Exp. 734. Fig. 3. Calculation of the Up flux for the Broad Band Horn System at the Exp. 734 detector with the 75m r decay space. For more details see 2 4 6 Ref. 2. Horn current is 285 kA. ENERGY. GeV - 146 - The Narrow Band Horn System, shown in Fig. 4, uses the same basic struc- ture, but three sets of collimators and beam plugs are used to define the al- lowed pion trajectories and hence the pion momentum. In order to produce good optical images at the defining collimators, a short, high density target is placed before the first horn, outside of the magnetic field. Such a horn sys- tem was originally designed by Baltay3 for 9 GeV/c pions and then redesigned bv Exp. 776 for 3 GeV/c pions and larger angular acceptance(140 mrad). Fig. 4. Schematic of the Narrow Band Horns used for Exp. 776. The dashed lines show typical pion trajectories. What is the short term status of the horns? The Narrow Band Horns used for Exp. 776 and the Broad Band Horns used for Exps. 734 and 816 are both in existence, but they both need repairs to insure their reliability during the next neutrino run. The present horn power supply has beer* in existence for 15 years with components dating back before then. We would like to take the power supply out of its wooden shack on top of the berm and place it in a more accessible structure at ground level. A new charging supply for the capacitor bank has been purchased, and we would like to redesign the modules with in- creased capacitance. Experience has shown that if the peak current is achieved with more capacitance and less voltage, greater reliability is likely. What kind of upgrades can we expect? Over the past few years we have been engaged in a rather unspectacular sort of upgrade—namely improving the reliability. Experimenters are interested in the integral number of neu- trinos. A 10% increase in the peak flux does no good if it is accompanied by a 50% increase in downtime. Because of the large pulsed currents, horns are subject to long term failure due to fatigue. Parts which can survive 101* pulses, may not survive 2 x 106. Since the horns are located in a very high radiation environment, the penalty for failure in radiation exposure and lost time is very high. With experience, we have achieved a high standard of reliability as shown in Fig. 5. In this plot of the number of protons on target vs. time is given for a two month period in Spring of 1986. - 147 - 3 0 ____.... While reliability is tremendously importa.it, it isn't much fun. What sort of technical advancements can be made to increase the neutrino flux? Here I will only be making suggestions and hints, not concrete plans. The Broad Band Hern system as originally designed by Bob Palmer5 is a pretty nearly optimized device. Hywel White, and to a lesser extent, I have looked at the Broad Band Horn, and not found any obvious ways to Fig. 5. Accumulation of protons on target make substantial improvements. during Broad Band v run during the spring The ingredients seem to be of 1986. The occasional short pauses are for AGS maintenance and repair. about right. There is a long (2 interaction lengths), relatively low Z (titanium) production target to maximize pion production in the forward forward direc- tion. Surrounding the target is a strong magnetic field to do the initial particle collection. I did a simple computer calculation in which I replaced the present horn with a perfect achromatic lens - that is, a lens which made all of the pions leaving the target into a parallel beam. Such an ideal device, produces 2.7 times the neutrino flux as the present horn. However, building lenses which are achromatic over a momentum range from 1 to 10 GeV/c is a v=ry difficult task. It may be that an improved device could be based on the ideas being tried in antiproton accumulators. The parts would be current carrying or current surrounded production targets followed by a lithium lens, and then a large horn to make the pions parallel. Unlike antiproton accumula- tion, there is no need to make the phase space particularly small. The diver- gence only needs to be smaller than the neutrino decay angles, and the size less than the 3^m diameter decay tunnel. Pion absorption in the material of the horns is 20%, and could only be reduced significantly at the risk of structural failure. Adding a third horn to reduce chromatic aberrations is yet another possibility. Narrow Band Horns seem like they present more room for improvement. The measured rates by Exps. 734 and 776 for the Narrow Band Horn is about a factor of 20 down on the Broad Band Horn. If one uses a ±15% momentum bite for the Narrow Band Horn, then the expected ratio is about 7. The Narrow Band Horn operates at the peak of the pion production spectrum, and the optics of the Narrow Band Horn should be cleaner than the focussing of the spectrum of the Broad Band Horns. Without having done the detailed calculations, it seems that a major portion of the loss must come from having to define the trajectories with the 0 beam plugs. A suggestion for stimulating thought would be to replace th« present Narrow Band Horns with a pair of Broad Band Horns with a dipole - 148 - in between two horns. The proton beam in this arrangement would not point at the detector, thus reducing the broad band background. The advantages of the Broad Band Horn for small angle production would be retained, and there would be the possibility for tuning the momentum and momentum bite more easily. A very rough schematic of such a arrangement is shown in Fig. 6. DIPOLE HORN #1 DIPOLE HORN #2 PROTON Ji PION BEAM Fig. 6. Schematic of possible Narrow Band System using horns and a dipole. The design of focussing horns at BNL has always had a lot of assistance from experimenters using neutrinos. We welcome that assistance at any time! CONCLUSIONS 1. Present Horn Systems can be made operational with some repair. The horn power supply will be rebuilt to provide improved operations. The reli- ability is expected to remain high, leading to an average of 0.5 x 1018 protons on target per day at present AGS intensities. 2. Theoretically, the neutrino intensity from the Broad Band Horn could be increased at factors of 2.7 times by replacing it with a perfect achroma- tic lens. These improvements would be difficult, but steps toward this goal might be a current carrying target followed by a lithium lens. 3. There is probably more room for improvement in the Narrow Band System, and their design should seriously be reconsidered before rebuilding them. 4. Suggestions and offers of assistance cheerfully received. ACKNOWLEDGMENTS Many members of the AGS Department made important contributions to the design, construction, installations and operation of these focussing horns. The members of the Beam and Physics Support Group under the leadership of W. Sims, R. Monaghan, G. Ryan, J. Sandberg, G. Smith, and P. Stillman were the primary builders and operators of the horns and associated power supplies. C. Pearson and A. Pendzick directed the Experimental Areas Group in the con- struction of the block house, installation of the beam transport and many other items. J. Walker and the design room provided a number of innovative designs in a short time. W. Leonhardt supervised all aspects of the thermal management system. Members of Exp. 776 provided the specifications for the conductor and collimator in the Narrow Band Horns. The physicists of Exp. 734 furnished many helpful suggestions for improving its Broad Band Horns. References 1. For a more detailed description see, A. Carroll, et al. "Overview of Recent Focussing Horns for the BNL Neutrino Program," Proceedings of the IEEE Particle Accelerator Conference, March 1987 (to be published) and references therein. 2. L.A. Ahrens, et al., Phys. Rev. D34, 75 (1986). 3. C. Baltay et al., Phys. Rev. Letter 44, 916 (1980). 4. A. Carroll et al., "Large Acceptance Magnetic Focussing Horns for a High Intensity Narrow Band Neutrino Beam at the AGS," Particle Accelerator Conference, 1985. Proc, In-IEEE Transactions on Nuclear Science Vol. NS-32 (1985). 5. R.B. Palmer in Proceedings of Informal Conference on Experimental Neutrino Physics, Ed., C. Franzinetti, CERN, Geneva, p. 141 (1965). - 150 - Neutrino Flux Calculations for the AGS Narrow Band Beam C. Chi, N. Kondakis, W. Lee, B. Rubin, R. Seto, C. Stoughton, G. Tzanakos Physics Department, Columbia University E. O'Brien, T. O'Halloran, K. Reardon, S. Salman Physics Department, University of Illinois B. Blumenfeld, L. Chichura, C.Y. Chien, J. Krizmanic, E. Lincke, W. Lyle, L. Lueking, L. Madansky, A. Pevsner Department of Physics and Astronomy, The Johns Hopkins University (Presented by N. Kondakis) Abstract We present results of calculations of v fluxes in the AGS neutrino beam with the new dichromatic horn. The wide band beam v , as v/ell as the y backgrounds, are discussed. The u fv ratio is about 8 x 10~3. The possible sources and magnitudes of uncertainties are discussed. Finally, the calculated fluxes are compared with beam measureiuents. - 151 - 1. The Beam line To produce the Narrow Band Beam (NBB), the 28 GeV proton beam is transported through the AGS U-line, and focused down to 2 mm before impacting on a 5-mrn diameter, 12 cm- long copper target. The secondary particles produced in the target pass through a magnetic horn system (Fig. 1), which uses two magnetic horns, and a series of collimators and beam dumps for focusing and momentum selection. The total length of the horn system is about 10 meters. The focused charged particle beam is allowed to decay over a distance of 80 meters in the decay tunnel. A 30-m steel beam dump (muon shield), at the downstream end of the decay tunnel, is used to absorb all particles except, Fig. 1. Schematic of the Narrow of course, the neutrinos. Band Horn eyetem. Two segmented ionization chambers (pion monitors) were placed at 40 m and 60 m downstream from the end of the dichromatic horn system. The role of these detectors was to measure and monitor the charged beam profiles and fluxes. 2. Flux Calculations All neutrino fluxes discussed below are assumed for a distance of 1 km from the target, along the beam line, where the E7 7 6 detector is located. At this distance, the detector subtends about 2.5 mrads. The calculation was done with a Monte Carlo program that rimulates the particle - 152 - production in the target, the transport through the focusing system, and the subsequent decays. a. Particle production. The Monte Carlo program generated particles in the target according to the production model of Sanford and Wang1. This model gives the pion, kaon, and antiproton production from semiempirical formulae obtained by fitting the experimental particle production data in p - Be collisions between 10 and 35 GeV/c. The model dependency of the calculation has been estimated by repeating the calculation, assuming a different production model, namely that of Grote, Hagedorn, and Ranft2, which uses particle production data in tabular form. b. Transport and decay. Each particle is transported through the beam elements (Fig. 1), and is allowed to decay along its path. The daughter particles from each decay are also transported until the decay chain is exhausted. All charged particles are allowed to undergo multiple Coulomb scattering and absorption, while they traverse the walls of the magnetic horns. The chain of transport-decay is terminated when a particle encounters a collimator, a beam dump, or the tunnel walls. Reinteraction in the target or the horn walls was not taken into account. Instead, a single exponential was used to account for the secondary beam loss due to interactions in the materials of the beam elements. We are currently in the process of implementing particle interaction, energy loss, and decays, inside the various materials. c. Results. The angular divergence of the focused charged particle beam in the decay tunnel is about 4 mrad. The momentum is 3 GeV/c at a horn current of 240 kA (3.5 GeV/c at 280 kA) with a momentum bite of 15 % . At these energies, about 30 % of the focused pions and almost all kaons decay before they reach the beam dump. The ratio of muon to pion decay is about 0.3 %. Table I shows the dominant sources of neutrinos and antineutrinos. The ir decay and the K decays constitute the primary sources of - 153 - the rauon neutrino dichromatic beam. A small fraction ( few percent) of WBB 1/ and f background is expected from Tablo I. Dominant v, v sources. pion and kaon decays occurring before momentum selection, while the muon decay and the Products various K decays are responsible for the u background. V The resulting NBB v V energy spectrum, calculated at a distance L = 1 km from •V,". the neutrino source, is plotted in Fig. 2. The contributions from pion and kaon decays are shown separately. The spectrum K" * it" e" V peaks at about 1.3 GeV at m K° * JT" e* v a horn current of 240 kA L « K? -» X* o" 7/ (1.5 GeV at 280 kA) with an energy spread a£/E = 15 %. The other component of the dichromatic beam (originating from the K decays) peaks at 3 GeV (3.5 GeV at 230 kA). The ratio of the v fluxes from kaons and pio'ns is Muon "Flu *Fo r ' ' 2B0 ••••(•• • • 1 • ...... about 0.04, as expected IOB r A ' TOTAL ». • from the K+/7r+ production f \ — ratio and the kinematics. 1 Note that Fig. 2 includes 1 also the WBB background ID* contribution. 10' The v background 10° . . . . 1 . . . , 1 . energy spectra due to the 4 E,IGtVI four most dominant contributions are shown in Fig. 2. Calculated v energy spectrum. It includes both NBB Fig. 3, along with the and W3B contributions. - 154 - total v energy spectrum. It is clearly shown that the main contribution below 2.5 GeV comes from muon decay, whereas Electron v Flux For I - 280 K+ decays are responsible torn », above 2.5 GeV. The v and VQ fluxes, integrated over the entire energy spectrum for a horn current of 280 KA, (expressed in f's/1012 POT/m2 at L = 1 km), are shown in Table II. The i v . .-.-1-. . . . I resulting vJv ratio is E, !G«VI 3 calculated to be 7.8 x 10" at Fig. 3. Calculated energy spectra for E =1.5 GeV (280 KA), and the main sources of v background. 8.3 x 10"3 at 1.3 GeV (240 KA). 3. Flux uncertainties Several assumptions were made in the beam calculations: (i) The various particles were not allowed to interact or range out in the beam Table II. Integrated v and v fluxes, dumps. We do not know 12 2 in fs/10 POT/m , at L - 1 km. at this moment exactly the error (especially v-tlavor Reaccion Flux in the u /v ratio) 1.21 X 108 introduced by this k+ - t/l^ 4.35 X 104 assumption. (ii) The Total 1.26 X 108 nuclear interactions in V / • eV^ 5.73 X 103 the materials and the a target were 1.42 x 10Z 3 approximated by a e 3.21 X 10 K° -* n~e*i> 8.25 X 102 single exponential. We o 3 estimate that they Total 9.91 X 10 can introduce an uncertainty as large as +30% to 40 %, depending on tne effective absorption length used. - 155 - (iii) in order to estimate the uncertainty from production we have compared the yields Production oF n' at 3° from several production 1 • 1 • • ' ' 1 models: n-Rnnft MODIFIED \ o Grots-Heaedof n-R6nFt __ - a. Sanford-Wang (SW) model, SenFord-Uonq ho - o - which was discussed previously. 8 X x L b. Grote-Hagedorn-Ranft (GHR). - 0 X The graphs in the atlas of X Lfrn particle spectra by Grote, 2 •....! , . . . 1 Hagedorn and Ranft are used 5 ID «' ttomintun (G»V/e) to obtain the GHR values for the secondary particle Fig. 4. ** momentum spectra at B - 3° production. c. A version of according to various production models. the GHR model (GHRW), modified to accomodate the proton reinteraction process in a "thick" target, which was used to fit the observed neutrino energy spectrum in the BNL WBB data3, was also used for comparison. A comparison between the momentum spectra for the three models, for ir+ at 0 =3°, is shown in Fig. 4. We are currently in the process of investigating the effects of the target size and the interaction of the beam in the horn plugs on the particle fluxes.( The latter effect was measured and _ , , , _ Tabla III. Integrated production, in particles was found to account for per interacting proton, for various modela. less than 5 % of the total Particle SW GHR GHRW charged particle flux.) + Table III shows the values * 1.17 1.22 1.54 of the integrated iC .895 .867 1.11 production for the three models. The integration is K* .135 .123 .153 performed over a wide K" .033 .044 .057 range of momenta (0-17 GeV/c) and production angles( 0 - 300 mrad). The difference in the absolute flux ranges from 30% to 40% (GHR over SW). Table IV shows the integrated production for the range of momenta - 156 - and production angles accepted by the horn system. The relative difference between Table IV. Integrated production (particles the SW model and the GHR per interacting proton) over the momentum models in the high momentum and angle range of horn acceptance for various ir.odelB. range is twice as large as the difference in the whole Particle SW GHR GHRW momentum range. This affects + directly the ratio of high * .213 .203 .294 energy to low energy u .161 .156 .218 fluxes. Indeed, the energy K+ spectrum calculated with the .022 .018 .025 GHR model appears to have K~ .007 .009 .012 about 30 % higher flux above .056 2.5 Gev than the one P - - calculated with the SW model. Thus, the uncertainty from production, estimated from the comparison of the various existing models, can be as high as +30 %. Finally, the statistical uncertainty is estimated to be less than ±10 %. In summary, the absolute v flux is estimated to carry an uncertainty between +80%,-10%, the vJv ratio between +30%.-30%, and the muon neutrino ratio v^/v^ between +20%, -20%. These uncertainties are given here as possible upper limits for the quoted values and have no real statistical meaning. However, when we take into account the flux measurements with the pion monitors, we believe that we can narrow down these uncertainties, as we shall discuss in section 4. We are in the process of recalculating the v and v fluxes for both the narrow and the wide band beams. These calculations take into account (i) target effects, (ii) secondary particle production coming from interactions with the materials in the beam (horn walls, collimators, plugs, tunnel walls), and possible subsequent decays, and (iii) additional decay modes which contribute to both the NBB signal and WBB background. - 157 - 4. Comparison with measurements In order to check the calculations against measured quantities we performed the following tests: (i) We used the pion monitors to measure Table V. Calculated and measured charged the radial profiles and particle intensities (particles/1012 POT) absolute fluxes of charged in the pion monitors. particles in the decay Pion Calculated Observed tunnel, and (ii) we used Monitor intensity intenoity the calculated u spectra 1 1.3 x 1010 1.7 x 1010 to generate Monte Carlo 2 1.7 x 1O10 2.3 x 1010 events in the detector according to known cross 1/2 0.77 0.74 sections. We then analysed these events in the same way as the data collected with the detector4. From this analysis we produced the v energy spectra and the neutrino rates for both the data and the Monte Carlo events. From the comparison of the measurements with the calculations we can draw the following conclusions: (i) The absolute charged particle flux, measured in the beam tunnel (see Table V), •as well as the measured neutrino rate at the E77 6 detector, normalized to the number of protons on target(POT), are systematically higher from the calculated ones by about 30%. Fig. 5. Measured and calculated charged particle flux profiles in the beam tunnel. (ii) If we normalize the - 158 - calculated charged particle flux to the measured flux in the beam tunnel, then, with this normalization, the charged beam flux profiles measured with the pion monitors are in reasonable agreement with the calculated ones as shown in Fig. 5. With the same normalization the measured neutrino rates are consistent with the Monte Carlo. (iii) As discussed in ref. 4, the measured u energy spectrum, normalized to the Monte Carlo below 2 GeV, has the expected shape; it peaks at 1.3 GeV for a horn current of 240 kA and it has a width of 23% (rms) consistent with the intrinsic beam width of 15% (rms) and the detector energy- resolution. The measured spectrum tail above 2 GeV has about two times as many events as predicted with the Monte Carlo. The question of additional contributions to the WBB background is under investigation as a more sophisticated beam flux calculation is on the way. This work was supported by NSF Grants PHY86-10898, and PHY86-19556, and by the U. S. Department of Energy, under contract DE-AC02-76ERO1195. References 1. J.R. Sanford and C.L. Wang, "Empirical Formulas for Particle Production in p-Be Collisions between 10 and 35 BeV/c". AGS internal report, BNL # JRS/CLW-1, March 1, 1967. -BNL report No. 11479, 1967, (unpublished). J.R. Sanford and C.L. Wang, "Empirical Formulas for Particle Production in p-Be Collisions between 10 and 35 BeV/c" (PART II). AGS internal report, BNL # JR8/CLW- 2, May 1, 1967. BNL report No. 11479, 1967, (unpublished). 2. H. Grote, R. Hagedorn and J. Ranft, Atlas of Particle Production Spectra, CERN report, 1970 (unpublished) 3. L.A. Ahrens et al., "Determination of the Neutrino Fluxes in the Brookhaven Wide-Band Beams", Phys. Rev. D34, 75 (1986), and H.D. White, private communication. 4. G. Tzanakos, contribution to these Proceedings. -159- The Liquid Argon Time Projection Chamber* Gerhard Biihler Department of Physics, University of California, Irvine, CA 92717 1 Introduction Time projection chambers (TPC) with liquid sensitive media are consid- ered to be promising tools for future neutrino experiments[l,2,3j. In the first part of this presentation the potentials of liquid TPC's are briefly sum- marized with emphasis given to the liquid argon chamber. The progress in developing a 104 kg (10 ton) device at University of California at Irvine and the current status of the project are outlined in the second part. 2 Potentials of liquid TPC's The tracks of ionizing particles within the sensitive TPC medium are read out by drifting the electric charge in a homogeneous electric field into a readout region where the signal is detected and transferred to the analyz- ing electronical components 2,3 . In addition, a magnetic field can be used 1 Supported by the US Department of Energy under contract No. DE AT03-76SF00010; talk presented at the BNL Neutrino Workshop, February 5-7, 1987, Brookhaven National Laboratory. Upton. NY 11973 - 161 - for improving particle identification. Thus, liquid TPC's provide a number of potential advantages compared to other detectors for neutrino physics. In contrast to sandwich type detectors the volume of a TPC is almost com- pletely sensitive, i.e. the sensitive medium is also the interaction medium for the primary radiation. A TPC is a direct counting device and yields information on the range, energy and energy loss of an ionizing particle and, therefore, enables particle identification. Given the two dimensional projection of the track on the readout region and the drift time information, a reconstruction of the three dimensional track pattern is easily possible[4j ("electronic bubble chamber"). Liquid TPC's are dense and—depending on the construction of the readout region—allow pattern reconstruction with fine granularity. Recently, it has been shown that the excellent scin- tillation properties of liquid noble materials (Ar, Kr, Xe) together with a controlled doping with hydrocarbons (e.g. TMA, TEA, allene) provides the possibility of building combined ionisation-scintillation detectors with im- proved energy resolution!5,6,7,8,9,10]. Scintillation light in the liquid TPC medium can also be used as a trigger signal. Some limitations, however, apply to the operaton of a liquid TPC. The low electron drift velocity in the sensitive media makes the TPC a low rate detector (~103 s"1) and the potentially long signal rise times in the detector require long integration times of the analyzing electronics. This makes the electronics sensitive to acoustical noise. In addition, there is virtually no charge multiplication in liquids and the charge recombination is significant. This leads to very small signal on the order of magnitude of fC cm"1 and requires sensitive and low noise readout electronics. If the medium is contaminated with impurities a substanitial fraction of electrons may be lost due to attachment. Consequently, the high purity requirements (< 1 ppb O2) require efficient purification systems for the detector. 3 Liquid argon TPC's In principal, there are quite a few media from which a liquid TPC can be constructed. The actual choice will be determined by the physical effects under investigation, the cost per mass, and the operational requirements of the detector. Research work on liquid TPC's so far has focused primarily - 162 - on the liquid noble elements argon, krypton and xenon, the hydrocarbons methane and tetramethylsilane (TMS) and various other components as dopants. Almost all of these materials have to be operated under cryogenic conditions due to their low boiling point. TMS is an interesting exception because it has a boiling point of 300 K which relaxes some of the opera- tional requirements of the other materials. Hydrocarbon media have the advantage of offering virtually free protons in high energy interactions. The advantages of using liquid argon as a detector material are: • It is comparatively inexpensive (1 $/kg @ 1000 1) • It is a noble element and does not attach electrons • It is inert (operational safety) • It has a relative high density (1.4 g cm"3 at boiling point) and • It provides the capability of constructing very fine grained detectors (1 m drift @ 1 kV cm"1 gives a diffusion broadening of the track of 1 mm) Table 1 gives examples of event rates that can be expected in a high Table 1: Event rates in liquid argon per day per 105 kg of sensitive mass 6 1 Eu = 1 GeV; $ = 10 ernes' ; 100% detector efficiency o (cm2/target/GeV) N Remarks total 0.67 x 10~38 3.5 x 104 42 2 1.85 x 10" 4.3 sin Qw = 0.23) Low energy; * = 106 cm^s"1; 100% detector efficiency a (cm2/target/GeV) N Remarks 44 vee —* vte 1.8 x 10" 0.042 Emin=5 MeV, 8B spectrum 40K+e- 3.8 x 10"43 0.049 energy (1 GeV) and a low energy (8B solar neutrino spectrum) neutrino environment. The data have been calculated on the basis of a continuous flux of 106 cm"2 s"1, a sensitive detector mass of 105 kg (100 ton) and 100% detector efficiency. - 163 - 4 UCI development The capabilities and technical requirements of liquid argon TPC's have been studied at UC Irvine with 1 1 and 50 1 devices for the last 10 years'4,11,12 . Currently, we are assembling a 7000 1 chamber which will have total and sensitive masses of 104 kg and 5 • 10'' kg. respectively. An exposure at the AGS has been approved to study the capabilities of a chamber this size. So far, the effort has focused on implementing and establishing the tech- nical requirements for the operation of this detector. In particular, these are o Purification of argon to the sub-ppb level (Ov equivalent); 12,13; • Maintenance of purity over extended periods of time'12] » Long distance drifting of electrons in liquid argon;12,14,15] • Three dimensional track imagingjlG • Energy loss studies for particle identification *• Implementation of components on large scale! 12] Figure 1 shows the purification results obtained with a large scale purifica- tion system capable of handling large amounts of liquid argon. Attenuation lengths (1/e attenuation of drifting charge) and purity levels have been mea- sured by drifting electrons over distances of up to 28 cm. Limited by the sensitivity o<" our test detector, the ultimately achieved purity was <0.2 ppb which corresponds to an attenuation length of >3.7 m at 0.5 kV cm"1. The purification system has been tested extensively and provides a stable and predictable operation over a period of many weeks. In this way, the first three operational reqirements listed above are satisfied. The three dimensional track imaging and the energy loss studies have been done with cosmic ray muons and stopping protons, respectively, us- ing a 50 1 instrument[4,16j. Figure 2 shows a two dimensional projection of the track induced by an energetic muon and an associated delta elec- tron. Figure 3 shows the charge deposited by stopping protons within the detector per unit length (normalized to the charge deposited by a mini- mum ionising particle) and the energy loss of protons (normalised in the same way), versus the penetration depth in the detector. Up to a value of about seven times the charge deposited by minimum ionising particles the dQ/dx curve follows quite closely the dE/dx curve which would allow particle identification by range and energy loss measurement. Beyond this, - 164 - the effect of recombination becomes more apparent and the correlation of deposited charge and energy loss is less pronounced. These findings sup- port, the approac1- of particle identification by combined range and energy loss measurements in liquid argon. We anticipate the completion of the detector assembly and a test run with cosmic rays within this year. After that the detector will be exposed to the AGS neutrino beam. References l] W. J. Willis and Veljko Radeka. Liquid-argon ionization chambers as total-absorption detectors. Nuclear Instruments and Methods in Physics Research, 120:221-236, 1974. J2] D. Nygren. 1974 PEP Summer Study PEP-144, SLAC, 1974. \'i] Emilio Gatti, G. Padovini, L. Quartapelle, N. E. Greenlaw, and Veljko Radeka. Considerations for the design of a time projection liquid argon ionization chamber. IEEE Transactions on Nuclear Science, NS-26(2):2910-2932, April 1979. BNL-report 23988. [4] Peter J. Doe, Hans-Jiirg Mahler, and Herbert H. Chen. Observation of tracks in a two-dimensional liquid argon time projection chamber. Nuclear Instruments and Methods in Physics Research, A199:639-642, 1982. [5] Tadayoshi Doke. Recent developments of liquid xenon detectors. Nuclear Instruments and Methods in Physics Research, 196:87-96, 1982. |6j Susuniu Himi, Tetsuhiko Takahashi, Jian-zhi Ruan(Gen), and Shinzou Kubota. Liq- uid and solid argon, and nitrogen-doped liquid and solid argon scintillators. Nuclear Instruments and Methods in Physics Research, 203:153-157, 1982. |7l J. C. Berset, M. Burns, K. Geissler, G. Harigel, J. Lindsay, G. Linser, and F. Schenk. Scintillation light from liquid argon and its use in a new hybrid detector. Nuclear Instruments and Methods in Physics Research, 203:133-140, 1982. [8] D. F. Anderson. Photosensitive dopants for liquid argon. Nuclear Instruments and Methods in Physics Research, A242:254-258, 1986. [9| D. F. Anderson. New photosensitive dopants for liquid argon. Nuclear Instruments and Methods in Physics Research, A245:361-365, 1986. [10] H. J. Crawford, T. Doke, A. Hitachi, J. Kikuchi, P. J. Lindstrom, K. Masuda, S. Nagamiya, and E. Shibamura. Sum signals of ionization and scintillation for rela- tivistic La ions in liquid argon, submitted to NIM, 1986. [11] Herbert H. Chen and John F. Lathrop. Observation of ionization electrons drifting large distances in liquid argon. Nuclear Instrurnci md Methods in Physics Research, 150:585 588. 1978. - 165 - 112] Peter J. Doe, Richard C. Allen, Steven D. Biller, Gerhard Biihler, Wayne A. Johnson, and Herbert H. Chen. A large scale purification system for a liquid argon time projection chamber, submitted to NIM, 1987. [ 13] Peter J. Doe, Hans-Jurg Mahler, and Herbert H. Chen. Initial results of argon purification in the liquid state. IEEE Transactions on Nuclear Science, NS-29:354- 357, 1982. [14] Herbert H. Chen, John F. Lathrop, and John Learned. Further observation of ion- izing electrons drifting in liquid argon. IEEE Transactions on Nuclear Science, NS- 25(1):358-361, February 1978. [15] Herbert H. Chen and Peter J. Doe. ^ong distance drifting of ionization electrons in liquid argon. IEEE Transactions on Nuclear Science, NS-28(l):454-457, February 1981. [16] Hans-Jiirg Mahler, Peter J. Doe, and Herbert H. Chen. Operation of a liquid argon time projection chamber. IEEE Transactions on Nuclear Science, NS-30(l):86-89, 1983. - 166 - 1 i • i • 1 I 0.075 i 0.100 to- 0.5 kV cm' b) Rapid circulation (a) t-O- l - 0.200 - \ First contamination 100 _ 50 Q • 300'- y< 1-0 10 20 40 Figure 1: Purity and attenuation lengths achieved in 480 1 of liquid argon A. attenuation length (cm): p. oxygen equivalent impurity concentration (ppb): Pjr.-r,: fraction of argon passed through the system: a) in slow circulation (only natural heat loss) (•) and b) in rapid circulation (additional heater power of 180 W) ( : ). - 167 - 3cm Figure 2: Two dimensional track in a liquid argon TPC Figure 3: Relative charge deposited and energ\ io^ of stopping proton? in a liquid argon TPC. normalised to the charge deposited and energy loss of minimum inni-ing par'icles. versus penetration depth in the liquid argon - 168 - PHYSICS CALIBRATION OF THE SOUDAN II NUCLEON DECAY EXPERIMENT USING BNL NEUTRINOS W. Anthony Mann for the Soudan II Collaboration' Tufts University Medford, Massachusetts 02155 ABSTRACT For neutrino energies near the nucleon mass, the shape of the Ev flux spectrum from the wide-band beam at the ACS resembles the shape of flux spectrum from atmospheric neutrinos. An opportunity is thus presented to mpasure the extent to which neutrino can events mimic decaying nucleons in a proton decay search, provided that a detector representative of the underground experiment can be operated in the Brookhaven beam. This crucial calibration measurement is feasible for the Soudan II experiment, wherein a 1.1 kiloton detector is assembled out of standardized five-ton tracking calorimeter modules. Each module provides fine-grained dE/dx sampling with independent signal readout. Details concerning neutrino exposures using a cluster of these modules is presented. INTRODUCTION Although current experimental searches for nucleon decay observe event rates underground which are completely believable as interactions of atmospheric neutrinos, a few special events recorded by the higher-resolution detectors seem unlikely as neutrino reactions and are compatible with nucleon decay hypotheses. The experimentalist's dilemna is poignantly illustrated by the contained event of Fig. 1, reported by the Frejus experiment last year.1 The event has about 900 MeV total energy and residual momentum consistent with Fermi motion. It is isotropic to a degree which is unusual for neutrino interaction topologies. However, the detection medium for the Frejus tracking calorimeter is iron; hence the possibility exists that nuclear rescattering plus detector-dependent effects have altered a neutrino event topology so much that an imitation nucleon decay is obtained. The extent to which neutrino mimicry of nucleon decay is prevalent can be gauged in part via event simulations in which neutrino reactions, nuclear effects, and detector limitations are treated using Monte Carlo techniques. Although much can be done with this approach, uncertainty concerning final state propagation within parent nuclei, together with the difficulty of accounting for all detector effects, limits the degree of confidence that can be placed on results. Fortunately, there exists another approach. - 169 - Fig. 2 shows the shape of the Vy flux spectrum for the horn-focussed, wide-band neutrino bean at Bookhaven (solid curve). For neutrino energies 0.8 < Ev < 5.0 GeV, the fall-off of the accelerator vy flux provides a reasonable approximation to the flux shape calculated for atmospheric Vy's (dashed curve). Comparison of the two curves provides energy-dependent: weights which, when applied on an event-by-event basis, can be used to convert v event distributions obtained at BNL into ones appropriate for atmospheric v events. Consequently, the extent to which neutrino events imitate nucleon decays in an underground search experiment can be directly measured, provided that a representative sub-unit of the underground detector can be operated in the Brookhaven beam. Ongoing nucleon decay searches can be classified according to two designs: The experiments of Mont Blanc (NUSEX collaboration) and Frejus use iron tracking calorimeters of planar geometry; the 1MB and Kamioka experiments use water Cherenkov detectors. There is, however, a new, fine-grained iron tracking calorimeter of honeycomb geometry which is being built for the Soudan II nucleon decay experiment. The Soudan II detector concept differs from that invoked in all other proton decay searches in that it is designed modular, for the expressed purpose of inserting modules into test beams. The main detector, depicted in Fig. 3, is assembled as a two-layer stack of 256 identical modules to a total mass of 1100 metric tons. The experiment is being installed in a new cavity in Minnesota's Soudan iron mine at a depth of 2200 meters water equivalent and will begin data-taking this year. THE STANDARD MODULE Soudan's massive underground detector is built with 256 replicates of the "standard module".3 in the design of these compact, portable units, special emphasis was placed on the tracking of particles and on measuring their ionization loss. These goals are achieved by fine- grained dE/dx sampling, high spatial resolution, and three-dimensional hit reconstruction. The basic detection elements are shown in Fig. 4. These are hollow, resistive plastic (Hytrel) tubes of one meter length and 15mm inner diameter; the tubes are captured within a laminate of 125 ira Mylar. Copper conducting lines on the Mylar run perpendicular to the tubes and are held at graded voltages so that a uniform axial-drift electric field is established within each tube. As illustrated in Fig. 5, ionization electrons are produced by charged particles passing through an argon-CC>2 atmosphere in the tubes and subsequently drift in the 200 V/cm axial field towards the closer end. The maximum drift distance is 50 cm. Most of the module mass is provided by 1.6 mm thick steel sheets which are corrigated so as to hold the tubes in a hexagonal, close- packed array (Fig. 6). Additional insulating sheets of 0.5 mm thick corrugated polystyrene are placed between the steel and the Mylar. The corrigated steel sheets and the assembly of tubes, copper strips, and Mylar (called a "bandolier") are stacked up to 240 layers (2.5ra). In - 170 - doing this the bandolier is fanfolded back and forth, with the steel and polystyrene sheets being interleaved-see Fig. 7. Each completed stacV is compressed with ten tons of force to achieve a uniform module height. A steel skin is then welded around four faces of a module. The skin keeps the stack compressed and provides the gas seal on those sides. The readout planes are mounted onto the two remain open faces of the "honeycomb" stack. At each readout plane, drifting electrons are detected by an orthogonal array of 63 vertical proportional wires (anode wires) and 240 horizontal cathode strips. The anode wires are mounted on an aluminum frame. The cathodes are etched copper on G-10 with Hexcel/G-10 sandwich backing; these are also attached to the aluminum frame. Each readout plane is aligned so that the cathode pad pattern matches the ends of the drift tubes. Finally, each module is sealed via steel covers. A cutaway drawing of a complete standard module is given in Fig. 8. The entire unit weighs 5 tons. Its production cost, including electronics (but. excluding auxiliary gas system, computer, etc.), is about 25K. The spatial resolution achieved with this module design is communicated in part by Fig. 9, which shows a standard module with one endplane removed; the granularity afforded by 7560 sampling tubes of 15 mm diameter each is apparent. For charge drifting down any one of the tubes, x-y information is provided by the avalanche onto a proportional anode wire and its image on an orthogonal cathode strip. The third orthogonal coordinate, z, is obtained by a relative time measurement of the drifting charge. That is, the electronic?, which uses flash encoders, records the pulse-heights and times of hits for both anodes and cathodes. Time and pulse-height matching between anode and cathode hits gives a unique 3-dimensional coordinate for each hit. The resolutions for reconstructed hit coordinates (x, y, z) are on the order of 15 ram, 10 mm, and 5 mm respectively. The pulse height inforraation-since it is a measureof dE/dx-can be used to determine the direction of particle tracks and to provide some particle identification. In summary, the Soudan 5-ton modules constitute a dense, slow- drift, time-projection "brick". The structure is sufficiently rugged to allow full instrumented ones to be stacked, shipped by truck or cargo boat, and transported down a mine shaft. TRACK IMAGING The capability of our drift-collection calorimeter scheme to distinguish particle types was studied using exposures of a planar prototype module to low-energy electrons, muons, and pions at Argonne's IPNS facility. Incidentally, this planar prototype design (see Ref. A) may be better suited for experiments using v beams such as neutrino oscillation studies, than is the more isotropic honeycomb design which is optimized for the proton decay search. For either geometry, some representative track images from the anode-wire versus drift-time view are shown in Fig. 10. A 300 MeV/c v+ meson which ranges to stopping is - 171 - displayed in Fig. 10a. Note that the pulse-height profile of each drift region crossing is shown, as measured by a flash ADC. An ionization shower at the end of the track tags the decay v+ + e+vv; the 2.2 microsecond decay time results in an apparent displacement of the positron shower from the parent muon. The increase in ionization as the track's velocity decreases can be seen in the last few gas crossings. VJhereas muon tracks are straight except for small amounts of Coulomb scattering, pion tracks can exhibit large angle scatters as shown in Fig. 10b. Electron tracks, on the other hand, typically begin straight but evolve into a ragged pattern characteristic of electromagnetic showers (Fig. 10c). CONFIGURATION FOR NEUTRINO EXPOSURES For exposures in an accelerator neutrino beam, the calorimeter modules can be clustered to form a compact, interconnected detector, whose lateral dimensions match the beam diameter and whose total mass ensures a reasonable event rate. A possible configuration for neutrino runs at Brookhaven is shown in Fig. 11. Here, nine modules are arranged into a single-layer, 45-ton unit. The drift directions of all Hytrel tubes within the honeycomb stacks are aligned. When the orientation of the drift axis is perpendicular to the incident neutrino direction, the detector's transverse dimensions are 3 meters (width) by 2.5 meters (height); the detector extends 3 meters along the beam direction. A requirement that useful interaction vertices occur at least 20 to 30 cm inside of the detector's exterior surfaces, implies a fiducial mass of 20 tons for the nine-module cluster. Based upon the intensities presently achievable in the horn-focussed, wide-band neutrino beam at Brookhaven, a useful vv event could be recorded every ten AGS pulses (1 event every 15 seconds, with a 100% duty cycle). The electronics readout of signals from a nine-module cluster is indicated schematically in Fig. 12. Sets of three adjacent anode-wire, cathode-pad endplanes are designated by arrows in the Figure. The anodes are read out along the top of the detector; the cathodes are jumper-ed together along each wall and are read out at the detector's downstream end. Preamps for anodes (and also for cathodes) which are associated with spatially remote portions of the cluster can be bussed together in a way which minimizes ambiguities. By multiplexing the readout in this way, the number of digitization channels required to service the cluster can be halved.5 The electronics which is Deing built for the Soudan nucleon decay search is, by design, self-triggering. For neutrino calibration running, however, we would trigger the detector on each AGS pulse. The trigger logic output would only be xatched, to provide checks off-line. Sizes of neutrino event samples required for calibration of the Soudan II nucleon decay search can be scaled according to the experience of the Monte Blanc experiment.6 We conclude that a few modest-duration exposures, each having a distinct beam-detector orientation (e.g. G = 0°, 30°, 45°, 60° in Fig. 11), are needed. At least 4000 v interaction - 172 - should be recorded at each orientation. With current AGS v intensities, each exposure requires about two days of running. Thus, calibration of the Soudan nucleon decay search using BNL neutrinos is relatively easy • ^ cany out. Further calibrations using v^ and ve neutrinos can of course be contemplated for the AGS booster era. FOOTNOTES AND REFERENCES 1. The Soudan II Collaboration includes the following researchers from Argonne National Laboratory, the University of Minnesota, Oxford University, Rutherford-Appleton Laboratory, and Tufts University: W.W.M. Allison, J. Alner, I. Ambats, D. Ayres, L. Balka, G.D. Barr, L. Barrett, D. Benjamin, J. Biggs, C.B. Brooks, J.H. Cobb, D. Cockerill, H. Courant, U. Das Gupta, J. Dawson, T. Fields, R. Giles, A. Gilgrass, M.C. Goodman, K. Heller, S. Heppelmann, N. Hill, D. Jankowski, J. Kochocki, K. Johns, T. Kafka, P.J. Litchfield, W.A. Mann, M. Marshak, E. May, R. Milburn, A. Napier, W, Oliver, G.F. Pearce, D.H. Perkins, E. Peterson, L.E. Price, D. Rosen, K. Poiddick, B. Saitta, J. Schlereth, J. Schneps, P. Shield, M. Shupe, N. Sundaralingam, J. Thron, S. Werkema, N. West. 2. R. Barloutaud for the Frejus Collaboration, to be published in the Proceedings of the Seventh Workshop on Grand Dnification/ICOBAN '86, Toyama, Japan, April 1986. 3. L.E. Price, "The Soudan II Detector as a Time-Projection Calorimeter", submitted to the XXIII International Conference on High Energy Physics, July 16-23, 1986, Berkeley, California; preprint ANL-HEP-CP-86-64. 4. I. Ambats et al., "Construction and Operation of Drift-Collection Calorimeter", contributed paper to the 1984 IEEE Nuclear Science Symposium, Orlando, Florida (November 1984); ANL-HEP-CP-84-79. 5. Jonathon Thron, ANL; private communication. 6. G. Battistoni et al., Nucl. Instrum. Methods 219, 300 (1984). - 173 - FIGURE CAPTIONS f ig. 1 : Nucleon decay candidate recorded by th& Frejus experiner;: fRef. I). .r: g. 1 : loaparibon or me sr.ape cf me neutrino flu* spectrum at tr.fc ACS versus the a ttnospne r IC neutr inr i :LX . fig. *.:: Install aticr. »f the S^udar. II nuileon decay experiment underground. Fig. i*: Sketch cf a hanccller assembly. consisting of Mylar sheet, copper drift elec:roaes, and Kyirel drift tuDes. Fig. 5: Cutaway view of a single drift tube vich surrounding stes] and insulation. F: E • £: Detail of the "honeycocc" stack of steel and drift tubes vitr.it. each ciocule. Fig. 7: Photograph shoving bandclier asstably fan-felded around the corrigated steel and insulating sheets. Fie. £; Cutaway drawing of a standard 5-ton oodule. T *. r. 9: View of oodule vith endplane reaoved, showing close-packed hexagonal array of drift tubes. Fig. 10: Anode versus drift tiar •'ews of test bean cu-plus (10a), pi-plus (10b), and ele*. - r. CICc). rig. 11: i^ine sodule cluster for iteutrino calibraiior. running at Brookhaven. Tie. 12: ?.*ine nedule cluster ( disasseeiiled )t showing locations of anode and cathode readout. Fig. 1 1 ' Ol 2 3 4 NEUTRINO ENERGY (GeV) Fig. 2 - 174 - Hr 0 Hytrel Tubes Fig. 4 Proportional Wirn cked ay Ctihoae Suipi) Fig. 6 Anode Uire Signal Cables Cathode Board Lifting Cover Strap Fig. 8 Fig. 9 - 175 - jon Mev;c "uo 350 HeV/c P,OM 400 heV tutci»oii Fig. 10 O IO »0 \O 2C 3O -O 1O 2O DRIFT DISTAKCE (CM) rig. HO 0 (a o rig. 12 \ - 176 - The Sudbury Neutrino Observatory presented for the Sudbury Neutrino Observatory (SNO) Collaboration [1] by PJ. Doe University of California, Irvine, CA 92717. Abstract A full engineering design study is underway for an observatory based on a 1000 ton heavy water Cerenkov detector located deep underground. The principal goal of the observatory is to measure the flux, spectrum and direction of the 8B solar neutrino. The detector is also sensitive to the flux of muon or tau neutrinos which may arise from oscillation of the SB neutrinos. An overview of the detector and its capabilities is given. 1 Introduction The principal source of energy of the sun arises from the fusion of light elements deep within the core of the sun, as described by the various models of the suns operation. At present, the only known way of testing these models is to detect the neutrinos resulting from the fusion process. These neutrinos have a well defined flux and spectrum depending on the particular solar model. To date only one experiment has provided measurements of the solar neutrino flux, a Cl/Ar radiochemical experiment by R. Davis et al [2jwhich has been operational in the Homestake gold mine for more than 15 years. This experiment has consistently reported a flux of 8B neutrinos which is significantly lower than that predicted by accepted solar models, a discrepancy which has become known as the "Solar Neutrino Problem" (SNP)[3]. - 177 - The carefully conducted Cl/Ar experiment has withstood critical ex- amination. One possible explaination is that the error lies with the solar model, in which the production of SB neutrinos is strongly dependent upon the temperature of the solar core, however, all reasonable adjustments to the solar model have failed to significantly reduce the flux of neutrinos. Other explanations point to new neutrino properties. The suggestion of vacuum oscillations, in which the neutrino changes flavour during passage from the sun to Earth (and hence is no longer detectable by the Cl/Ar ex- periment), has recently been supplemented by matter oscillations, in which oscillations may be greatly enhanced by passage of the neutrino through solar or terrestial matter. Whatever the explanation of the SNP it is of profound significance to particle physics, astrophysics and cosmology. Given the range of possible explanations of the problem and their diverse effect upon the neutrinos arriving at the Earth, it is desirable that any detector addressing the SNP have wide sensitivity to minimise ambiguities arising from insufficient data. The SNO heavy water Cerenkov offers the possibility of measuring the flux, spectrum and direction of the 8B neutrinos and in addittion is sensitive to the flux and direction of other types of neutrinos arising from oscillations. 2 Detection Techniques The SNO detector will make use of the water Cerenkov technology pio- neered by current proton decay experiments. The central fiducial volume of the detoctor will consist of 1000 tonnes of 99.85% pure D-iO. The unique capabilities of the SNO detector arise from the following three reactions; 1. vt + d —>• p + p + e~ 2. ux + d —• ux + p + n 3. ux + e~ —> uT + e~ Reaction 1 occures via the charged current and has a threshold of 1.44 MeV. Essentially all the remaining energy of the incident neutrino is car- ried away by the electron, which is detected by the Cerenkov light emmit- 8 ted. Thus this reaction will measure the B ue flux and spectral shape in - 178 - real time. Directional information, though poor, is also avaliable from the forward-backward asymetry of the emitted electron. Reaction 2 takes place via the neutral current and all flavours of neutri- nos may participate in it equally, thus this reaction will be used to measure the total neutrino flux, independant of flavour [4]. The reaction may be detected via the Cerenkov light from the gamma rays resulting from the capture of the free neutron. The simplest way is for the free neutron to be captured by a deuteron, n + d —> t + -7 producing monoenergetk gamma rays of 6.25 MeV, which interact in the water and produce Cerenkov light. The cross section for neutron capture by a deuteron is low, but the efficiency for detecting reaction 2 may be improved by the use of additives to the D^O. All neutrinos may participate in the elastic scattering reaction 3, how- ever, since since ue interactions involve both the charged and the neutral currents, whereas u^ and uT involve only the neutral current, the cross section for vt dominates by a factor of six. The reaction is detected via the Cerenkov light produced by the recoil electron. Since this electron is constrained kinematically to a narrow forward cone, this reaction gives ex- cellent directional information. Since the recoil electron shares energy with the outgoing neutrino, it may have any of a continuous distribution of en- ergies up to that of the incoming neutrino, hence the spectral information from this reaction is poor. 3 Physics Goals A primary objective of the observatory is to measure the solar ue spectrum above 5 MeV in real time with energy and directional information, thereby addressing the SNP as raised by the Cl/Ar experiment. This would be carried out via reaction 1 above. In addition the detector would be sensitive to all neutrinos above 2.2 MeV via the neutrino disintegration of the deuteron given by reaction 2. Comparison of the fluxes measured by the two reactions would determine whether the problem was due to defects in the solar model or due to prop- erties of the neutrino itself. Should neutrino oscillations be responsible - 179 - for the flux measured by the Cl/Ar experiment, then the 8B spectrum shape may be significantly changed. Depending on the neutrino masses and mixing angle, either the low or high energy part of the spectrum may be reduced(5|. With an accrate determination of the total ut flux via reacnon 1, this information may be used to subtract the component of the vt flux from the total i/x flux measured via the elastic scattering reaction and thus be used to search for any i/^ or uT signal originating from the direction of the sun. The detector maj be used to address other physics questions[6]. Little reliable information exists as to the ultimate fate of massive stars. This is thought to be a two stage process, an initial rapid collapse of the core, followed by a more extended cooling phase. Each stage produces copious neutrinos. The SNO detector, by measuring the multiplicity, energy and time distribution, can provide direct information concerning the collapsing core, for stars located within our galaxy. Such stellar collapses occur at a rate of approximately one every 10 years. The detector may also be used to search for proton decay in a mode independant way. Should a proton in the deutron decay, and assuming charge conservation, it will produce an energetic positron which is detected by the Cerenkov light it produces. The free neutron will subsequently be captured with the emission of 6.25 MeV of gamma rays. By requiring the delayed coincidence, the backgrounds are reduced to that coming from atmospheric, neutrinos. It should be possible to improve the limit on mode independant decay from the present value of 2.2xlO26 to 2.0xl030 years. Other accessible physics includes searching for oscillations of atmo- spheric neutrinos passing through the Earth, the very low muon background of the SNO detector may provide addittional useful data to complement that of the existing proton decay detectors. One may contemplate direct- ing the neutrinc beam from an accelerator towards the SNO detector. The neutrino beam from Fermilab passes within a few degrees, and may offer the possibility of a long baseline oscillation experiment complementing the values of 6m2 and sin226 accessible via solar neutrinos. - ISO - 4 The Detector and Laboratory The physics goals of SNO require a very bw background envoirement both from local and cosmic radiation. A suitable site has been found at a depth of 2073 m in the Creighton mine operated by the International Nickel Cor- poration (INCO), near Sudbury, Canada. The laboratory will be located in non ore bearing rock in an area of the mine that will remain operational throughout the anticipated life of the experiment. Another essential requirement is access to a large amount of high purity D2O. A stock exists in Canada for use in future CANDU reactors. We were fortunate to be able to negotiate with AECL the loan of 1000 tonnes of D20 for the project. A conceptual design of the laboratory and detector is shown in figure 1. All materials used in the construction of the laboratory will be selected for low radioactivity. The heavy water is housed in a 10 m diameter acrylic vessel, surrounded by light water. Located in this light water at a distance of 2.5 m from the walls of the acrylic vessel are approximately 2,400 20 inch diameter Hamamatsu photomultiplier tubes, providing 40% photocathode coverage. The light water is contained in a stainless steel vessel, 18 m diameter, which rests against the cavity liner consisting of 1 m of low activity concrete. The thickness of the concrete, light water and the location of the PMTs are chosen so as to minimise the natural radioactivity to which the D^O would be subject. 5 Project Status A full engineering design study is underway in order to quantify in detail the parameters of the SNO conceptual design. A 700 foot long drift is under excavation in order to allow a geotechnical survey to be made of the rock at the site of the iaboratory cavity. An engineering design has been completed for the acrylic vessel housing the D2O which has shown that construction of such a vessel is feasible in the mine enviroiment. Sources of low activ- ity materials for the construction of the laboratory have been identified. Measurements and simulations show that the background for the charged current and elastic scattering reactions are under control. Measurement techniques for analysis of the extremely low activity levels in materials - 181 - concrete 20.0m 1.0m ^^/^)a=$==y==aK==i 30.0 m Figure 1: A conceptual design of the detector. - 182 - neccessary to ensure feasibility of the neutral current reaction are being developed and initial results are encouraging. The results of these measurements, calculations and simulations will be included along with technical documents and signed agreements in the final SNO proposal which will be completed in September 1987. 6 Summary Using the charged current reaction the SNO detector will measure the flux and spectrum of SB neutrinos coming from the sun. Combining these re- sults with those of the elastic scattering reaction it will be sensitive to any 8 B i/e's which have oscillated into v^ or uT. If radioactive backgrounds can be maintained low enough the SNO detector will be able to measure the total SB flux irrespective of neutrino flavour via the neutral current reaction. An engineering design study is underway to ensure that the detector may be constructed to meet the physics goals, produce detailed designs and construction cost estimates. A program to measure extremely low activities in materials, in order to demonstrate feasibility of the neutral current reaction is continuing. References The Sudbury Neutrino Collaboration: R.C. Allen, H.H. Chen, P.J. Doe University of California, Irvine, CA 92717, USA. H.C. Evans, G.T. Ewan, H.W. Lee, J.R. Leslie, J.D. MacArthur, H.B. Mak, W. McLatchie, B.C. Robertson, P. Skensved. Queens University. Kingston, ON, K7L 3N6, Canada. D. Sinclair, Oxford University, Oxford, 0X1 3NP, U.K. J.D. Anglin, M. Bercovitch, W. F. Davidson, C.K. Hargrove, R.S. Storey. National Research Council of Canada, Ottawa, ON. KlA 0R6, Canada. - 183 - E.D. Earle. Chalk River Nuclear Laboratories, Chalk River, ON. KOJ UO, Canada. G. Aarsma, P. Jagam, J.j. Simpson. University of Guelph, Guelph, ON. NlG 2W1, Canada. E.D. Hallman. Laurentian University, Sudbury, ON. P3E 2C6, Canada. A.B. McDonald. Princeton University, Princeton, NJ, 08554, USA. A.L. Carter, D. Kessler. Carleton University, Ottawa, ON. K1S 5E6, Canada. [2j J.K. Rowley, B.T. Cleveland, and R. Davis, Jr., Solar Neutrinos and Neutrino Astronomy (Homestake 1984), AIP Conf. Proc. 126,1 (1985). [3] For a current overview of the "Solar Neutrino Problem" see the articles by Joseph Weneser and Gerhart Friedlander, Science, 235, 755 and 760 (1987). [4] H.H. Chen, Phys. Rev. Lett. 55, 1534 (1985). [5] A paper describing the physics potential of the SNO detector in the light of the new theoretical developments concerning neutrino oscilla- tions has been submitted to Phy. Rev. Lett. [6] For details of other physics accessable to the SNO detector see Report SNO-85-3, "Feasibility Study for a Neutrino Observatory based on a Large Heavy Water Detector Deep Underground." July 1985. - 184 - REPRODUCED FROM BEST AVAILABLE COPY The Standard Model and Beyond 185 \\Qkp ELASTIC SCATTERING OF MUON NEUTRINOS AT B.N.L. K. Abe, L. A. Ahrens, K. Amako, S. H. Aronson, E. W. Beier, J. L. Callas, D. Cutts, H. Diwan, L. S. Durkina, B. G. Gibbard, S. H. Heagyb, D. Hedin, J. S. Hoftun, M. Hurleyc, S. Kabe, Y. Kurihara, R. E. Lanou, A. K. Mann, M. D. Marx, M. J. Murtagh, Y. Nagashima, F. M. Newcomer, T. Shinkawa, E. Stern, Y. Suzuki, S. Terada, D. H. Whited, H. H. Williams, Y. Yamaguchi, and T. York Physics Department, Brookhaven National Laboratory, Upton, NY 11973 Department of Physics, Brown University, Providence, RI 02912 Department of Physics, Hiroshima University, Hiroshima 730, Japan National Laboratory for High Energy Physics (KEK), Ibaraki-Ken 305, Japan Physics Department, Osaka University, Toyanaka, Osaka 560, Japan Department of Physics, University of Pennsylvania, Philadelphia, PA 19104 Department of Physics, State University of New York, Stony Brook, NY 11794 Presented by L. S. Durkina In this paper measurement, of the purely leptonic reactions: vye->v e and and \Jve-»\Jve, and the semileptonic reactions: vvp-»vyp and vyp-*vvp are presented and discussed in terms of the standard model. The data also places limits of interest on the magnitudes of a possible neutrino charge radius and a neutrino magnetic moment. The data reported here were taken at the Broc aven National Laboratory Alternate Gradient Synchrotron (A.G.S.) in a 170 ton, Fir.e-grained target detector. The neutrino beam and the apparatus and its performance have been described in detail in earlier publications.1'2 In the standard electroweak model, the differential cross sections for neutrino electron elastic scattering are given by (-) 2 vue) GpmeEy 2 2 2 2 where Y = l-Ee0e/2me and ; the vector and axial vector coupling constants 2 2 are related to sin 6w by: gv = - - 2 sin 9w and g& = - - . Within this model a precision measurement of sin26w comes from a measurement of the ratio of the cross sections, R = a(vpe)/a{~vve). 19 The \>pe and \>ye data were collected from 2.26 x 10 protons on the neutrino producing target (P.o.T.) and 3.4 x 1019 P.O.T. respectively. The neutrino electron elastic scattering data analysis, procedures, and the treatment of backgrounds have been described previously.^»* aNow at Ohio State University, Columbus, Ohio 43210 bNow at Lockheed Aerospace, Sunnyvale, CA 94304 cNow at M.I.T. Lincholn Laboratory, Lexington, MA 02173 <%ow at Los Alamos National Laboratory, MS H846, Los Alamos, NM 87544 - 187 - _ 2 Shown in Figure l?and 2 are the final \jye(vye) data as a function of 6e in the interval ee<0.03 rad with 21OMeV To determine the cross sections o(ve) and cr(vye) and their ratio, we have indirectly measured the integrated incident neutrino fluxes using samples of + quasielastic events vyp->y n and uyn-»vi~p with small momentum transfer, Q2<0.4 (GeV/c)2. Samples of 3.38x10^ y+n and 8.87xlO4 y~p (after background subtraction) were obtained. Correcting the signal and normalization samples for acceptances and efficiencies yields the total cross sections: 42 2 o(vye)/E- = [1.16 1 .20(stat) 1 .14(syst)] x 10~ cm /GeV 2 2 o(vye)/Ev = [1.85 1 .25(stat) 1 .27{syst)] x lO"** cm /GeV The fully corrected ratios of the normalized cross sections for uye and \>ye scattering yield directly the catio, R: R -- a(uye)/a(uye) = 1.60 •+ .41 1 .17 - .31 (stat) (syst) The systematic error on this ratio is smaller than the systematic error on the individual cross sections due to cancellation of systematic uncertainties (e.g. acceptances, energy scales, ...) in the ratio. Comparing this ratio5 to the standard model cross section we obtain sin29w = .192 * '^7 (stat) 1 .013 (syst) This value is dominated by systematic errors. Even though these results are statistically, limited systematic errors important to any future elastic scattering experiments, will be discussed. The dominant systematic error arises from uncertainties in the backgrounds of the normalization samples. With tight cuts on the quasielastic data^'^, 36% {27%) of the final p~p (y+n) samples consisted of single pion events (yNir) witi-> an additional 4% (3%) from multipion events (pNirir). Uncertainties in the cross sections and acceptances of these backgrounds led to an uncertainty in F o? 7%. - 188 - The excellent experimental resolution in 6e (13 mrad/VE^) combined with the 2 large uye statistics led us to consider the Be dependence on the two Y in do(« e)/dY; namely the flat Y term and the term in (1-Y)2. Monte Carlo shapes corresponding to the two terms are shown in addition to the data points in Figures 3a and 3b. 2 2 Fitting the relative contribution to the 0e shapes to the data points in 6e 2 2 and distribution determines (gv+gft) and (gv-g^) , yields the four 67% C.L. regions shown in Figure 4. Only one region is seen to be consistent with 7 vve-*Vpe in the standard model with sin 0w=.231, the world average value. The region also contains the more precise values: gv=-.O79±.O6O and g^=-.4831.042 determined previously from the \> e and upe cross sections. This calculation is first use of a Y-distribution in a ue elastic scattering measurement. (—) The v^e elastic scattering also proves to be a sensitive probe of neutrino structure. Any gauge theory of weak and electromagnetic interactions allows a non-zero charge radius, In the standard model with massless, left-handed neutrinos, the magnetic dipole moment, defined as fe/2me is identically zero. The contribution to 2 2 dc»(vye)/dY, of a possible magnetic dipole moment is: aemf [(l-Y) /Y] Fixing sin26w as in the charge radius limit, we obtain a 90% C.L. limit on f of: f<.95xlO~9 Bohr Magnatons. This limit approaches in sensitivity the bound, f<10~-1-0, obtained from astrophysical arguments. Since the magnetic dipole moment contributes as f2 to the elastic scattering cross section it will be difficult to improve the quoted limit on f. A future experiment decreasing the overall experimental error by a factor of ten will only improve this limit by slightly better than a factor of three. Low energy uee elastic scattering experiments are very sensitive to a magnetic dipole moment and should improve this limit in the near future. Due to the interference term, it will be easier for future experiments to improve on the quoted charge radius limit. Unfortunately the standard model prediction of The up and up elastic scattering data were obtained from separate exposures of .55xl019 p.o.T. and 2.5xlO-L^ P.O.T. respectively. The up and u^p differential cross sections depend on the quantities: Gp, Mv and M^, and 2 and up and jjn, in addition to sin 9w. Details of these differential cross - 189 - sections are given in reference.10 AIL these quantities are known to a precision better than that required by the measurement with the exception of HA which we chose to constrain to the world average value. The neutrino proton elastic scattering data analysis, procedures, and the treatment of backgrounds have been described previously. Elastic proton scattering candidates were single tracks (Q2>.35(GeV/c)2) fully contained in our detector. To separate protons from pions (muons), separate confidence levels (C.L.) for each hypothesis were constructed for each candidate event from the observed energy deposits in the scintillators and PDT's. The results are shown in Figure 5. Clear separation between protons and pions (muons) is observed. After data selection the resulting samples of 1686 uyp and 1821 v^p candidates contain backgrounds from: a) \>vn->vyn, b) neutral current single pion production, and c) a small contribution from multipion reactions. In addition corrections were necessary for elastic scatters produced by the measured contamination of "wrong-helicity" neutrinos in the beam. After background subtraction final samples of 951 u^p-^v^p and 776 \>vp-»vvp remain To determine the differential cross section the integrated incident neutrino flux was calculated as in the v^e analysis using quastelastic events. Shown in Figure 6 are the extracted absolute differential cross sections da(v2p)/dQ and dcj(\iLp)/dQ2. The error bars are statistical in nature with an additional shape systematic error of 18% and 8% added to the points at Q2=.45 and .55(GeV/c)2 respectively. An additional 11% scale uncertainty has been assigned to each of the cross section measurements. Constraining MA to the present world average value and fitting the differential cross sections to the standard model we obtain: sin26w = .220 ± ,016(stat) + "°^ (syst) The solid curves in Figure 5 represent this best fit to the data. Unlike the vye analysis the result is dominated by systematic uncertainties. The dominant sources of systematic error in the VypCw^p) differential cross section consisted of: 1) 4% (4%) uncertainty from the single and multipion backgrounds to signal and normalization reactions, 2) 6% (3%) uncertainty due to knowledge of the neutrino flux shape as a function of energy, and 3) 4% (4%) uncertainty from secondary scattering of protons leaving the C12 nucleus. This last uncertainty required detailed nuclear Monte Carlo calculations which are discussed in detail along with these other systematic uncertainties in reference 12. 2 If sin ©w is fixed to the value .220 and MA is constrained to the world average value, a search ;;ay be made for additional terms in the axial vector 2 form factor, GA(Q ), due to neutral current contributions from heavy quark currents or a "non-standard" isoscalar axial vector current10. Writing 2 2 2 GA(Q )=GA(Q )Q+n), one finds n=.12±.O7, one finds n = -l --07, or equivalently 0.0 - 190 - Insensitive to the choice of any n in this range. Any future experiment measuring neutrino proton elastic scattering will have to deal with this fundamental form factor uncertainty. There is seen to be good agreement between sin26w obtained from u^e and VyP elastic scattering. Furthermore these values of sin2ew are in good agreement with values of sin26w determined from masses of the W- and Z-bosons9, and inelastic electron-deuteron scattering, and from deep inelastic scattering7. Within present experimental errors of about seven percent, the weak neutral current parameter is a universal constant. We are grateful to P. Langacker and W. J. Marciano for many informative discussions. This work was supported in part by the U. S. Department of Energy and the Japanese Ministry of Science and Culture through the Japan-U.S.A. Cooperative Research Project on High Energy Physics. REFERENCES 1. L. A. Ahrens et al. , Phys. Rev. D34, 74 (1986). 2. L. A. Ahrens et al., preprint E-734-86-2 (Accepted for publication in N.I.M.). 3. L. A. Ahrens et al., Phys. Rev. Lett. 54. 18 (1985). 4. L. A. Ahrens et al., Phys. Rev. Lett. 51, 1514 (1983). 5. There is only me previous measurement of R which yields: sin26w=.215±.0321.013. Details of this measurement can be found in F. Bergsma et al., Phys. Lett. 147B. 481 (1984). 6. K. Abe et al., Phys. Rev. Lett. 58, 636 (1987). 7. "Status of the Weak Neutral Current," U. Amaldi et al., (to :e published). 8. L. A. Ahrens et al., "Perspectives in Electroweak Interactions," XX Recontre de Moriond, ed. J. Tran Thanh Van, p. 45 (1985). 9. C. Rubbia, "Procedings of the 1985 International Symposium on Lepton and Photon Interactions," Kyoto, Japan (to be published) L. DiLella, ibid. 10. J. E. Kim et al., Rev. Mod. Phys. 53., 211 (1981). 11. K. Abe et al., Phys. Rev. Lett. 56, 1107 (1986). 12. L. A. Ahrens et al., "Measurement of Neutrino-Proton and Antineutrino- Proton Elastic Scattering", (accepted for publication in Phys. Rev.) - 191 - 0.01 0.02 e2(radian2) Fig. 1 The vpp e distribution in for a) predominantly electron events, and b) predominantly photon events. c o X3 C o q d en 1- > LJJ 0.01 0.02 0.03 2 2 #e (rod ) , Fig. 2 The \> e distribution in 9e for a) predominantly electron events, and b) predominantly photon events. - 192 - 1.00 T3 O in o 0.50 \ 8 (l\ d CD cu > 0 \N H en Ui LLJ -0.50 V ) 0 030 XT 1 - 1.00 -1.00 -0.50 0 0.50 1.00 I ' I ' i • i • - CM -a b o 60 - ) k_ Fig. 4 The four areas in gv vs g^ in 50 i space (67% C.L.) allowed by the measurement of da(\>pe)/dY. 8 40 _ o I, d 30 CO 20 ill-i - > 10 UJ 0 if, i' 0 0.010 0020 0 030 rod Fig. 3 The observed distribution in 6e (points and the Monte Carlo distribution (histogram) for: a) a (1-Y)2 term and b) a flat term plus background. - 193 - o ,0.0 0 0.5 1.0 0 0.5 1.0 Q C.L. PION (SCIN) C.L. PION (PDT) Fig. 5 C.L. for proton hypothesis vs. C.L. for pion hypothesis by measurements in the scintillators (left) and PDTrs (right) 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 02 (GeV/c)2 Fig. 6 The measured (data points) flux averaged differential cross sections for vyP and vpP elastic scattering. - 194 - THE EFFECT OF EXTRA NEUTRAL GAUGE BOSONS ON NEUTRINO-ELECTRON SCATTERING S. Godfrey and W.J. Marciano Physics Department Brookhaven National Laboratory Upton, NY 11973 ABSTRACT The effects of additional neutral gauge bosons on neutrino-electron scattering cross sec- tions axe examined. Existing data is shown to provide bounds in the 100-250 GeV range for a class of EQ inspired models. Estimates of the precision reachable in ongoing mea- surement? indicates that those bounds should approach 400 GeV and a proposed new experiment at Los Alamos may probe mass scales of order 800 GeV. INTRODUCTION The discovery of additional massive neutral gauge bosons beyond the Z would have pro- found implications. Besides signaling new forces in nature, their specific properties could weil point to a particular grand unified theory (GUT). Indeed, many GUTS predict the existence of relatively light additional neutral gauge bosons with well specified couplings. Such bosons may eventually be produced and studied at high energy colliders if they are not too massive. For example, Fermilab's pp collider has a discovery potential that will extend to masses of about 400 GeV when 1030/cm2 — sec luminosity is achieved. The SSC will be able to push the search to 5-10 TeV; but that is still rather far away in time.2 To complement the direct production searches, it is useful to look for indications of ad- ditional neutral gauge bosons in low energy phenomenology or use the existing data to constrain their properties. Depending on the fermion couplings, detailed studies3 gen- erally place bounds in the 100-300 GeV range on their masses. Those bounds provide a benchmark that future experiments should aim to surpass. They also provide an ob- jective means of comparing the discovery potential of very different high precision iow energy measurements such as v — e scatterhre. polarized electron scattering, atomic par- ity violation, etc. - 195 - In the analysis presented here, we examine the effect of additional neutral gauge bosons on neutrino-electron scattering cross sections. We find that existing data provides bounds in the 100-250 GeV range for a class of E$ motivated models. Those constraints are sim- ilar and complementary to other neutral current measurements. We note that ongoing measurements should push those bounds to order 400 GeV and that a proposed new experiment4 is capable of probing mass scales of order 800 GeV, a significant advance- ment. GENERAL ANALYSIS We consider the appendage of N — 1 weak neutral gauge bosons to the standard model, such that N ui(l). (l) t=i The fermionic electroweak neutral current interaction Langrangian is given by N £int. = -eA" (i) J^ (x) - -±- Y, *Z? {*) 4 {*) (2) COo (7^^ 1=1 where jem = £ gem f fjRiitfR + f 1 -I- "/- (3) with Qy-m = electric charge, g = e/ sin 6w and Q\ and Q\- depend on the model. (We leave the c2- as model dependent normalization factors.) In the standard model, N = 1 2 e m and Z\ is identified with the ordinary Z boson such that c\ = 1, Q'f = — sin ^Q - 2 e m and Q'/L = T3f - sin 6wQ f with T3f the weak isospin charge T3e = -I, TZv = +|. If the Zi are mass eigenstates, neutrino-electron scattering cross sections can be written as o 7T tp . Ti.. 2 „ 2 2 7T _ + e +) 2GlmtE. , ,£ (4) 7T - 196 - 2 5 2 41 2 where Gp = g /4y/2rr^ = 1.16636 x l(T GeV~ , [2G\mtj-K = 1.72 x l(T cm /GeV) and from Eqs. (2) and (3) one finds 1=1 N (5) Note that in the v eee croscrosss sectionssections,, thertheree existexistss aa chargechargedd currencurrentt contributiocontributionn that t changes e_ to e_ — 1. In the standard model, N = 1 and mz = rnz such that 5 =sin 6w (6) and one reproduces the well known cross section formulas. Our subsequent discussion will focus on modifications of that result due to extra Z{ bosons. E6 INSPIRED MODELS The EQ GUT7 provides a nice example of how extra neutral gauge bosons arise in realistic extensions of the standard model. It contains 3 massive diagonal weak neutral gauge bosons. The extra two are conventionally1'2'317 denoted by Zx and Z^. (They are not necessarily mass eigenstates.) In that basis ex -Ct/> - \/%sinOw (7a) Qt =Qt, = Qt, = Vh- (7c) The mass eigenstates Z, Zv and Zvi are related to Z\, Zx and Z^ by an orthogonal transformation which depends on 3 mixing angles. However, to simplify the analysis, we assume Z = Z\. That should be a good approximation, since neutral current phenomenol- ogy limits Z\ mixing to be very small. With that simplifying assumption Zn —Zx cos (f> + Z^p sin cf> Zni = — Zx sin 6 + Zf/, cos - 197 - and Q^ = i cos <£-,/#, sin v Q eL = QlL= cos V'1 - x/fsin^v/ (9) From those charges, one finds via Eq. (5) .2 L7TI 2 (10) Even with the simplifying assumptions we have made, the result still depends on 3 un- 2 2 known parameters —/-, $ , and <^>. Therefore, in the following discussion, we consider the two illustrative scenarios: case (1) mZi7 ~ m\ (11) case (2) m| < 2 e+ ~ -s2 - |52^ (cos<£ + vTsi-71-^) (^ cos<^ - \/^sine/)) (12) Those examples illustrate typical bounds presently provided by experiment and the po- tential of future measurements. - 198 - PRESENT EXPERIMENTAL CONSTRAINTS •Existing data can be employed to bound the mz,, and m^, discussed in the previous section. One can use the average experimental cross sections 6 1 42 2 a (j^g _> j^g) * * IEV = 1.60 ± 0.20 x 10- cm /GeV (13a) ex 42 2 a [9jxe _> pMe) P JEV = 1.24 ± 0.15 x 10' cm /GeV (136) or the sometimes directly measured ratio R = °L^2lA _= 1.29 ± 0.22 (13c) O [Ut Ut) ( v ee cross sections are not yet competitive with these measurements; so we do not discuss them.) The cross section results imply je_|exp = 0.278 ± 0.024 (14a) |e+rp = 0.215 ±0.025 (146) which are to be compared with the standard model prediction e_ = 0.272 ± 0.004 (15a) (Standard Model) e+ = -0.228 ± 0.004 (156) 2 (found using sin 80 = 0.228 ± 0.004 appropriate for u Me scattering). The agreement is very good and thus provides a constraint on extra neutral gauge boson effects. In the case (l) scenario, we consider the e_ constraint along and find by comparing Eqs. (1), (4) and (15) and using mz - 91.5GeV case (1) mZf| ~ mz , £ 215GeV (90% C.L.) (16) Zi| In case (2), we employ all three experimental values in Eq. (13) and compare them with the predictions that follow from Eq. (12). The resulting 90% C.L. constraints on mZt) as a function of - 199 - 300.0 250.0 200.0 - =5; 2 150.0 - ef 100.0 < 50.0 - -90.0 -45.0 0.0 45.0 90.0 (degrees) Fig. 1: 90% confidence level bounds on m^ from existing data. The dotted line is the bound from a (v^e), the dot-dashed line is from a (i^e), and the solid line is from R = cr^e) /cr(j/Me). 300 -90 -60 -30 Fig. 2: 90% C.L. bounds on m^ from Cs atomic parity violation experiments. - 200 - FUTURE PROSPECTS An ongoing CHARM II experiment at CERN is capable of irr proving the determination of R in Eq. (13c) by about a factor of 4 (statistically). Assuming that systematic uncer- tainties can be controlled, that would improve the bounds on r. t^t| and mz , given in our previous section by about a factor of 2. It means that they ar^ probing a mass scale of about 400 GeV, the same as Fermilab's pp collider potential. A proposed new Los Alamos experiment4 at LAMPF would measure the ratio R' = -. Z^L^A (17) to ±1.7%. In terms of e+ and e_, that ratio is given by For the standard model, one, therefore, expects A deviation could signal the existence of extra neutral gauge bosons or boimd their prop- erties. For illustrative purposes, we consider the case mz , 3> nizn and lake So, a 1.7% measurement of R' probes mzn at the level of about 800 GeV. For other values of 4> we give in fig 3 the mzn mass scale probed by such a measurement of R'. We also plot there the mass scale probed by a 2% measurement of R and 5% measurements of a [y^t —• i/fj,e) and a [u^e —> O^e). The R1 determination is clearly the best probe for a large range of In conclusion, we have found that existing v ^e scattering data is quite competitive with other neutral current constraints on additional neutral gauge bosons. Future high preci- sion measurements which will aim to determine sin By/ and confirm radiative corrections of the standard model are capable of probing for such bosons up to about 800 GeV. They will thus provide an important window on physics beyond the standard model. ACKNOWLEDGMENT This work supported under Contract DE-AC02-76CTT00016 with the U.S. Department of Energy. - 201 - 800.0 700.0 600.0 500.0 42- 400.0 - 300.0 V 200.0 - 100.0 '- -90.0 -45.0 0.0 45.0 90.0 $ (degrees) Fig. 3: Expected 90% C.L. bounds on mZr). The dotted line gives the bounds from a 5% measurement of o (v^e), the dashed line gives the bounds from a 5% measurement of a [Pfj.e), the dot-dashed line gives the bounds from a 2% measurement of R, and the solid line gives the bounds from a 1.7% measurement of R'. - 202 - REFERENCES 1. R. Robinett and J.L. Rosner, Phys. Rev. D25, 3036 (1982); N. Deshpande and D. Iskander, Nucl. Phys. B167, 223 (1980); J.L. Rosner, Comrn. Nucl. Part. Phys. 14, 229 (1985). 2. P. Langacker, R.W. Robinett and J.L. Rosner, Phys. Rev. D30, 1470 (1984); H. Haber, in Supercollider Physics (World Scientific, Singapore, 1986)edited by D.E. Soper, p. 194. 3. L.S. Durkin and P. Langacker, Phys. Lett. 166B, 436 (1986); V. Barger, N.G. Deshpande and K. Whisnant, Phys. Rev. Lett. 56, 30 (1986); D. London and J.L. Rosner, Phys= Rev. D34, 1530 (1986). 4. D.H. White et a/., LAMPF Cherenkov Detector Proposal #1015, Jan. (1986). 5. S. Sarantakos, A. Sirlin and W. Marciano, Nucl. Phys. B217, 84 (1983). 6. F. Gursey, P. Ramond, and P. Sikivie, Phys. Lett. 60B, 177 (1976). 7. D. London and J.L. Rosner, Phys. Rev. D34, 1530 (1986). Our mixing angle - 203 - ~< THE WEAK NEUTRAL CURRENT3 Paul Langacker University of Pennsylvania. Philadelphia. Pennsylvania 19104 ABSTRACT The results of a detailed analysis of existing data on the weak neutral cur- rent and i.he IV and Z masses are presented. The weak angle is found to be sin" "iv - 1 - A/^. A/1 -- O.'J.'-iO * 0.0048. where the error includes full statist), cal, systematic, and theoretical uncertainties. Allowing p = MW/{MZ cos &w) to vary one obtains p - 0.908 ± 0.0086. Implications for tests of the •tandard model at the level of radiative corrections, non-standard Higgs representations, mt and heavy fourth family fermions, grand unification, and possible additional Z bosons are discussed. I. Introduction Recently, many new high precision experiments in deep inelastic scattering from isoscalar and non-isoscalar targets, up elastic scattering, ue scattering, atomic parity violation, e+e" annihilation, and the W and Z masses have been completed. As we await a new generation of even more precise experiments, mainly at e+e~, ep, and hadron colliders, it is worthwhile to make a systematic and critical study1 of existing results, with the goals of testing the standard model2 at the level of radiative correc- tions, extracting as accurate a value of sin2 9w as possible for comparison with grand unified theories, supersymmetry. etc., and searching for indications of (or setting lim- its on) such new physics as additional Z bosons, heavy fermions. or non-standard Higgs representations. We have attempted to incorporate all published data on j/-hadron, ue, eN, /J.N, and e+e reactions, atomic parity violation, and the W and Z masses, with the exception of those for which, in our opinion, either experimental uncertainties or aWork performed in collaboration with Ugo Amaldi. Albrecht Bohm, L.S. Durkin, Alfred K. Mann, William J. Marciano, Alberto Sirlin, and H. H. Williams. - 205 - Reaction sin2 9w Deep inelastic (isoscalar) 0.233 ± .003 _ (.005] 15.1/20 (y \ p ->{v\ p 0.210 ± .033 13.1/14 { ( u\ e -. y'M e 0.223 ± .018 ± [.002] 4.1/11 W, Z 0.228 ± .007 ± [.002| 1.9/3 Atomic parity violation 0.209 ± .018 ± [.014] 5.9/6 SLAC eD 0.221 h .015 ± [.013] *0.4/10 fiC 0.25 ± .08 .1/1 All data 0.230 ± 0.0048 145/184 Table 1: Determination of sin2 &w from various reactions. Where trvo errors are shown the first is experimental and the second (in square brackets) is theoretical. In the other cases the theoretical and experimental uncertainties are combined. difficulties in the theoretical interpretation preclude useful or reliable quantitative constraints. We have also tried to use the best available theoretical expressions, to make realistic estimates of theoretical uncertainties, and to ensure that similar ex- periments are treated as uniformly as possible. Deep inelastic neutrino scattering experiments are analyzed using a QCD-improved parton model in which the Q2- dependent quark distribution functions, determined from charged current data, are weighted with the appropriate neutrino spectra and cuts for each reaction. Elec- troweak radiative corrections are included except where their effects are negligible compared to the experimental uncertainties. II. Results (a) sin2 6w The values of sin' 0w determined from various reactions and from a global fit to all data are listed in Table 1. For many of the individual reactions the experimental and theoretical uncertainties are displayed separately. The central values for all fits assume mt = 45 GeV and Mjf = 100 GeV, for the masses of the t quark and Higgs - 206 - Boson, respectively, whiie the theoretical uncertainties assume mt < 100 GeV, 1 TeV, three fermion families, and reasonable ranges for all other parameters. The theoretical uncertainties for deep inelastic scattering are broken down in Table 2. The sin2 Bw values for the various reactions are in remarkable agreement, indi- cating the success of the standard model. This is shown in Figure la, in which the 2 2 various sin 6W values are displayed as a function of the typical Q values of the reactions. 2 The best fit to all data yields sin 9W - 0.230 ~ 0.0048. All data are in excellent agreement with the standard model for this value. The \2 per degree of freedom (147/184) is slightly low (possibly due to conservative overestimates of systematic errors or to correlations between the various experiments that have not been taken into account), but nevertheless reasonable. The last entry (All data) in Table 1 includes certain reactions (e.g. deep inelastic scattering from non-isoscalar targets and u e e —> u e e) that are less precise than those listed explicitly in Table 1. Our rationale for including these results is that they will be useful in studies of limits on deviations from the standard model, and it is desirable to use the same data sets for all global fits. It is reassuring, however, that reasonable variations on the data set yield consistent results. For example, the first six reactions in Table 1 plus e+e~ data yield sin Bw = 0.228 + 0.0048, while a fit to only the most precise experiments of each type yields 0.230 ± 0.0051. Similarly, the four recent high precision deep inelastic 3 6 2 experiments " give sin Bw = 0.234 ± 0.007 compared to the value 0.233 ± 0.006 obtained when the older experiments are included. In contrast, the recent CHARM and BNL-E734 u ^ e experiments78 yield the average 0.213 ± 0.022. This is pulled up a non-negligible amount (to 0.223 ± 0.019) by the older experiments. 2 + We do not quote a sin Bw for e e~ reactions. This is because at PEP and PETRA energies the forward-backward asymmetries An, I = fi or T, are nearly an absolute prediction of the standard model and the cross sections (relative to QED) Ru depend 2 2 only weakly on sin 6W. All values of sin Ow from 0.1 to 0.4 give a good description of the data, and to first approximation the \-2 distribution is nearly fiat for sin2 0w in that range. (b)p and sin2 Ow 2 The quantity p = Mw j[M\ cos Ow) is exactly one (in our renormalization scheme) in the standard model or any SU2 x L7j model in which all symmetry breaking is due - 207 - Quantity Value Ap V + bnu + m .125 ± .020 I + .002 +.008 i ±.006 S/U .46 ± .10 I ±.0007 ±.0003 ! T.0004 i CIS .15± .15 j +.0002 (S - S)/2S Ox 1 | ±.0003 DV/UV .39 ± .06 | ±.0006 1 *.C001 T-0007 KMC angles Uiu = .973 ± .002 T.0003 _ — (3 Families mc (GeV) 1.5 x .3 ±.0041 ±.0005 T-004 AQCD(MeV) 250 + 100 T.0001 — — «i .1x1 + .001 ±.001 mt (GeV) 25-100 ±.0012 ±.002 ±.0015 MH (GeV) 10-1000 ±.0002 ±.001 ±.001 Other rad. corr - ±.001 — — Higher twist j . ±.002 — Total ±.0054 + .0084 ±.0075 Table 2: Theoretical uncertainties for deep inelastic scattering. The third column refers to the sin2 8w fit 2 2 with p = 1. while the last two columns refer to the \p.3\n Bw) fit. U = /J zu(x.Q o)dx is the first 2 2 moment of v.(x.Q ) evaluated at Q O = 5 GeV~. i'v and Dv refer to the valence quark distributions, •\-QCD is an effective leading order QCD A parameter, and RL = {F2 -2xFi)/2xF1 is the longitudinal 2 2 structure function (replacing RL = 0.1 by a QCD inspired RL(z. Q ) changes sin 0W by only +.0004). Assuming three fermion families it is sufficient to parameterize the transitions between u. d. c. and 3 3 + by an effective Calibbo angle. For more than three families A sin 9W K we increases to I ' ^ -0.001 leading to a total theory error Asin2^ = "r* . All theory uncertainties except [U + D)f{U + D) are computed with r = <7?£/<7^£ fixed (to avoid double counting). Several additional small (< .001) uncertainties (e.g. from the shapes of the quark distributions at Q2,) are due almost entirely to the charm threshold and are not independent of mc. - 208 - I 0.3 - mT0p=45GeV ( A-0.230 0.2 H 0.1 0.3 ~ mT0p=100GeV r- 0.227 0.2 h4 * i * CD cvi 0.1 .E 0.3 if) "m =200 GeV r- 0.222 TOP m 0.2 - 0.1 - 0.3 ~ m =400GeV • ^-0.209 0.2 r * $ • - 0.1 i I I I I 10"6 10"4 10"2 10° 102 104 Q2 (GeV2) Figure 1: (a) sin"^ for various reactions as a function of the typical Q2, determined 2 2 for mt - 45 GeV. The best fit line sin Qw — 0.230 is also shown, (b-d) sin 9\V values determined for mt = 100,200, and 400 GeV. - 209 - Reaction sin2 9w p Correlation x2/d-f- deep inelastic (isoscalar) 0.232 ± 0.014 ± [-008] 0.999 ± .013 ± [.008] .90 15.1/19 {v\p-^u\p 0.205±.041 0.98± .06± [.05] — 13.0/13 {Z\e-^Z\e 0.221 ± .021 ± [.003] 0.976 ± .056 ± [.002] .12 3.9/10 W, Z 0.228 ± .008 ± [.003| 1.015 ± .026 ± [.004] .19 1.6/2 AUdata 0.229 ±.0064 0.998 ±.0086 .63 145/183 Table 3: Determination of p and sin2 Ow from various reactions. Where two errors are shown the first is experimental and the second (in square brackets) ia theoretical. to Higgs doublets.1* However, p / 1 can occur if there are Higgs multiplets with I > \ with significant vacuum expectation values (VEV's). Fits to p and sin2 Ow are presented in Table 3, and the various theoretical un- certainties for deep inelastic scattering are detailed in Table 2. One findsc p = 2 0.998 ± 0.0086 and sin 9W = 0.229 ± 0.0064, remarkably consistent with p = 1. This implies 90% c.l. limits 1 ^7^' < 0.047,i.;; M and < ^x±1 > < 0.081 (16) on the VEV's of Higgs triplets with /3 = 0 or ±1, respectively, relative to that of the ordinary Higgs doublet (these limits assume that only one new VEV is present so that there are no cancellations). The allowed region in the p — sin2#iy plane for various individual reactions and the global fit to all data are shown in Figure 2. (c) Radiative Corrections The data are now sufficiently precise to begin testing the standard model at the radiative correction level. A conventional measure of radiative corrections is the The effects of nondegenerate heavy fermion doublets are absorbed in the radiative corrections. c A fit to the most precise experiments of each type yields p = 0.998 ± 0.0089 and sin" &w = 0.229 ± 0.0066. 'ihe first six reactions in Table 1 plus e+ e~ and coherent pion data yield p = 0.996 ± 2 0.0084, sin 6W = 0.227 ± 0.0064. - 210 - 1.5 T 1.4 oil data — deep inelastic — W,Z 1.3 \ \ ' \atomic\ .' eD I — vp 1.2 \ p \ \ / 1.1 1.0 / 0.9 0.8 o 0.1 02 ^ 0.3 sin2 Figure 2: The allowed regions in the sin2 Ow -p plane at 90% c.l. for various individual reactions and by the global fit to all data. - 211 - parameter Ar defined by A/u- •- r (2) sin0H.(l - A)^ where .4,, = (TTQ/\/2GF)^ - 37.281 GeV. Ar represents the radiative corrections relating Gf (measured in muon decay) to the W and Z masses. A simultaneous fit of deep inelastic (isoscalar target) data and the W and Z masses to Ar and sin2 Ow yields the allowed region shown in Figure 3. The corresponding value Ar = 0.077 ±0.037 is in excellent agreement with the value 0.0713 * 0.0013 predicted for mt = 45 GeV and MH - 100 GeV. However, the Ar - sin*0w fit is not the best test of radiative corrections, because the value of sin" 8W extracted from the data itself depends on the radiative corrections assumed. In particular, any noncanonical contribution to Ar (such as a very large mt) could also affect sin' 8W. A better measure is obtained if the M\y and Mz predictions are written in terms of sin20° =sin2^ - As2 (3) where sin2 8° is the value (.242 ± .006) obtained for the weak angle from deep inelastic scattering if all radiative corrections (to both oNC and occ) are ignored, and Zis2 2 represents the radiative corrections. For our canonical mt and MH, AS is —0.009 ± 0.001. Then Mw = r (4) sin0°(l -6wY- s where As2fl - Ar) 6 - Ar x— = Ar + 0.035 ± 0.004 (5) W sin2701' ' 6w i-epresents all of the radiative corrections relating deep inelastic scattering, the W 2 and Z masses, and muon decay. The allowed region in sin 0° - Sw is also shown in Figure 3, and one obtains 6W = 0.112 ± 0.037. This is consistent with the prediction 6W ~ 0.106±0.004 for our canonical mt.MH assumptions and establishes the existence of electroweak radiative corrections at the 3 a level. A similar conclusion can also be reached from the W and Z masses, listed in 2 Table 4. The standard model predictions for Mw and Mz (using sin 6W from deep inelastic scattering) are in excellent agreement with observations, but the predictions without radiative corrections (Ar = As2 = 0) strongly disagree with experiment. - 212 - 2 si•n a°a 0.21 0.22 0.23 0.24 0.25 0.20 1 1 i I i i i i i i 90 /o - 0.20 Ar = 0.0713 0.10 - Y) _ = 0 106 // '// - —0.10 Ar ( 'C 0 - V W Sw = 0 0 - (NO RADIATIVE CORRECTIONS) — - 0.10 - - -0.10 -0.20 i I i I i I i I 1 0.20 0.21 0.22 0.23 0.24 0.25 2 Sin £ W 2 2 Figure 3: The allowed region in the sin 0w - Ar (or sin 6" - bw) plane determined from deep inelastic (isoscalar) data and the W and Z masses. - 213 - Group Reference UA2 (CERN) 80.2 ±0.8 ±1.3 91.5 ±1.2 ±1.7 R. Ansari et ai, Phys. (80.7) (91.9) Lett. 186B: 440 (1987). UA1 (CERN) 83.5-1.0 ±2.7 93.0 ±1.4 ±3.0 G. Arnison et al., Phys. (80.7) (91.9) Lett. 166B, 484 (1986). UA1 + UA2 combined 80.9 ± 1.4 1.9 ±1.8 Prediction from deep inelas- 80.2 ±1.1 91.6 ±0.9 tic (with radiative corrections; 3 sin 6W = 0.233 ± .006) Prediction from deep inelastic 75.9 ± 1.0 87.1 ±0.7 (without radiative corrections; sins 8" = 0.242 ± .006, Ar = AaI=0) Table 4: The W and Z masses (in GeV). The first uncertainties are mainly statistical and the second are energy calibration uncertainties that are 100% correlated between Mw and Mz for each group. The numbers in parentheses are the standard model predictions for the global best fit value sin2 8w = 0.230. The last two rowa are predictions of the standard model, using sin 6w determined from deep inelastic scattering, with and without radiative corrections, respectively. (d) Heavy fermions Within the standard model with 3 fermion families the only major uncertainties are mt and MJJ, which affect the radiative corrections. The Higgs mass dependence is small although not completely negligible as long as MH < 1 TeV. It typically introduces an uncertainty of 0.002 in the sin2 Ow value extracted from most reactions other than deep inelastic scattering. For larger MH the perturbative calculation of radiative corrections becomes suspect (because of the large Higgs self coupling) so we will restrict ourselves to the case MJJ < 1 TeV. The sensitivity to mt (or to splittings between fourth family fermions) is much larger. For example, Ar —» 0 for mt ~ 245 GeV and the other radiative correction parameters exhibit similar sensitivity. The sin2 Ow values obtained for various reac- tions are shown in Figure 1 for mt = 45, 100, 200, and 400 GeV. There is little 2 sensitivity for mt < 100 GeV. For larger values the sm 0jy from deep inelastic scat- tering stays almost constant, while the other determinations decrease. Clearly, the data are inconsistent with mt much larger than 200 GeV. To quantify this we have 2 performed fits to mt and sin Ow for various (fixed) values of MH, including the full rnt - 214 - 400 MH = 100 GeV MH = 1000 GeG' V 300 MH = 10 GeV 200 100 0 j i 0.200 0.210 0.220 0.230 0.240 2 sin 9 W 2 Figure 4: Allowed regions (90% c.l.) in sin 8W - mt for Higgs masses of 10, 100, and 1000 GeV. and MH dependence of the radiative <-drections to all processes. The allowed regions for Mff = 10, 100, and 1000 GeV are shown in Figure 4. The corresponding upper limits on mt alone are mt < 175 GeV, 180 GeV, and 200 GeV for MH = 10, 100, and 1000 GeV, respectively, all at 90% c.l. Similar limits can be obtained from the Ar — sir 8w fits, which use only deep inelastic scattering and the W and Z masses. It should be emphasized that all of these limits assume that there is no new physics that produces compensating effects. One can place similar limits on the mass splittings between the quarks or leptons in a fourth fermion family: \mt> - mbi\ < 180 GeV and \mL - mv,\ < 310 GeV for - 215 - Quantity Experimental Standard Model Correlation X2/d.f. Value Prediction eL(u) 0.339 ±.017 0.345 33.6/48 iL(d) -0.429 ±.014 -0.427 £R(u) -0.172 ±.014 -0.152 (R(d) -O.Ollj/gij} 0.076 g\ 0.2996 ± 0.0044 0.301 33.6/48 3^ 0.0298 ± 0.0038 0.029 9L 2.47 ±0.04 2.46 d -_+o.48 5.18 g'A -0.498 ± .027 -0.503 -0.08 7.5/13 g^ -0.044 ± .036 -0.045 -0.249 ±0.071 -0.191 -0.98 -0.88 15.8/15 Cu 0.381 ±0.064 0.340 0.88 0.19 ±0.37 -0.039 Table 5: Values of the model independent neutral current parameters, compared with the standard model prediction for sin2 9w = 0.230. We do not give correlations for the neutrino hadron couplings because of the non-Gaussian x2 distributions. However, the neutrino hadron constraints are accurately represented by the ranges listed for the raxiables 3? = ej(u)2 + £i(d)2 and 0,- = tan~1(ei(u)/ei(ii)), i = L or R, which are very weakly correlated. M// - 100 GeV. Such splittings yield contributions to the radiative corrections that are independent of the sign of mti - m^, so they cannot cancel the effect of large mt. (This is true lor most but not all possible extensions of the standard model) These limits become more stringent as the average doublet mass increases. (e) Model Independent Fits Model independent fits to the uq, ue and eq are presented in Table 5. Most are now determined uniquely and precisely1 and are in excellent agreement with the predictions of the standard model. (F) Additional Z Bosonse Many extensions the standard model predict the existence of additional Z bosons. A heavy fourth family could also in principle relax the constraints on the KMC angles if its mixings with tlie firnt two famiiie? is large. This would increase the sin2 f*ir from deep inelastic scattering and would make the limit? on the mass splittings more stringent. eThere have been several recent analyses of extra Z bosons based 011 earlier data sets1" ". - 216 - For the simplest case (one extra Z) the physical (mass eigenstate) bosons are Z, - Z\'cos Z-> = Z'{ sin 6 + ZUosd ' (6) where, under reasonable assumptions, the lighter boson Z\ is the particle observed by UA1 and UA2, Z'{ is the SU2 < U\ boson which couples to g\{Jzi - sin QwJEim)-, Z2 couples to a new current g2J'l, and 9 is a mixing angle. The extra Z manifests itself (a) because the Z\ mass is reduced by mixing, (b) because the Zy couplings are modified by mixing, and (c) by Z2 exchange. As an important example of an extra Z, we consider Z(/3) - cos3Zx + sin/3Z^,, 2 with [gilgiY ~ 5Afl sin (?w/3. This is the extra boson in Er, models which break to G >'• Uifl, where G contains the standard model. Zx and Z^ are the gauge bosons v/nicn occur for SOW —> Sb\, < UXx and Ec> —' SOW x Uiv, respectively. The special case ^n — \\Zx~ V \Z->I> — ~Z{P = n ~ Ian"1 T/|) occurs iri many superstring models. We will follow the formalism in Ref. 10. We assume A^ = 1, which occurs if the underlying group breaks directly to SU3 x SU2 x Ui x U[ (limits on Mz2 and 0 scale roughly as \/A and 1/vA, respectively). Limits on Mz., and 6 are presented for two cases: a.) The constrained Higgs case. This case, which is the analog of p = 1 in SU2 x f/1? occurs if all SU2 •'• U\ breaking is due to Higgs doublets (this is expected in superstring models). The free parameters are sin2#w, Afz,, anJ 0. Mz, is related by where Mo - Mw / cos 8w would be the Z\ mass in the absence of mixing, (b) The unconstrained Higgs case. This is the analog of p =£ 1 and occurs if there are Higgs 2 triplets, etc., with significant VEV's. In this case sin 0jy, M^, M^O, and 0 are all arbitrary. The 90% c.l. lower limits on the Z2 masses for the constrained and unconstrained cases, respectively, are 273 and 249 GeV (Zx), 154 and 151 GeF(Zv,), 111 and 112 GeV{Zrj), and 325 and 343 GeV {ZLR, the extra boson which occurs in SU2L X SU2R X U\ models.) Except for Z^, the limits show a modest but not dramatic improvement over those in Ref. 10 (which was based on a much earlier data set). The 90% c.l. lower limits on Mz2 and 0 range are shown for Z{0) as a function of cos (3 in Figure 5. I0i must be smaller than ~ 0.05 except for a small region near the Zn. The relative - 217 - -z 400 — CONSTRAINED 300 — UNCONSTRAINED 100 in c o o CD Figure 5: Lower limits on Mzn and allowed 0 range (both at 90% c.l.) for an Ee boson Z(P) = cos/? Zx + sin/? Z$ for constrained and unconstrained Higgs. The special casesZx, Z^, and — Zn are indicated. - 218 - weakness of the constraints on Z2 is due to the fact that most theoretically favored extra Z's tend to couple fairly weakly to the ordinary quarks and leptons (and more strongly to exotic fermions such as heavy Majorana neutrinos). At the present time the indirect limits on heavy Z's (with A ~ l) from the neutral current1" are somewhat more stringent10'11 than limits from direct searches + pp —> Z2 + X, Z2 -> / /~ at the SppS except for a small region in /? near the Zn. This situation will presumably change in the near future: for example, the FNAL pp collider should be sensitive to bosons up to around 400 GeV and the SSC would be sensitive up to 1 — 2 TeV. III. Conclusions The weak neutral current (including the W and Z masses) has long been a major quantitative test of the standard model. A number of recent high precision exper- iments allow even more stringent tests of the model and limits on deviations. We have made a careful analysis of existing neutral current data, attempting to use the best possible theoretical expressions for each reaction, to make realistic estimates of theoretical uncertainties, and to treat similar experiments in a uniform way. Our major conclusions are (a) There is no evidence for any deviation from the 2 standard model, (b) A global average to all data yields sin 0W = 0.230 ±0.0048. (c) This corresponds to the MS definition sin2 Ow{Mw) = 0.228 + 0.004, which is larger by about 3cr than the prediction 0.214^o!oo4 °f minimal SU$ and other "great desert" models (the discrepancy is worse for larger mt), and closer to (though still some- what below) the prediction (~ 0.237) of many supersymmetric GUTS, (d) Allowing p = M^/(M§ cos2 Qw) to vary, one finds p — 0.998 ± 0.0086, which is impressively close to unity and which places upper limits of 5 - 8% on the vacuum expectation values (relative to the ordinary Higgs doublet) of many nonstandard Higgs represen- tations, (e) The radiative correction parameter 6w is determined to be 0.112 ±0.037, consistent with the expectation 0.106 for mt ~ 45 GeV and establishing the existence of radiative coi rections at the 3 o level, (f) The radiative corrections are very sensi- tive to mt and the mass splittings between additional quarks or leptons. Consistency of the various reactions requires mt < 180 GeV (90% c.l.) for MH = 100 GeV, as- suming no (compensating) new physics beyond the standard model, (g) Most of the In some models comparable limits have been obtained12 from electroweak radiative corrections to charged current data. - 219 - uq,ut, and eq neutral current couplings are now determined uniquely and precisely. (h) At present the weak neutral current (and the W and Z) give the best limits on the masses and mixings of many theoretically popular additional Z bosons, but the limits (typically 120 - 300 GeV) are still relatively weak. REFERENCES 1. U. Amaldi, et al., to be published, and references theirin. 2. S. Weinberg, Phys. Rev. Lett. 19, 1264 (1967); A. Salam in Elementary Particle Theory, ed. N. Svartholm (Almquist and Wiksells, Stockholm, 1969) p. 367; S. L. Glashow, J. Iliopoulos, and L. Maiani, Phys. Rev. D2, 1285 (1970). 3. CDHS: H. Abramowicz et al, Phys. Rev. Lett. 57, 298 (1986). 4. CHARM: J.V. Allaby et al, Phys. Lett. 177B, 446 (1986). 5. CCFRR: P.G. Reutens et al, Phys. Lett. 152B, 404 (1985). 6. FMM: D. Bogert et al, Phys. Rev. Lett. 55, 1969 (1985). 7. CHARM: F. Bergsma et al, Phys. Lett. 147B, 481 (1984). 8. BNL E734: L.A. Ahrens et al Phys. Rev. Lett. 54, 18 (1985). 9. J. E. Kim, P. Langacker, M. Levine, and H. H. Williams, Rev. Mod. Phys. 53, 211 (1981). 10. L. S. Durkin and P. Langacker, Phys. Lett 166B, 436 (1986). 11. D. London and J. Rosner. Phys. Rev. D34, 1530 (1986); E. Cohen et al., Phys. Lett. 165B, 76 (1985): J. Ellis et aL, Nucl. Phys. B276, 14 (1986); V. Barger. N. G. Deshpande. and K. Whisnant, Phys. Rev. Lett. 56, 30 (1986); Phys. Rev. D35, 1005 (1987); J. Rosner, Comm. Nuc. Part. Phys. 14, 229 (1985); F. del Aguila et al., Nucl. Phys. B283, 50 (1987) and CERN 4505/86, 4536/86: P. J. Franzini and F. Gilman, Phys. Rev. D35, 855 (1987). 12. W. J. Marciano and A. Sirlin, Phys. Rev. D35, 1672 (1987). - 220 - SECOND CLASS CDRRENT EFFECTS IN TAD LEPTON DECAY? M. Derrick Argonne National Laboratory INTRODUCTION About thirty years ago Weinberg classified the weak charged current according to its G-parily transformation properties. One, that we now know is the dominant interaction and that forms the basis of the Standard Model, was called first class (FC). This current behaves under the G parity operation as: GVG = V and GAG = -A, where V and A stand for the vector and axial vector components of the hadronic weak current. A second possibility was a current that behaved oppositely under the G parity transformation: GVG = -V and GAG~ = A. Such currents were called second class (SC). The corresponding weak form factors would be dominated by the following mesons: Current Meson J G F.C. V P 1" + + F.C. A a.,(1270) 1 + S.C. V aQ(980) 0 + S.C. A b.,(1235) 1 + Since the axial current is only partially conserved, there is also an induced pseudoscalar form factor that is dominated by the pion pole. Many experiments in 8 decay, in muon captive and in neutrino interactions have searched for evidence of such effects but with no lasting result. The nuclear physics experiments have little sensitivity to the second-class vector current, but give upper limits to the second-class axial current, which corresponds to a tensor form factor, of about 20% of the weak magnetism term. Absolute conservation of the vector current in CVC requires that such a second-class current, which leads to a scalar Zorm factor, be zero, although small isospin breaking effects are expected from a u/d quark mass difference. S. Weinberg, Phys. Rev. 112, 1375 (1958). L. Grenachs, Ann. Rev. Nucl. and Part. Sci. 35^, 455 (1985), 3 B. Holstein, Phys. Rev. C29, 623 (1984). - 221 - NKOTRIHO EXPERIMENTS High sensitivity experiments at high momentum transfer are required to see the effects of SCC since such currents, if they exist, are weaker than the FCC and since they are proportional to momentum transfer. Possibilities of such experiments obviously exist at BNL with the high-intensity neutrino beam. The challenge is to find evidence for the second-class form factors when the Fig. 1. Quasielastic and nucleon resonance production in Meson P, a.,, ( f) (ao,b.,, ?) neutrino scattering. N,A main experimental features of quasielastic scattering and nucleon resonance production are dominated by the first-class currents and the P and a^ poles. One possibility is to measure the nucleon polarization Which, as shown in Fig. 2, can change by factors of two at medium Q for a tensor form factor half as large as the normal axial term. Fig. 2r. Predicted nucleon polarization for the reaction vn •+• \i p at 1 GeV (Ref. 5): Curve (b) is with no SC axial current; curves (a) and (c) cure for a SCC with half strength compared to the wea£ magnetism term. B7IDEHCE FROM TAB LEPTOH DECAY More sensitive searches have become possible in the last few years with the collection of many thousands of examples of tau lepton decay. In t-his case, the experiment is done in the s channel and the final state meson can be searched for directly as shown in Fig. 3. S. J. Barish et al., Phys. Rev. D16, 3101 (1977). M. Derrick, Proceedings of the Sixth International Conference on Electron and Photon Interactions at High Energies, Bonn (1973), Ed. H. Bollnik and W. Pfeil, Worth Holland (1974), p. 369. - 222 - Fig. 3. Tau decay. The high tau mass of 1.784 GeV also increases the sensitivity as compared to a typical Q of 0.5 GeV2 that dominates the quasielastic neutrino scattering. The One-Prong Anomaly in Tau Decay The principal decay modes of the tau are quite well known/ as shown in Table I - which was compiled for the Berkeley conference.6 The branching ratio of 6.4 + 0.4 for the iT-p TP final state is taken to be equal to that measured for Table I Tau Decay Branching Ratios Decay Mode Dominant Branching Fraction % T + Resonance One-Prong Three—Prong e V V 17.9 ± 0.4 e T v" V V 17.5 + 0.3 V T V iT 10.9 ± 0.6 " X iT TP p" 22.1 + 1.1 VT -1- 3TI"• v a" 6.4 ± 0.4 T 2TT a^ (6.4 ± 0.4) 5.2 ± 0.5 K~VT 0.7 ± 0.2 (Kir)"VT K*(890) 1.1 ± 0.3 (KKU)-Vx 0.22 + °^]] °-»:°o:;? Total 76.6 + 1.5 12.7 + 0.7 P. Burchat, Santa Cruz preprint SCIPP 86/72. - 223 - the TT TT+TT final state by isospin invariance since the three-charged final state is dominated by the a., (1270) resonance. The decay modes; involving K mesons are small as expected from the Cabibbo angle. The topological branching ratios for the tail decay are well measured and 4 are: B-, = 86.6 ± 0.3%; B3 = 13.2 ± 0.3%; B5 = (10.2 ± 2.9) 10~ ; B? < 1.9 • 10~^. The value of B^ = 13.2 + 0.3% agrees wif- the sum of the individual three-prong decays of 12.7 + 0.7%, given in Table I, but this is not the case for the one-prong topology where there is a deficit of decays that have not been identified amounting to 10 ± 1.5%. This is a large anomaly, particularly since the measured modes agree well with simple theoretical expectations. A number of recent experiments have addressed this missing one-prong issue. 8 +1.9 The TPC collaboration reports a branching ratio of (13.9 ±2.0 ".,)% for the decays T -»• TT v + multiple neutrals. The data can be interpreted as a i weighted sum of the three modes: B „ + 1.6B _ + 1.1B „ , where rT2n° Tr"3-n° TTTPT\ B B A = 1I-.non * n * neutrals' similar analysis by the MARK II collaboration gives the individual values: B = 6«2 ± 0.6%/ if 2 if B r, = ° + n'4%an d B r, = 4'2 + i*9%- If B „ is set to 6.4 ± 0.4% deduced from the three-charged particle decay of the a^, then the TPC data i gives 1.6 B + 1.1 B = 7.5 ± 2.8%. it 3 TT° TF ir° n O 10 The rate for the decay T~ •* TT3TI V)T has been estimated by Gilman and Rhie from the e e annihilation cross sections to four charged pions in the T mass energy region. Specifically, CVC gives the following relationship: r(t~ + TT"3ITOV ) mT + - + - T 3 r 2,2 22,2 2x2a(ee+2TT2Tr) = m —: — > e (% - e ' < T + 2Q )dQ en + e v VT) 2*0. m" 0 See, for example, C. Akerlof et al., Phys. Rev. Lett. _55_, 570 (1985) H. Aihara et al., Phys. Rev. Lett. _5_7_, 1836 (1986). ^ K. K. Gan et al., SLAC preprint 4110 (1987). F. J. Gilman and S. H. Rhie, Phys. Rev. D31, 1066 (1985). - 224 - The cross section for ee •»• 2T 2T is well measured from threshold up to the T mass, as shown in Fig. 4(a), and these results give T( T •*• TT 3 7r v )/ F(x~ + e" v ) = 0*055, or a branching ratio for T •*• IT 3it°v of slightly less than 1%. The TPC measurement then implies B_ = 7.6 ± 2.8%, in agreement 1 rn with the value of 4.2 •.*-,* given by the MA^UC II group. I.4 I.6 0 (GeV) Pig* 4. Energy dependence of the cross section for: (a) e e "*" 2 IT TT (Ref. 10), (b) e+e" + nir+iT (Ref. 16). Both of these analyses were done ignoring more complicated final states such as T~TinvT, IT" nir° 11° vT. The low values for the five-prong decay modes, measured by the HRS collaboration11 of B, , = (5.1 ±2.0) 10~4 and °TT- = B +o (5.1+2.2) 10 , severely limit the branching ratios for these higher multiplicity final states. Because of the 1 "*" if ^ n decay, an upper limit to B of 0.3 ± 0.2% can be estimated since only three of the six events of 5^TT° observed by the HRS group have two T+T~ mass combinations below 415 MeV. In a similar way, an uoper limit to B of 0.18 + 0.03% 11 B. G. Bylsma et al. , Phys. Rev. D_ (April 1987) 12 P. Burchat et al., Phys. Rev. D35, 27 (1987). - 225 - can be estimated since isospin conservation predicts B < B . IT" r\tP TP ~ TT t]ir TT~ We conclude that MARK II and TPC experiments give indirect indications of a substantial branching ratio for the decay T •* TT n« \>T, which goes far to solving the one-prong anomaly. Direct Observations of n Meson Production in "Eau Decay Two experiments have presented direct evidence for n meson production in tau decay by the observation of a peak in the YY effective mass. The HRS experiment, done at /s = 29 GeV, has an integrated luminosity of 300 pb . The selection of T pair events is quite straightforward at this energy. The standard cuts yielded 4004 events in the 1-1 topology and 2553 events in the 1-3 topology. The analysis depends on reconstructing n •*• YY decays via measurement of electromagnetic showers in the barrel shower counter. Each of the 40 wedge- shaped modules consists of three sections: a 3X Pb-scintillator sandwich, a single-layer, 14-wire proportional chamber (PWC) in which the wires are + aligned along the e e~ beam direction and finally an 8XQ Pb-scintillator sandwich. The PWC plane is at a radius of 2.03 m from the interaction point. Each of the two scintillator sections is read out by two phototubes, one at each end of the approximately 3 m long modules. The energy resolution i K ' 0 16 2 is l~gj = ~*~g— + 0.06 with E in GeV. The positions of the electromagnetic showers along the beam direction, z, were measured by current division in the PWC wires to an accuracy of ~ 2.5 cm. Since the expected momentum spectrum of 1 mesons is hard and since photons from high T° decays almost always hit the same shower counter module, we show in Fig. 5(a) the YY mass spectrum for combinations where: (i) the photons hit separate modules, (ii) Ey > 1 GeV for both clusters, and (iii) no other photon shared the same module. A significant signal is seen both at the TP and at the TI mass. The data have been further divided into a low and a high energy sample with Ey^ + Ey2 less than or greater than 4.5 GeV. As expected, the 1 signal persists in the YY mass plot for the high energy data of Fig. 5(c), but is less prominent in the low energy spectrum of Fig. 5(b). The T° production populates the latter spectrum primarily because of the requirement that the two-photon clusters occur in separate modules: a module spans an azimuthal angle of 9°. ' M. Derrick et al., ANL-HEP-PR-86-106. Phys. Lett., to be published. - 226 - To study whether the one-prong T-decay events come from the ir nv or TT+nirO"v final states, the data of Fig. 5(a) were subdivided into 229 events with two and only two neutral clusters (Fig. 5(d)) and 145 YY combinations from 113 events with tiree or more neutral clusters (Fig. 5(e)). A minimum energy .:.'t of 100 MeV was applied in defining a separate cluster. The enhancement of the n mass in the inclusive data persists in the events with only two photons, whereas there is no significant signal for n^. > 3 selections. Photons from the n nir°"^ final state can be missed either because 200 400 6oo 8oo ;ooo Mry(MeV) 1 v and Pig. 5. Effective mass of YY system for events with EY1, E^2 > Ge having the photons in separate modules: (a) all combinations; (b) combinations with E-y] + Ey2 * 4°5 GeV; (c) combinations with E^ + Ey2 > 4.5 GeV; (d) events with two and only two photon clusters; (e) events with thres or more photon clusters. The lines show fits to a smooth background function, plus contributions at the T° and n masses. - 227 - they hit the cracks between modules or because they are coalesced with other photons in the event. Monte Carlo and other studies indicate that such effects are small - at about the 7% level. The 2Y data of Fig. 5(d) is therefore evidence that the Tr nv final state is being observed. The corresponding decay branching ratio is (5.1 ± 1.0 ± 1.2)%. The CRYSTAL BALL (CB) collaboration has presented evidence for inclusive H production in tau decay using data taken at the DORIS storage ring at about vs = 10 GeV. Figure 6 shows the YY mass spectrum after removal of photons that are within 3 a of the u° mass. There is a peak at 550 ± 4.3 MeV with a width of 20 + 4.1 MeV that shows n production at a significance level of 5.5 0. if the final state is assumed to be ft nn v^, then the corresponding branching ratio is (7.5 ± 1.2 + 2.5)%. The events observed in the CB seem to have additional photon activity so the two direct observations are not obviously compatible, although they do agree that A production in T decay is substantial. uoo.o 300.0 200.0 Fig. 6. Effective mass of the YY system in the CRYSTAL voo.o BALL experiment. 0.0 o.t 200.0 VOO.O GOO.O 600.0 1000.0 lM«V/c»] r The quantum numbers of the it in the u rn»T final state are G = - and J = 0 , 1 so the decay manifestly occurs through a second-class current. For + P the x i nir vt decay, the G parity is even but many J combinations are possible. However, the final hadronic state, consisting of a P and an 1 in a relative p wave can have J = 1 that corresponds to the allowed FCC. Such a decay could proceed through the intermediary of the P(1600) resonance. However, a photoproduction experiment shows no evidence for this decay and gives a limit for the branching ratio of (p(1600) -»• nir ir /p(1600) + all j of less than 2%. 14 M. Gilchrise, Review talk given at Berkeley meeting (1986) and S. Ksh et al. (CRYSTAL BALL Collaboration) (to be published). 15 M. Atkinson et al., Z. Phys. C30, 531 (1986). - 228 - Comparison with @+e~ * if1"* n The conserved vector current again allows an estimate of the branching ratio + P for the allowed x~ ir~Tnt°vT decay to a J = 1~ final state from the measured cross section for e+e~ "*" n if" n. Figure 4(b) shows the data for this e+e~ cross section in the appropriate energy range. The corresponding value for B is ~ 0.25%, much lower than the inferred results from the TPC and MARK II groups, and from the direct measurement of the CRYSTAL BALL collaboration. This comparison indicates a strong violation of CVC as does the HRS observation of the forbidden decay T~ "*• T~nvx. Search for Second-Class Axial Currents The ARGUS collaboration17 has studied the decay T~ + if IT IT TT° V^; their value of (4.2 + 0.5 + 0.9)% for B , is lower than, but in agreement with, 2 TT~ ir TT° 5.2 ± 0.5% given in Table I. The IT f IT mass spectrum, shown in Fig. 7(a) has a strong uP signal corresponding to B_ = (1.5 ± 0.3 ± 0.3)%. 1 OMeV/c: 40 • ARGUS 30 r 20 r h 10 0 i- 0.5 1.0 1.5 Moss r-7T-jT° [GeV/c2] Fig. 7. (a) Effective mass of ITv v° system for t -»• IT" n TT ir°v . (b) Distributions of normal to W decay plane with respect to the batchelor pion as compared to the expectation for different JP values of WT system. 16 B, Delcourt et al., Phys. Lett. 113B, 93 (1982); V. P. Druzhinin et al., Phys. Lett. 174B, 115 (1986). 17 H. Albrecht et al., Phys. Lett. 185B, 223 (1987). - 229 - T This IT TI TT mass spectrum shows no evidence for the decay * * 0VT , which, on the face of it, is in disagreement with the HRS result. However, in the latter experiment, the detection efficiency is a strong function of 3n mass being about six times lower at 550 MeV than at 785 MeV. The acceptance depends on the details of the experimental equipment and so a limit on T~ -s- ir~nvT from the data of Fig. 7(a) can only be given by the ARGUS collaboration themselves. The CRYSTAL BALL measurement can also be checked by the ARGUS data. To esttolish the spin-parity of the w w system, it is necessary to measure the distribution in the angle iff, which is that between the normal to the w decay plane and the batchelor pion in the w rest frame. The result, which is shown in Fig. 7(b) is completely consistent with J = 1~ although up to 50% of 1 , which corresponds to the second-class axial current, is allowed by the data. CONCLUSIONS Since the establishment of a second-class vector current would be a major contribution to physics and could be an indication of the so-far unexplored scalar (Higgs) sector, it is necessary that several experiments report the same results. This is not the case so far in the measurement reviewed here. However, several groups are actively pursuing this issue, and we can look, forward to an experimental clarification over the next several months. If it turns out that CVC is upheld and inclusive H production is no more than a fraction of a percent of tau decays, then the major mystery of the missing one-prongs will require further detective work. Work supported by the U.S. Department of Energy, Division of High Energy Physics, Contract W-31-109-ENG-38. 18 E. L. Berger and H. J. Lipkin, ANL-HEP-PR-87-0 5; C. K. Zachos and Y. Meurice, ANL-HEP-PR-87-09. - 230 - REPRODUCED FROM BEST AVAILABLE COPY Summary and Conclusions SUMMARY AND CONCLUSIONS F. S. Merritt The Enrico Fermi Institute University of Chicago INTRODUCTION This workshop has provided a good review of our current understanding of both the experimental and theoretical aspects of neutrino oscillations. But the most important topic, which I will concentrate on in this review, has been: What is the best way to discover neutrino oscillations? And the second topic, which has made this workshop particularly interesting, is: Have neutrino oscillations already been discovered? We now have conflicting indications from four different accelerator experiments, three of which are Brookhaven experiments. The discovery of neutrino oscillations would mean the simultaneous discovery of lepton non-conservation and non-zero neutrino mass. Because these are such very fundamental subjects, this would have an enormous impact on both theory and experiments over the next decade. Unfortunately, although the impact of this discovery might be very dramatic, the experimental signals appear to be at the 1% level or below. Since there is almost no theoretical indication of what the oscillation parameters might be, it will take at least a 3 or 4 sigma effect, probably from several experiments, to convincingly establish oscillations. It looks like we must rely on very precise measurements, with very good control of systematics, in order to discover oscillations or to push the limits much beyond where they are now. One of the chief benefits of a workshop like this is that it allows the different experimenters to confront each other's results, and to try to identify problems and ways of improving the measurements. I will spend most of this review in discussing the systematic errors of the experiments, and ways of resolving the discrepancies. I will concentrate on criticisms and problems since that is the point of the workshop. But I want to emphasize that the results presented here from E776 and E816 are more in the nature of status reports than final results, and should not be judged by the criteria applied to final results. - 233 - SOLAR NEUTRINO OSCILLATIONS There has been a discrepancy for many years between the predicted and mea- sured solar neutrino flux. The most recent values are: theory = 8.2 ± 2.5 SNU (3-sigma errors) and experiment = 2.1 ±0.3. Vacuum oscillations of ve —• v^ could account for a 50% difference if the mixing angle were very large (sin220 « 1.). The possibility of matter-induced oscillations (the MSW effect) has been dis- covered and investigated over the last year, and we have had an excellent presenta- tion of it here. The bottom line is that even more than a 50% suppression could be produced, even by small mixing angles (sin220 < 10~4) due to the varying matter density of the sun. This is a very beautiful and subtle effect, and it would be a shame if it didn't actually occur in Nature. However, I believe the view of most physicists is that there is still at least a 10% chance of a mistake in the solar model, or perhaps in some other aspect of the theoretical prediction, or possibly in the experiment. Until more of the neutrino spectrum is measured, it is impossible to draw 90% confidence level conclusions about oscillations. The situation might change in the next few years when we get results from the new Gallium experiments, for which the predictions are less sensitive to the solar model due to the lower energy of the detected neutrinos. Until then, the best measurements and limits on neutrino oscillations come from accelerator experiments. THE NEW ACCELERATOR OSCILLATION EXPERIMENTS We have had detailed presentations from four neutrino oscillation experiments. The results are summarized in figure 1. The contours from BEBC and E734 are 90% confidence levels, and exclude the regions above the contours. The results from E776 and E816 indicate a positive signal within the cross-hatched areas; these are 1-sigma contours. Although most of the cross-hatched regions are excluded by the other contours, none of the results are in drastic disagreement with oscillation parameters in the region of Am2 ss 5 and sin220 « .015 (which is just barely excluded by each of the four experiments). But no one *s suggesting that we change the Particle Data Book just yet. - 234 - 1000.0 I I -. 11 r i' | 100.0 10.0 rvl 0.1 _ a) PS- BEBC b) BNL-E734 c) BNL-E776 d) BNL-E816 /PS-191 0.01 I I * I 1 I I • 1 I 1 I I I • i • .0! 0.1 1.0 .001 z sin (z6) Figure 1: The four new oscillation results presented here;, a) and b) are 90%CL limits, excluding the region above the curves, c) and d) show positive signals within the cross-hatched regions (l-sigma contours). - 235 - In all of these experiments, there are two primary sources of background: 1) misidentification of final-state TT°'S as final state electrons, and 2) ue contamination in the beam. The most difficult problems in the analyses are in the determination of these subtractions and their uncertainties. I will review the analyses of each of the experiments, with emphasis on these systematic errors. BEBC This experiment ran in the CERN PS beam, using a 19.2 GeV proton beam with horn focusing to give an average neutrino energy of 1.5 GeV. The bubble chamber was located 825 m from the target, so the first maximum should occur for Am2 = 2.2 eV2. Separation between e and fi events was excellent, since an e in a bubble cham- ber produces several signatures. In this experiment, each electron was required to give at least two signatures. The identification probability for an e was estimated to be 95%, and the background due to mis-identified (i and p was negligible. After cuts, 470 v^ charged-current events were observed, with backgrounds of 24 ± 5 events. The number of electron events observed was 4, with a calculated background of 3 events due to ve contamination in the beam (corresponding to A% ue contamination in the flux); therefore no signal was observed. As a check, the measured energy of the 4 ue events was somewhat higher than that of the u^ events, as expected from the calculation of wide-band background. This limit appears to be totally dominated by statistical error. The uncertainty in the wide-band background calculation is perhaps 20%, small compared to the statistical error. E-734 This experiment has the advantages of higher statistics (due to a larger fiducial mass) and longer time for analysis relative to the other Brookhaven experiments. It has used the BNL wide-band beam (< Ej, > « 1.2 GeV) and is located 96 m from the decay pipe, so the first maximum occurs for Am2 ss 15 eV2. The detector consists of 112 planes of liquid scintillation counters interspersed with 224 planes of proportional drift cells (both x and y planes). It was designed io measure i/^e —• z/Me as well as v^p —* (i~p, so it can also identify uen —+• e~p - 236 - events. The oscillation measurement was made by measuring the ratio of final state e~p to n~p (quasielastic events only). There were 653 e~p candidates. A third of these were subtracted as due to various specific backgrounds, leaving 418 events. Most of this background subtrac- tion was based on the data itself, and the Monte-Carlo did not play an important role here. However, very different kinematic cuts were applied to the fip and ep events in order to get clean identification; the acceptance for fip was a factor of 10 less than for ep, and the relative acceptance correction introduced an uncer- tainty of 14% in the ratio. The resulting spectra after acceptance corrections were compared to the Monte-Carlo beam calculations, and agreed in spectral shape, normalization, and Q2 dependence; these comparisons are shown in figures 2 and 3 (taken from L. A. Ahrens et al., Phys Rev D31, p. 2732, 1985). Finally, the ut background was subtracted, assuming an estimated 20% error in the K/ir ratio, to get the final limits on e~p production. The 90% CL contour is completely dominated by systematic rather than sta- tistical uncertainties, with approxixaately equal errors of 14% each from the ac- ceptance correction and the ue background calculation. (a) 0.2 0*0 az a* ai o.e IJO t.2 a*i(G»v/«i*J HO. 3. The Q1 distributions te) v,n—*~p ud (W vltn-*H~p comtTBCted from Uw fully corrected dtt* of sets (i) •ad (ii) oompand with tbt tbeontictJ dulributioa (MA -1.03). The verticil icale ia in arbitrary units because Oq^E) has bees auumed in extracting the spectn of Fis> 2. —HO. 2. (p events. (b> - 237 - E-776 This is a new detector, built specifically to search for v^ —> vt oscillations; unlike the other experiments presented here, E776 uses a narrow band neutrino beam formed by a new two-horn focusing system. The mean secondary momentum is 3 GeV, giving a v^ spectrum with peaks at 1.27 GeV [un) and 2.91 GeV (i/#). The detector is located 1 kilometer from the decay pipe, giving a first maximum for Am2 « 1.6 eV2, similar to that of BEBC. Beam monitors measure the secondary flux and angular dispersion (but not the TTjK ratio). The detector consists of 90 planes of drift tubes(45 x and 45 y), separated by .25 radiation lengths of concrete. The drift tubes are read out using 6-bit flash ADC's; scintillator planes after each 10 planes of drift tubes are used for timing. Electron events are separated from muon events principally by the shower pattern as measured by the flash ADC's, using both the longitudinal and transverse shower development. The target is followed by a toroidal spectrometer, which measures muon momentum to 6p/p — 25%. Events with many tracks are difficult to reconstruct, so the group has presented results only for events with < 2 tracks. Events are classified as "electron" only if Ee > 700 MeV, 90% of the energy of the shower is contained within the Moliere radius, and there are no missing planes of drift tubes. Events are classified as "TT0" only if there are two clear showers, with a reconstructed mass of < 2m2. The number of observed events with a final state electron is corrected for calculated backgrounds due to mis-identified 7r°'s and to ut contamination in the beam. The excess, calculated in the table below, is interpreted as an oscillation signal. E776 RESULTS: 1-trk 2-trk Total Data: N(M) 606 263 869 N(e) 20 12 32 Electron backgrounds: misidentified 7r° 13 4 ue contamination 5 2 7 Electron excess: 14 7 21 - 238 - E776 has not quoted systematic errors, and so has presented a 3-4 sigma signal based on statistical errors only. However, it is impossible to know how to interpret this result without some estimate of systematic errors. I will assume that the omission of these errors indicates not that they are hardly worth mentioning, but rather that the reader is encouraged to make his own estimates. The background from misidentified n° events is calculated from the number of data events with an identified TT° (=4), and the ratio of Monte-Carlo v^ events which are classified as "TT0" (=9) to those classified as "e" (=7); this gives a background of 4 * (7/9) « 4. As yet, there is no definitive comparison of data and Monte Carlo to show that the Monte-Carlo is correctly modelling the ir°/'e separation, or even the total number of TT° events. The E776 group plans more extensive Monte-Carlo studies, and also plans to study identified ir° events from their wide-band run to study systematic errors in 7r°/e separation. But until these studies are done, we must consider the background of 4 events as only a rough estimate — the final background could easily be larger by a factor of 2 or more. From estimates of possible errors from members of the group, the sigma is probably in the range of 4 - 8 events; I will use ±5 as a best estimate of this error. The calculation of vt contamination in the beam has been carefully done, but again it is difficult to check this calculation directly against the data. It is somewhat surprising that the calculated v^jv^ ratio i? so similar to that of the other experiments, since the beams axe quite different. The best check of the calculation comes from comparing the observed energy spectrum of v^ events with the Monte-Carlo prediction, as shown in figure 4. The high-energy part of the spectrum is expected to be due to K —• fii/, and the data is about a factor of two higher than the Monte-Carlo. This might indicate that the K/ir ratio is underestimated by a factor of two, and consequently that the vt contamination from K —* itevc is also underestimated (the E776 group has instead assumed that the high-energy region in the data is due to tails from momentum resolution). This has led to the suggestion that the ue background be increased from 7 to 11 ± 4, and this is what I will assume. In any case, a « 30% error seems appropriate until the discrepancy in spectra is resolved. - 239 - DATA 1 ta • • • 4 • IUILB 1 U > U « U I Figure 4: Comparison of E776 v» spectra from data and Monte-Carlo. The diacrepancy above 2.5 GeV iuggMta a pombk prot^m in the K/x ratio. Finally, the relative acceptances of i/M and u, events is estimated to be w 1; I will arbitrarily assume 1.00 ±.15. Putting all three of these errors together gives a total background of {(4 ± 5) + (11 ±4)}(1.00 ± .15) = 15 ±6.8, and consequently a signal of 17 ± 5.7 ± 6.3, where the second (and larger) error is systematic. Adding the statistical and systematic errors in quadrature gives a total error of 8.9 events, and a signal of about 2 standard deviations. £-816 This experiment first ran in the CERN PS neutrino beam and reported a possible oscillation signal there. The detector has been moved to Brookhaven and has had one long run there. It is located just downstream of E734, at L=150m, so the first maximum occurs for Am3 « 10 eV2. The calorimeter consists of 10 planes of flash-tube chambers separated by 3 mm steel plates. Each cell is 5 mm x 5 mm, and adjacent planes are separated by .17 radiation lengths. The 10 target planes are followed by a hodoscope, used for triggering, and this is followed by an additional 30 planes of flash-tube-Fe modules like those in the calorimeter. An important aspect of the detector is that the flash tubes are all parallel, so that only the vertical projection of each event is measured. Because of this, - 240 - one-track events (like the quasi-elastics used in E734) cannot be used — a stray charged particle entering the sid* of the detector could mimic a one-track event. There must be at least two tracks in order to determine a vertex, so to look for an oscillation signal the group has compared "one-track, one-shower" events (from ue) to "two-track" events (from Uy). Electromagnetic showers are rather easy to identify because of the fine-grained sampling. Electron events are identified by a shower which begins at the event vertex. Backgrounds from 7-induced showers are determined from the data by using "disconnected" showers (those that begin downstream of the vertex) due to 7's that travel through a distance D of at least one module (.17 radiation lengths) before showering. The distribution of the disconnected events is extrapolated to D=0 to get the background to the e signal. The vt excess observed in 1T1S events is shown in figure 5-a below. As a control sample, "two-shower" events, due to ir° production, are shown in figures 5-b and 5-c. The spike at D=0 in the 1T1S plot has contributions from ir° -*• -77 (determined froxn the extrapolation) and from vt contamination in the beam (determined from the standard wide-band calculations). The oscillation signal is found by subtracting these: E816 Results: Total electron events (D=0) = 93 Extrapolated ir° events = 31 u contamination = 27 Excese s electron signal = 35 The Monte-Carlo program has been used to simulate the data and to obtain the 1T1S, 2S(both), and 2S (closest) curves, as shown in figure 6. This indicates that the extrapolation method indeed works, and the Monte-Carlo qualitatively agrees with the data. However, the quantitative agreement between data and Monte-Carlo does not seem so good. One feature in particular of figure 5 seems disturbing: if the disconnected events in figure 5-a are due to 7r°'s with overlapping showers, then one would expect the exponential slope in this plot to be the same as that of figure 5-c. This appears to be borne out by the Monte-Carlo simulation shown in figure 6, but in - 241 - Figure 5: "Disconnection" plots of the separation between event vertex and beginning of shower, for (a) 1-track, 1-shower events, (b) 2-shower events (both showers plotted), and (c) 2-shower events, with only the closest shower plotted. a t* i. O D Figure 6: Same as figure 5, but plotted from a Monte-Carlo simulation. - 242 - the data the 1T1S slope is significantly smaller than the 2S(closest) slope. This may be an important issue, since a larger slope would give a larger intercept in figure 5-a, and consequently a smaller oscillation signal. Moreover, it looks like fitting only the six left-most points would give a bigger slope, agreeing better with the 2S(closest) slope, and also would give a higher intercept. Is it possible that the events with D>2 are in part due to some kind of background (e.g., 1-track events in coincidence with an electron or photon entering the side of the detector downstream) ? Also, one would naively expect the slope of figure 5-b to be exactly half that of 5-c, assuming that both 7's have the same conversion length. This appears to be about right in the data, but not in the Monte-Carlo. What effects determine these slopes? Much higher Monte-Carlo statistics would help in understanding the expected relationship between the three slopes, and this might help a lot in understanding the data. In addition to the fits presented, one would like to see a simultaneous fit of the 3 data plots, with relative slopes constrained to agree with a high-statistics Monte-Carlo. By making &n eyeball fit to the six leftmost points in figure 5-a, I get an intercept of 41 instead of 31, and on this basis I will assume a systematic error of ±10 for the intercept, in addition to the statistical error of ±4.. If we also assume a 20% error in the ue background calculation, this gives a total systematic error of ±12 events. Adding this in quadrature with the statistical error gives a total error of ±15 events and a 2.3 sigma signal. Fortunately, only 1/3 of the data has been analyzed so far, so we can expect a considerable improvement in statistics, which will allow more detailed studies of systematic effects and better checks between data and Monte-Carlo. Conclusions Systematic errors are important in all of the Brookhaven experiments, and in both E776 and E816 there are additional checks and studies that have to be made before we have final results. I don't think either experiment has an effect as large as 3 sigma at this time, and it would be highly premature to say that a definite oscillation signal has been seen. It is quite possible that backgrounds and the oscillation signals will change by more than one sigma with more detailed - 243 - analysis. On the other hand, no obvious mistakes have appeared at this workshop. Even with possibly pessimistic assumptions about errors, both of the new experiments show at least a 2-sigma excess of z/e events. There is no reason to believe that the effects will soon disappear, and there is every reason to believe that errors will become smaller over the next year in both of the new experiments. The situation will probably become clearer if the experimenters make a serious effort to compare the individual steps in their analyses, and to make as many cross- checks as possible. Efforts in this direction are already underway. Some specific ways in which comparisons can be made have been suggested: 1) E776 is starting on the analysis of their wide-band data. The high statistics of this are necessary for studying some systematic effects such as the separation of TT° and e events. This will also make it easier to compare their analysis to that of the other experiments. For example, it would be interesting to see if their calculation of vt contamination in a wide-band beam agrees with that of the other groups. This would help to eliminate any doubts about the calculation of t/e background in the narrow-band beam, particularly if the E776 group presents a detailed comparison of the two beam calculations. 2) Each group should present their acceptance for i/M and ue events as a func- tion of Ev, as well as their calculated incident fluxes. This would help in evaluating relative acceptance errors, and also would make it much easier to compare the cal- culations of ue background. For example, even though E734 and E816 have both presented calculated spectra, I have been unable to convince myself that their cal- culations of vt contamination are consistent at the 20% level. I would like them to make it easy to do this, or make the comparisons themselves. This could virtually eliminate vt contamination as a source of discrepancies between experiments. 3) The E734 data has used quasi-elastic (one-prong) events while the E816 analysis has used multi-track events. E734 will use their data to do an E816- type analysis, and this will hopefully allow for a close comparison between the two experiments, as well as a good comparison of problems in multi-track versus single-track data. E734 also took data during the last E816 run, and is working on analysis of that now. - 244 - 4) I hope all three experiments will present a more detailed analysis of n° events, including their acceptance for identifying a two-shower disconnected event and for misidentifying a 7r° as an electron, both as a function of energy. This might help a great deal in reducing TT° background as a possible source of discrepancy. Even if the errors are reduced and the significance of the signals in both E816 and E776 are improved, I do not believe that these experiments alone will consti- tute a convincing proof of neutrino osciliations so long as we still have the BEBC and E734 limits to contend with. However, the new experiments may give a strong enough indication of oscillations so that a new experiment, designed to thoroughly explore the regions indicated, will be a very high physics priority. POSSIBLE FUTURE OSCILLATION EXPERIMENTS A Two-Detector Oscillation Experiment The largest errors in the Brookhaven experiments are from ue contamination and from misidentified 7r°'s (and perhaps also in relative ue and v^ acceptance). The errors from these two beckgrounds are comparable, and to make a signifi- cant improvement in the oscillation measurements, both sources of error must be reduced. The most reliable way of simultaneously reducing both of these is to build two identical detectors located at different distance from the decay pipe, possibly at the locations of the present E816 and E776 detectors. We can think of the upstream detector as being a monitor of both TT° identification and of vt contamination. An oscillation signal would appear as a difference in the i/g/t/^ ratio between the detectors. Moreover, if a narrow band beam is used, this ratios should change as a function of beam energy in a specfic way. This tests the fundamental oscillation phenomena — that the neutrino identity change as a function of distance — and I think it is the only totally convincing way of measuring a small oscillation signal. The strongest requirement for the two new detectors is that they be the same, so that systematic effects cancel. This technique has been used at Fermilab and CERN in u^ disappearance experiments, and the relative rates in upstream and downstream detectors could be calculated to a quoted error of about 1%. Beyond this, one would obviously like to have the best possible ir°/e and 7r+//i separation in both detectors. The two-detector experiment would require a great deal of - 245 - running time because of the limited flux at the downstream detector, but all of the systematic errors that have been mentioned would be dramatically reduced. Even if the present indications of oscillations go away, a two-detector experiment is still probably the best way to improve limits in the small sin220 region. A Tagged Neutrino Beam This facility would use a neutral wide-band beam to produce similar fluxes of tV, Vp, ue, and vt from Ki decays. Both the type and the energy of each neutrino can be determined from measurements of the charged pion and charged lepton from the decay. This would greatly reduce the uncertainties in beam composition (e.g., ue background in oscillations of vu), and would simultaneously give measurements in four different neutrino channels. There are two problems with such a facility that need further study. First, it does not address the problems of 7r° Ve confusion. From the present E-776 and E-816 analyses, it appears that this background may be similar in size to the vt background. In that case, eliminating the vt background would only reduce Q errors by a factor of \<2. Perhaps the TC /ue background can be reduced in the present detectors or in new detectors, but in any case it must be considered in evaluating the tagged beam facility. Secondly, the rates from tagging are much less than those of a conventional beam. Although the interaction rate in the E-734 detector has been calculated to be a few thousand in a run of 2xlO19 protons, this will be reduced by necessary kinematic cuts. If a tagged beam is used with a two-detector experiment, then the statistical error wiil be determined by the rate in the downstream detector, and this will mean an additional large reduction in statistics. Long Baseline Experiments Mike Murtagh has presented a study of long baseline experiments; his con- clusion is that a baseline of up to 8 km is feasible, and would extend the region of sensitivity in Am2 by a factor of 10 for a reasonable amount of running time (10 protons on target). Such an experiment is probably the only way to explore the lower Am2 region, and this might be the best route to take when the present situation with E-776 and E-816 is resolved. - 246 - But from figure 1, the region that most nearly compatible with all four ex- periments is sin220 ^ .1 — .2 and Am2 % 2 — 6 eV2. The baseline needed to explore this region at Brookhaven energies is in the range 0.1 - 1.0 km. From the data presented at this workshop, that appears to be the most important region to explore in the next round of oscillation experiments. - 247 - LIST OF PARTICIPANTS Robert K. Adair, Brookhaven National Laboratory Pierre Astier, University of Paris Neil Baggett, Brookhaven National Laboratory Milla Baldo-Ceolin, University of Padua Anthony Baltz, Brookhaven National Laboratory Stephen Barr, Brookhaven National Laboratory Gregorio Bernardi, Boston University Steven Biller, U. of California, Irvine Barry Blumenfeld, Johns Hopkins University Furio Bobisut, University of Padua Gerhard Buhler, U. of California, Irvine Alan Carroll, Brookhaven National Laboratory* Jacques Chauveau, College de France Augustine Chen, Fermi National Accelerator Laboratory Cheng-Yi Chi, Columbia University, Nevis Labs Chin-Yung Chien, Johns Hopkins University Tina Chrysicopoulou, Boston University George Cowan, Los Alamos National Laboratory Raymond Davis, Brookhaven National Laboratory Malcolm Derrick, Argonne National Laboratory Milind Diwan, Brown University Peter Doe, U. of California, Irvine Jacques Dumarchez, University of Paris Lisa Duncan, Johns Hopkins University L. Stanley Durkin, Ohio State University Eric Forsyth, Brookhaven National Laboratory Stephen Godfrey, Brookhaven National Laboratory Gertrude S. Goldhaber, Brookhaven National Laboratory Maurice Goldhaber, Brookhaven National Laboratory Howard Gordon, Brookhaven National Laboratory Jacob Grunhaus, Johns Hopkins University William Hogan, University of Illinois Peter Jack, Columbia University, Nevis Labs Drasko Jovanovic, Fermi National Accelerator Laboratory Stephen Kahn, Brookhaven National Laboratory Chung Kim, Johns Hopkins University Nicholas Kondakis, Columbia University, Nevis Labs John Krizmanic, Johns Hopkins University Paul Langacker, University of Pennsylvania Robert Lanou, Brown University Donald Lazarus, Brookhaven National Laboratory Wonyong Lee, Columbia University, Nevis La'~s* Jean-Michel Levey, University of Paris Chong-Sa Lim, Brookhaven National Laboratory Eric Linke, Johns Hopkins University Lee Lueking, Johns Hopkins University William Lyle, Johns Hopkins University Leon Madansky, Johns Hopkins University W. Anthony Mann, Tufts University William Marciano, Brookhaven National Laboratory* - 248 - Frank Merritt, University of Chicago Michael Murtagh, Brookhaven National Laboratory* Yorikiyo Nagashima, Osaka University Edward O'Brien, University of Illinois Thomas O'Halloran, University of Illinois Zohreh Parsa, Brookhaven National Laboratory Aihud Pevsner, Johns Hopkins University Kevin Reardon, University of Illinois Jack Ritchie, Stanford Linear Accelerator Center Brad Rubin, Columbia University, Nevis Labs Nicholas Samios, Brookhaven National Laboratory Jack Schneps, Tufts University Richard Seto, Columbia University, Nevis Labs Michael Shaevitz, Columbia University, Nevis Labs Paul Sheldon, University of Illinois Jack Smith, SUNY, Stony Brook James Stone, Boston University Chris Stoughton, Columbia University, Nevis Labs Gregory Sullivan, University of Illinois Hiroshi Takahashi, Brookhaven National Laboratory Anne-Marie Touchard, University of Paris George Tzanakos, Columbia University, Nevis Labs Francois Vannucci, University of Paris/Boston University* Thomas Weiler, Vanderbilt University Joseph Weneser, Brookhaven National Laboratory V. Zacek, CERN *Organizing Committee - 249 -