- 55 -

CHARGED CURRENT OF POLARIZED MOONS

G. Smadja and G. Vesztergambi*)

DPhPE, CEN-Saclay, 91191 Gif-sur-Yvette Cedex, France

(Paper was presented by G. Vesztergombi)

ABSTRACT The polarization of the muon beam can be used to test the presence of right-handed couplings in charged current interaction of muons in process /*.+Jf-*v+ X. The experimental feasibility and the limits which can be obtained on the mass of right-handed inter• mediate are discussed.

1. INTRODUCTION At first glance it seems to be hopeless to detect charged current weak interaction of muons, because the typical electromagnetic cross-sections are about a million times larger even at an incoming muon energy of several hundred GeV. One should not forget, however, some remarkable merits of the muon beam.

a) Energy Due to the kinematic properties of pion decay the average energy of muons is 3 times higher than the one of . This may turn out to be rather important. On one hand, the weak cross-sections are linearly proportional to the beam energy and on the other hand the energy can be critical in presence of thresholds. In addition, the incoming muon energy can be preselected which provides more flexibility in the study of threshold phenomena.

b) Helicity Due to their extremely small (if any) mass the helicity of neutrinos is uniquely pre• determined. In case of muons one can select helicity at will. This provides an unique possibility to look for such type of weak interactions which are impossible in case of neutrinos as it was noticed by K. Winter^. Namely, if the pion momentum is denoted by

pv then the decay muon with momentum

pFORW ^ (forward decay in tr-system) will have "unnatural" helicity (i.e. opposite to the helicity of the with the same lepton number). One can get "natural" helicity selecting muon momenta BACK 2 2 p^ » (m^/m^-p^ (backward decay in ir-system). Thus if one is interested in normal left-handed interactions then the muon beam energy should be lowered relative to the parent pion energy. Even in this case it remains about a factor two higher than the average neutrino energy from the same pion decay.

c) Beam handling Beam phase space can be measured easily. The well collimated muon beam spot can reduce by order(s) of magnitude the required lateral size of the target and the interaction vertex is well identified.

Severe difficulties compensate the flexibility of muon beam.

x) On leave from the Central Research Institute for Physics, Budapest, Hungary. - 56 -

i) One needs ah extremely good (~10"<') hardware rejection against events which have a muon in the final state in order to catch weak fishes from the QED ocean.

ii) The final state is rather complicated. In absence of neutrino detection the relevant kinematic information should be extracted from the analysis of hadronic shower.

With modern experimental techniques these problems can be overcome in most of the kinematical range, thus at least in some areas muon experiments can challenge and/or complement neutrino experiments.

2. RIGHT-HANDED CURRENTS The theoretical interest for weak effects with "unnatural" right-handed polarization can be summarized in the following way: a) The dominantly V-A structure of weak interactions is well established at present ener• gies but the search for deviations should still proceed. b) The standard SU^(2) x U(1) model is highly asymmetric and unaesthetic. c) Right-handed neutrinos and intermediate seem to be one of the simplest candidates 21 which can "bloom" in the desert between 100 GeV and the grand unification mass 1. In the following we discuss the experimental possibilities to search for right-handed

neutrinos by muon beam in the framework of SUL(2) x SUR(2) x U(1) model. We start with a

"manifestly right-left symmetric" Lagrangian where WL and WR are coupled to V-A and V+A currents, respectively:

L W= CV+A)-WR + H.C.]

where e. g. CV + Al^v^^ijf,)^ or (V + A)^ ü^ft+^d. The combinations fV + hA)lep and (V + hA)^^ represent leptonic and hadronic currents having non-vanishing. matrix ele• ments between only définit helicity states. For simplicity, here and in the next we neglect masses and Cabbibo or KM angles ( h = +_ 1 ). That is in a given vertex the transition is

prohibited, for example between )UR(h =+1) and VL(h =-1).

The left-right symmetry of however is broken by an asymmetric vacuum. The Higgs potencial and the vacuum expectation values of the Higgs-fields are arranged to yield to mass eigenstates which are linear combinations of unmixed chiral eigenstates,

W.. = W.-cosi* - W„-sin$ \ ' L K . > for definiteness M„ > M„ = w sin "2' "T W + 2 L' í WR-cosl} The modified Lagrangian reads

= A cos h ^$z{ [N- í t -CV+A)siniî] W1 + [CV-A)sin4 +(V+A)cos^ ] W2 + H.C. | .

In case of left-handed v£ neutrinos (and also ju^) the (V+A) leptonic current does not give any contribution, in contrast with the hadronic current because (u, d) quarks are occuring always in left-right symmetric combinations inside the nucléons. Thus one gets the "left-handed" effective four- Lagrangian in the form: J

2 LLEFT= g f{V-A)i«.-cosé [(V-AX.rfCos^- (V+AWsing ]+ CV-A)tep-sintj [CV-A)<..^in4+(V+A)n.)|Coslt11 8 I M^ i

x) At present energies Q dependence is negligible. - 57 -

After some rearrangements one obtaines

.LEFT jcosj^sin |CV-A)¡ CV-A^CV+A^staiMsC lep^had 2 8 M: M: M " ^| "1 "'2 Í This interaction can be studied by standard neutrino scattering because by default left- handed neutrino (and right-handed antineutrino) beams are available.

Assuming however the existence of right-handed neutrinos the situation will be re• versed and one should retain only (V+A)^ leptonic currents which provide the effective four-fermion Lagrangian for right-handed neutrino (orp."^) scattering:

sinlj ,cos é 1 1 CV+A) CV ^CV ^siitfcos* had +A -A M: M: M2""M¡. 2 J

The cross-section calculations are reduced to the evaluation of matrix elements which has the general form:

A h C V + )+ C V + h A C lePf "had ) =< I T" W had A > In this notation the differential cross-section can be written as

v 22 2 2 = |A (-1;-1) |?cJL + |A C-1,+D| -C = O" c LR LL °LEFT a(+1 +1) C a 2 I ' I'RR + I (+I'-I)|2-CRL RIGHT where the meaning of cr„ is self-explanatory and

2 2 • 2x 2, cos ¿ sin ^ sxn cos c = *» + Ç . _c sin£ cosÇ "LL "RL * M: RR »»2 »»2 ' IJR M: M1 M2 1

Some representative diagrams corresponding to different terms are shown in Figure 1.

After trace calculations one can get

a 2 h h + 1+h 2 °ij • I cvVl • i j W f ?)ci+h ) K2(Pk)

where and K2 represent définit kinematic functions of particle momenta. Due to the fact

that in our calculations the masses are neglected and K2 are depending only on the CM- energy and CM-scattering angle which is equivalent io the scaling variable y. Thus there remain only two possibilities i) h.h. =+1 yields da / dy »«• 1 1 J 2 ii) hjh. =-1 yields d» / dy oí (1-y) .

Of course, one has x s 1 for "elastic scattering" on quarks. From these the usual proce• dure gives for charged current scattering on isoscalar nuclei

Cx.y) q to + (1-y)2 q (x)

(x,y) =

In the general case the muon beam consists of yu£ and yU^ components. Thus the charged - 58 -

current cross-section for negative muon beam with polarization ¿ can be written as a sum

= ~2~ LEFT + 2 RIGHT = ~~a-CLL + -J"0^ -CRL '

It is worth to remark that the left-right mixing term is independent of muon polarization, in accordance with the fact, that it is parity conserving. Of course, this left-right sym- metry can be broken by mass terms and for too heavy the ^pjgjp part would be zero due to energy conservation. For completeness, we write down the differential cross-sections in a more explicit way:

2 + ~7 ff + a 2 + 2 CRL oxdy - — «L " R RL°° 2 q+O-y) ^ + ^ [q+ 0 -yâj) 4 ^+Ci-y3 q}

2 d *** 1 + * _+ A 1 x _+ _ 1+J. axd7= —°L+—RL —

where the transition ju." *—» )X is formally achieved by substituting — à and ' q(x) <-* q(x). One gets the corresponding neutrino cros-sections simply by setting X = + 1:

2

+ AW= *l + 0 + «Sl ~ H^Kl M-^Kl

2 = + 0 + 2 AW < °k ~ [^N-y) q]ÍL * [q+N-y) q]4 - In summary, the muon cross-sections consist generally of 3 parts: the parity violating piece includes pure left- and right-handed contributions, the parity conserving part contains their mixing which is within our approximation independent of A. In the case of neutrino scattering the pure right-handed term is lost. The remaining terms contain li^ in sinC/J)^

and sin2(L5R/M2 combinations. Thus it is practically impossible to deduce any limit on the right-handed intermediate boson mass, M~ from neutrino scattering.

3. PRESENT LIMITS ON RIGHT-HANDED PHENOMENA. 3-71 A number of partial reviews have been published on this topic . One can derive limits for mixing angle £ and ratio 6= M^/M^ from existing experimental data in the following interactions: yu-decay ("direct,inverse"), ß -decay, non-leptonic decay of strange particles and high energy v scattering. These measurements can be classified (see Table 1) according to the following criteria: a) sensitivity to massive right-handed neutrinos, b) they give bounds on £ , the mixing angle,

c) they give bounds on 6= M^/M2, d) special assumption (if any) are required about hadron structure. Theoretical and experimental efforts hav* been concentrated in the low energy leptonic and semi-leptonic area. By definition they were not sensitive to massive (greater than 1 2 GeV/c ) neutrinos due to the lack of energy to produce them. - 59 -

3.1. Pure leptonic processes

All the classical parameters are more or less sensitive to the (V-A) structure of muon decay. Latest compilation is shown in reference"^. The Michel parameter of energy spectrum gives a limit on mixing angle |C I i 0.06 .

The angular asymmetry |PM of emitted from polarized muon decays defines an ellipse J with axis x and y |x| =|ó*- % IS 0.23 and |y | = |S + Ç | S 0.115 . Inverse muon decay (i.e. scattering) measurements are preferring (V-A), but their accuracy is not good enough to deduce stringent limits on (V+A) parameters 8^.

From Figure 2 which was taken from Sakurai's review based on talk of Strovink in Blacks- berg conference one can deduce that pure leptonic processes can allow as low as 220 GeV mass for M2 at mixing angle less than 0.06.

3.2 Semi-leptonic processes

Longitudinal polarization of electrons in pure Gamow-Teller nuclear is found 91 to be equal to (-c/v) • P^J = 1.001 + 0.008 . p — This gives a bound on the parameter y : | y | < 0.09 .

Angular asymmetry of electrons from decay of polarized Ne^ nucleus^ defines a hyper• bola like area in (6,4) plane shown in Figure 2. The semi-leptonic bounds are shrinking considerably the (6,£) domain allowed by pure leptonic processes but the minimal bound on M2 is increased only up to about 250 GeV.

3.3 High energy neutrino interactions

V-scattering on nucléons is very sensitive to right-handed currents in the high-y region, and bounds are valid whatever the mass of right-handed neutrinos. The CDHS experi• ment^-' yields a bound on mixing angle: |Ç I < 0.095 (90 % C.L.) . It does not however give a significant constraint on 6= M^/M^ mass ratio.

3.4 Non-leptonic weak processes

Large enhancement factors for right-handed currents are found in hadronic weak processes but for their derivation additional assumption on hadron structure are necessary. Though this assumptions can be well founded, due to the complexity of hadrons one can not exclude the existence of other possible phenomena which can interfere with left-right symmetric weak effects distorting their appearance. Due to the absence of neutrinos either in the initial or in the final state these bounds are independent of right-handed neutrino mass. Only the right-handed intermediate boson mass does affect the matrix elements.

3.4.1 HvDeron_deçays: A-»Wir , Z-+NTTf ATT f Q-* STT 12) I.I. Bigi and J.M. Frere •* argue , that "left-right couplings introduce a correction factor (1 - 120 sin tj) into the factorizable contribution to the AI = 3/2 amplitude for P- wave decays of hyperons". They use the observed departure from pure left-handed current - 60 -

contribution as upper limit for the mixing angle

sin Ç I < 1/120 (no limit for 6 ).

According to M. Denis J the applicability of factorization is questionable because it is neglecting the effect of soft gluons. In addition, right-handed effects are expected to give similar contribution to each process which is not the case.

13) J.F. Donoghue and B.R. Holstein ' say: "The most sMngent bounds come from the devia• tion from PCAC predictions in K decays both for AI = 1/2 and AI = 3/2. In the limit of no mixing

M2 > 300 GeV ( « 6 < 1/20) . If the right-handed quark mixing angles are equal to their left-handed counterparts and

M2 is larger then sin £ < 0.004" . This limits however are also very model dependent be• cause they rely e. g. on the bag-model.

3.4.3 Kj?_-_Kg_mass_differençe

14 7 G. Beall et al. -* gets è < 1/430 corresponding to M2 > 1.6 TeV. M. Denis -* taking into account t-quark and "would be Goldstone" effects can remain however within the experimental limits if

¿as 0.15 (M2 as210 GeV).

3.5 Overall conclusion from présent data

Neglecting the controversial non-leptonic processes the best fit to low energy data

obtained by Maalampi et al.*'-' provides M^/M2 = 0.22 or in terms of upper limits

M1/M2 < 0.29 and |Ç|< 4.2° (68.3 % C. L.)

which means M2 > 275 GeV in case of R| = 80 GeV. There are experiments in progress to im• prove limits arising from j*or ß-decay. No experimental attempt is known, however, to get

limits on M2 mass in case of massive right-handed neutrinos. Therefore it would be important to perform experiments with right-handed fi beams which could give unique results on ( 6 , ij )

independently from VR mass and free from hadronic structure assumptions. Of course, y¿

mass should be within the kiñematically allowed limits of yuR scattering. Thus observation of the production threshold would provide exact value of m , unattainable for other experiments. R

4. EXPECTED BOUNDS FROM fx EXPERIMENTS

4.1 No-mixing

In order to get a feeling for the experimental sensitivity, we discuss some special ca• ses in detail. If the mixing angle £ is so small that one gets

CRR>> CRL then the formula shows that there is no practical possibility to extract information on right-handed currents from v>-scattering. Thus fx scattering provides unique possibility

to measure M? directly i.e. one can discover the right-handed current even in total absence - 61 -

of left-right interference. One can perform 2 measurements at different muon polarizations,

for example, taking ^o = 0 and Jk = /\ (= 0.9) one gets:

2 No = Monitor^ 1 + . J q(x) + (1-y) q(x) J = MonitorQ . 1 • [ ^ +

2 + + Monitor1• — H T4[ qW C1-y) qCx)Jl = Monitor- •

crR cr,-v-*)-

OA)cr0 -CT, A 2 ^o

because one expects o^^í CL which implies C|«(1-A)cT . Error propagation gives

1 KCl -50

where K = Monitor^/MonitorQ denotes the relative number of incoming muons with à ^ and

^0 polarization, respectively. For K = 4 and X = 0.9 one gets numerically ,4

which means that ijN, o= 100 events can produce one standard deviation limit on right-handed M M mass -]/ 2 \/0.01 » 0.316 corresponding to M2 > 250 GeV. It seems to be an easy experiment. Don't forget, however, that in order to improve this limit by a factor of 4 2 2 one requires (2 ) = 256 times more muon (i.e. running time).

4.2 Right-handed boson is extremely heavy

t ien e muon c < C If M2 is so large that RR ^"- RL ^ ^ scattering is reduced formally to the neutrino one. Even in this case the muon beam has the advantage that the normal weak inter• action will be suppressed by a factor of (1 -A)/2 relative to the mixing -term. Within our approximation measurements with jj^ and fx beams provide

2 2 <7~ = cJL fq(x) + (1-y) q(x) ] + c^ [q(x) + (1-y) q(x)]

2 2 2 C L [qCx) + (1-y) q(x)] + cj^ [q(x) + (1-y) q(x)]

In case of magnetic field reversal (i.e. beam conjugation) one finds - V = > It is worth to define the combination

2 1 c + 2c CT (1-y) er" _ t -^) LL q RL * ^ q + 2 ^RL D(x) 2 + 2 er" d-y) cr (1-X)c L q + 2C^L q I-* c LL 2 rl Z,

where one can neglect cRLq relative to the first term if Ç < (1 -X)/2 . In this case the mixing angle is given by the formula: £2 ~ cRl/cLL * ^ " q/q ^

That is the sensitivity is increased by a factor of 20 in muon case relative to the neutrino one if the muon polarization is equal to à = 0.9, which makes the experiment less sensi• tive to the error in q/q ratio determination. - 62 -

5. EXPERIMENTAL DETECTION OF CHARGED CURRENT EVENTS

5.1 Rates -38 The cross is

5.2 Signature The final state is characterized by three features which can be used against potential backgrounds : i) the absence of muons in the final state ii) a large missing energy 2 iii) a hadronic shower at high 0 . 2 As the Q distribution of events with large missing energy clearly plays a key role in the measurements, the detector should have a good angular resolution. 5.3 Backgrounds The main contributions to the background arise from events with fake muon interactions, such as muon decay in the initial state, or events where the scattered muon is undetected because it is soft or decays. i) Muon decay in the initial state There is only an electromagnetic shower at a rate of .8*10 ^ decays/muon/meter. These 2 2 events will be strongly suppressed by requiring a hadronic shower with Q > 1 GeV . ii) Undetected final muon a) Decay of the final muon According to Monte Carlo calculations, a cut on the transverse momentum of the had• ronic shower in the final state reduces the ratio background/signal to a few percent. b) Loss of soft final muons Such events are eliminated by a request of a large missing energy in the final state.

5.4 Triggering

A trigger would require: i) A large local energy deposition y > .2 which is readily obtained by the calorimeter threshold. ii) No muon in the final state. One can check that there is no muon with energy less than '^"^BEAM ^ inserting a beam analysis magnet and muon identifier after the calorimeter. iii) A missing energy requirement y< .8 combined with muon veto will reduce the trigger rate to the level of 10"*' events/incoming muon. 2 The final event selection is performed by an off-line analysis imposing the high Q requirement. Thanks to the length of the proposed calorimeter we can estimate the remaining background by selecting events when the hadronic shower is well separated from the eventual shower at the decay of the scattered muon. - 63 -

5.5 Detector

The detector should consist of two parts: a dense, fine grained calorimeter and a veto-system to identify the surviving muons. The veto-system can be built from standard ele• ments. The fine granularity can be achieved by a novel design based on scintillating fibres. The parameters of a possible uranium calorimeter are summarized below:

uranium plate thickness 1.5 millimeter scintillating fibre diameter 0.5 millimeter

number of plates 6000 3

average density 14.4 g/cm ? total length 12 m = 17280 g/cm lateral width 40 cm lateral segmentation 1 millimeter longitudinal segmentation (x,y) interleaved 8 millimeter number of read-out channels by 2x2 fibres 1200000 channels

If one uses lead instead of uranium then all the above parameters should be rescaled by the density factor 9u / 9T>t •

By this detector 1 day running with )i=0 and 4 days with ^=.9 can provide a bound

M, 2T 250 GeV ( 68.3 % C.L. ) . 13

In case of ^=.95 after 150 days (1.5*10 incoming /xR) it is possible to reach

M2 S 450 GeV ( 68.3 % C.L. ) .

In order to realize this theoretical possibilities significant developements are required in the fibre read-out technology which would make feasible the digitization of the infor• mation from about one million optical channels. Some preliminary studies would be very use• ful by the help of the uranium calorimeter proposed by the EMC collaboration^ for bb studies.

REFERENCES 1) K. Winter, Phys. Lett. 67B (1977) 236. 2) T. G. Rizzo and G. Senjanovic, Phys. Rev. D25 (1982) 235. 3) M. A. Beg et al., Phys. Rev. Lett. 38 (1977) 1252. 4) J. J. Sakurai, Proc. Int. Conf. Neutrino 81, Hawaii, p. 457. 5) J. Maalampi et al., Nucl. Phys. B207 (1982) 233. 6) G. C. Branco and J. M. Gerard, CERN Preprint, 1982 oct, TH-3441. 7) M. Denis, Thesis, Univ. Catholique Louvain, 1982. 8) M. Jonker et al., Phys. Lett. 93B (1980) 203. 9) F. W. Koks and J. van Klinken, Nucl. Phys. A272 (1976) 64. 10) B. R. Holstein and S. B. Treiman, Phys. Rev. D16 (1977) 2369. 11) H. Abramowicz et al., Z. Phys. C, Particles and Fields 12 (1982) 225. 12) I. I. Bigi and J. M. Frère; Phys. Lett. 110B (1982) 255. 13) J. F. Donoghue, B. R. Holstein, Phys. Lett. 113B (1982) 382. 14) G. Beall et al., Phys. Rev. Lett. 48 (1982) 848. 15) R. W. Clifft et al., SPS Fixed Target Workshop, CERN, 1982, Internal Note EMC/82/14. - 64 -

Table 1

Present bounds on left-right symmetry

Valid for Without additional PROCESS massive theoretical assumptions?

Muon-decay: <0.06 NO NO YES Michel parameter

Muon-decay: ^P^ |<5 +$1 * 0.115 NO YES e-asymmetry |0-Ç| * 0.23

Beta-decay : |à + Ç| «? 0.09 NO YES e-helicity/ (v/c)

Beta-decay : Hyperbolic area NO YES e-asymmetry

v,)f-scattering < 0.095 NO YES YES (CDHS)

Hyperon decays Factorization -¿•1/120 NO YES hypothesis

PCAC K -* 3'TT < 1/250 < 1/20 YES Bag model

< 1/430 YES Neglect t-quark AM KL,S <, 0.15 YES t-quark+"Soldstone"

i —M,

YES LC~j^-scattering Possible Possible upto-20 GeV YES - 65 -

X = -i fiL+ q — V[ + q X=-i [l~L+ q — V^+q

_ cos f u sin f M cosf ,, _ sinf H /'-violated P- violated

w l| + w2| PL—y— ülMl—y— K äa/dy ~ 1 d07dy~0-y)2 UL cosf dL "L sinf dL W1? + W2P

-conserved -conserved dR cosf UR dR sinf UR .P u u P u Ml > lMl J> l ML b Ml S l + w2c3 d07dy~(l-y)2 d07dy ~ 1 UR sinf dR UR cosf dR dL sinf-"ULdL sinT"UL

X=+i /¿R+q~ u'R+q X=+1 /iR+q — u'R+q

— sinf i _ cosf / _ sinf i _ cosf ; /'-violated P- violated Mr £ urMr f- üR W1Í» + w2^ wi<; + W2Í; dOVdy ~ 1 dO~/dy~(l-y)2 UR sinf dR UR cosf dR dL sin*f "_UL dL corf "UL

_ sin f ; _ cos f . i sinf , _ cosf i -conserved conserved P P- Mr--7'---UrMr---;"-I>r W1< + W2¿ d07dy~i(l-y)2 u, ^—d, iu, ^=—d, d07dy ~ 1 dR cosf UR dR sinf ÖR L cosf L L sinf L

Figure 1 Representative SUT(2)*SU (2)*U(1) diagrams

2 M(WR) (GeV/c ) 600 400 300 250 220 20'

O) c 10 O)

tr i 5 .05 - u

Figure 2 Low-ended bounds on right-handed 2 2 6= M (WL)/M (WR) ^ current oarameters