ff/' T

MEASUREMENTS ON THE RARE DECAY

i,

WIĽLEM VAN DOESBURG

<" "-- t, ,-; •'',,

•.(-."V.íľ'-CrTí'í VRIJE UNIVERSITEIT TE AMSTERDAM MEASUREMENTS ON THE RARE DECAY -» e+e-

ACADEMISCH PROEFSCHRIFT

ter verkrijging van de graad van doctor in de wiskunde en natuurwetenschappen aan de Vrije Universiteit te Amsterdam, op gezag van de rector magnificus dr. H. Verheul, hoogleraar in de faculteit der wiskunde en natuurwetenschappen, in het openbaar te verdedigen op vrijdag 4 december 1981 te 13.30 uur in het hoofdgebouw der universiteit,

De Boelelaan HOS

door

WILLEM VAN DOESBURG

. geboren te Amsterdam

Serv'Impri AMSTERDAM 1981

O5^.E3iaiíSKB4^ „„ Promotor : Prof. dr. H. Verheul Coreferenten : Dr. NW. Tanner Dr. E.G. Michaeüs

3v S'/

\

- • — VOOR RENÁTE VOOR MIJN OUDERS ? Lay-out : AUTHOR tekstverwerkingsprogramma 1 [- (CERN-Horst von Eicken) i f,, | Type-werk : Renáte van Doesburg 'i "'" | Figuren : A. Pomper/W.C. van Sijpveld 'jf I Drukwerk : Serv'Impri, Amsierdam I

,JĽ^^^.^^ CERN - GENEVE CHAPTER 1. INTRODUCTION AND SURVEY.

1.1. Introductory remarks.

In 1935 Yukawa suggested that the nuclear forces were mediated by the virtual exchange of a particle. This so-called meson was finally observed around 1948, and is known as the tT-meson or pion with a mass of about 140 MeV, The pion has isospin one, and thus + o appears in three charge states IT , TT and tľ ; the spin of the pion is zero (it is a boson), and it can therefore be absorbed or created individually in nuclear interactions. The pion is unstable and decays into leptons or gamma rays, with -8 -16 life-times of 2.6*10 sec (charged pion) and 0.8*10 sec (neutral pion).

It was recognised that pions are the most important constituents in the nuclear force, and hence an enormous effort was made during past decades to investigate the properties of the pion especially in the pion-nucleus system, both experimentally and theoretically. In its interaction with the nucleon, the pion generates many resonances or excited baryon states. One of these resonances is the (3,3)- or i-resonance which, with a width of about 100 MeV, dominates the pion-nucleon interaction between' 100 and 300 MeV pion energy. Consequently, a lot of research activity in this so-called intermediate energy range is going on to reveal further details of the strong interaction.

Pions may be found in cosmic rays; in fact, this was the way they were first discovered. For experimental studies however, accelerators are needed to produce pion beams; accelerators designed for this purpose were put into service in the early fifties. The second generation of these accelerators are the "meson factories", from which at present good pion beams can be obtained. These meson factories include the Los Alamos Meson Physics Facility (LAMPF), the Swiss Institute for Nuclear Research (SIN) and the TRl-University Meson Facility (TRIUMF). Also at the European Organisation for Nuclear Research (CERN) in Geneva, pion beams are produced at the 600 MeV proton-synchrocyclotron. In addition, at the Medium Energy Accelerator (MEA) of NIKHEF-Amsterdam a pion beam is about to be produced mainly by the effort of the Free University of Amsterdam (see e.g. ref.l).

w At ^CERN, a general purpose magnetic spectrometer called OM1CR0N" was set up for measuring processes in the domain of intermediate energy physics. While building up and testing the detectors for this spiectrome ter, an experiment was performed on the backward elastic scattering of pions from deuterium (refs.2,3). The first of fieiaf experiment with the spectrometer was on the backward elastic scattering of pions on carbon and oxygen (ref.4). The second experiment, which is the subject of this thesis, was an investigation of one of the decay modes of the neutral pion, namely o + - Tf —*• e e . The decay rate of this rare process is a probe to the "size" of the neutral pion rather than a probe to the pion-nucleus interaction. It o was favourable for the investigation to produce the TT at the A-resonance (which will be explained in ch.3). The aim of the experiment was to establish a value for the branching ratio for the above rare decay; so far from only one experiment a value for this branching ratio was claimed with a large error, and it is hoped that the final results of the experiment will yield a value with a statistical error of the order of 10X. In this thesis the set-up of the experiment will be presented together with its first results, deduced from the first experimental runs performed in 1980.

1.2. Survey of this thesis.

In this presentation, apart from various general descriptions, the author has given more detailed accounts of those parts of the experiment where he has mostly been active.

In chapters II and IV the OMICRON spectrometer will be presented together with the experimental set-up for the rare-decay measurements; chapter V contains a description of the electronics and data-acquisition. In chapter 111 a theoretical resume is given and, in addition, a discussion of the lay-out chosen in our experiment. The last chapters contain the description of the analysis and the first results, based on the 1980 data.

***

In order to gain experience in the field of intermediate energy physics, the Department of Physics of the Free University of Amsterdam decided in 1976 to detach a few of its scientific associates at institutes where experiments with pions in this energy range were envisaged. In this manner the author of this thesis was the first to be stationed at CERN, and the Free University became a member of the OMICRON Collaboration. A considerable time was spent at CERN assisting in the build up of the apparatus and participating in various experiments. During the first two years of the detachment, the author of this thesis also participated in a couple of experiments "r me-onic atom* (refs.5,6). These experiments involved measurements of the ;'„ oub interaction widths and shifts in pionic atoms, which provides

ys-fäict-jy^^m^^ij-jy^- important information on the threshold behaviour of the pion-nucleus interaction (see e.g. ref.7).

1.3. Acknowledgement

It should be emphasized that the work presented in this thesis represents basically the effort of all the members of the OM1CRON Collaboration who participated in the rare decay experiment. Whenever a member of the Collaboration has been particularly responsible for or involved in some activity, his name has been entered into the text. In addition, the author owes many thanks to those who have remained unnamed.

^^ "'"" " ' References :

1. Pionen als spionnen, H.Verheul, rectorial oration VU-Amsterdam. 20-10-1979 2. A.Stanovnik, G.Kernel, N.W.Tanner. T.Bressani, E.Chiavassa, S.Costa, G.Dellacasa, M.Gallio, A.Musso, M.Panigňini, K.Bos, D.Frame, E.G.Michael is, W.van Doesburg, and J.D.Davies, N.l.M. 177 (19B0) 369

A.Stanovnik., G. Kernel, N.W,Tanner, T.Bressani, E.Chiavassa, S.Costa, G.Dellacasa, M.Gallio, A.Musso, M.Panighini, K.Bos, E.G.Michael is, W.van Doesburg, and J.D.Davies, Phys.Lett. 94B no.3 (1980) 323

E.Bason, K.Bos, T.Bressani, E.Chiavassa, S.Costa, J.D.Davies, G.Dellacasa, M.Gallio, E.G.Michael is, J.V.Jovanovich, G.Kernel, W.Lourens, N.Mirfakhrai, A.Musso, M.Fanighini, S.Playfer, M. Rapetti, F.Sever, A.Stanovnik, N.W.Tanner, R.van Dantzig, C.W.E. van Eijk, W.van Doesburg, and A.G.Zephat, paper presented at the 9th Int.Conf. on High Energy Phys. and Nucl. Structure, Versailles, July 6th-i0th 1981, EP Internal Report (CERN) 81-04

J.Konijn, J.K.Panman, J.H.Koch, W.van Doesburg, G.T.Ewan, T.Johansson, G.Tibell, K.Fransson, and L.Tauscher, Nucl.Phys. A326 (1979) 401

J.Konijn, W.van Doesburg, G.T.Ewan, T.Johansson, and G.Tibell, Nucl.Phys. A360 (1981)187

J.de Kam, Ph.D. thesis VU-Amsterdam, March 1981 CHAPTER 2. THE OMICRON SPECTROMETER.

In this chapter, the OMICRON spectrometer will be presented, its configuration at CERN and its magnetic field with .subsequent párame terisat ion.

2.1. General review.

In 1973 a working party called "OMICRON working party", formed by various physicists mainly from Oxford (GB) and Turin (I), started to make plans for a general purpose magnetic spectrometer of large solid angle and momentum acceptance, The desirability of such an apparatus arose from the physics interest in certain processes such as low energy pion scattering, rare decay-events and events like pion double charge exchange; a proposal for a spectrometer to enable such physics experiments was submitted to the Physics 111 committee which at that time governed the physics of the CERN 600 MeV-synchrocyclotron or SC (refs. 1 and 2). The. above physics interest was recognised, by the Physics III committee, and work started both at the participating institutes and at CERN for the "manufacturing of wire-detectors, the design of beams and preparation-pf'software and, of course, the preparation and assembly of the magnet. After a short period, an initial physics proposal (ref. 3) was submitted to the Physics ill committee by the thus established "OMICRON collaboration" where a small group of experiments was presented in détail, chosen, from the long list of possible experiments with such a large spectrometer. These experiments were approved in general terms, and the committee decided that approval and machine-time for each specific experiment would be considered in due course. The first of these experiments to be approved was the experiment of backward pion scattering on carbon and oxygen (exp. SC73), the o + - second was the determination of the branching ratio for 1ľ-e e

The magnet which was found to be available (on loan) for the OMICRON spectrometer was a bubble chamber magnet at the Rutherford Laboratory, known as the Mil. However, the existing pole pieces, designed for a bubble chamber, were not at all suitable for a spectrometer. New pole pieces were required and the magnet poles were re-designed using a computer program at the Rutherford Laboratory (see ch.2.3) to give a field-distribution- that deviated 3 from the central field value by about 10K within approx. lm of volume around the centre. The pieces of the magnet were shipped to CERN, and assembled in the so-called Proton Hall next to SC (see fig.2.1). The availability of beam lines.to this hall was adequate to provide beams of pions, muons, neutrons and protons. At the SC the beam height is 1.25m above floor level and, in order to put the magnet centre at this height, the magnet had to be put into a pit with a suitable amount of re-inforcing necsssary to carry its weight of about 185 tons. ?' % "^ '

X'ýš'V' 'SYNCHROCYCLOTRON

PROTON HALL — —IL

fig.2.1. PÁoíon. ŕia££ with, beam confaicjuAation fan OMICRON The diameter of this pit was made 4.8m, which allowed rotation of the magnet about a vertical axis; the magnet was mounted on a slewing ring capable of rotation to any ang le. By a suitable choice of the angle of rotation of the magnet with respect to the beam transport line (see fig.2.1), the beam was brought into the spectrometer.

In its present state, the OMICRON magnet is rectangularly shaped 3 3 with a total volume of about 7m and a useful volume of about Em , the latter extending slightly over the pole-surface which is

1.87x0,99m (for a sketch of the magnet with dimensions see fig.2.2).

beam

1872

992 lower pole

1600 3670

fig.2.2. Top and bide, view o j the OMICRON magne-t [oitt dimemiom in. mm)

The principal field direction is vertical (along the i-axis), and power is supplied to the coils from two jjeiucra tors witli a maximum power of 1MW each to produce values up to 10 RCnur, a I t tin .iraRiiet centre (note: the magnet is capable of providing VC Kuausü at .ibout 4MW supply). The beam lines use! to fee-1 OMICRON air the ones marle'1 B and C in fig.2.1; for the experiment described in this thesis (he C-pipe beam was used.

2. ü. Beam configuration.

As stated above, we chose the C-pipe beam (labelled CS7) for our experiment rather than the B-pipe beam which carried a heavy background of neutrons (for a detailed report on these two beam lines, see ref.6). As shown in fig.S.I, this beam line consisted of the following quadrupole lenses (L) and bending magnets (M), in successive order from the SC extraction channel: LAI, LA2, LF1, LG1, LC2, MP5, LC8, L

The whole design of the beam was such that a good (achromatic) - focus should be obtained at the target inside the spectrometer, 'j while at the same time unwanted background due to particles from the beam-halo that do not interact in the target and hit the wire :; detectors, should be reduced to an acceptable minimum (see also ,,: ref.8). To this end, an optimised value was reached for the above '.',} angles and the setting for the magnetic field, which amounted to a '.'•[ J central field value of 5.095KG. r : The design of the beam-line was performed by G.Kernel using v

"Transport" and "Decay-Turtle", CERN computer codes frequently used T; for beam design, with the requirement of a good focus together with ' maximum beam-intens i ty. As a result, the focussing elements were [ made up in such a way that the resulting beam in the drift space •:; between LC9 and LD3 was focussed vertically and was horizontally '.; parallel; it was then made parallel in LD3/4, and finally focussed ;,- in both planes in LD5/6 and LG4 (see again fig.S.I). The col lima tors in the concrete wall - as indicated in fig.2.1 were not used. In practice, a good focus was obtained inside the magnet (see also ch.4.2). The dimensions of the beam-spot in horizontal and vertical projections were measured and FWHM-values of 4Si2mm and

40±2mm respectively were obtained for a FWHM area of about 15cm . At the position of counter S2 (see ch.4.), about 10cm upstream of the target, the beam was almost circular with 42i2mm FWHM-diameter. The FWHM of the momentum distribution was measured to be 5'/,, and the 6 intensity of the beam was of the order of 2x10 negative particles per second (for an extracted proton beam of about 4MA).

The beam did not only contain pions but also electrons and njuons. A gas-cherenkov counter downstream of LG4 measured the elactron-component to be about 25X ; in the experiment however, this counter could not be used because it badly affected the quality of the- beam focus at counter S2. The muon- component was estimated at about 5X, or i G inr\ I mb mostly from pions decaying in flight upstream of MP5.

2.3. The magnetic field of the OM1CR0N magnet.

The purpose of a spectrometer such as OMICRON is to enable momentum-determination of charged particles that describe, under varying experimental conditions, curved paths within,,the magnetic field. Since this is done by solving the equations of motion of V. those particles by numerical integration, easy access to the field values at any given point inside the magnet is essential. Therefore, the magnet was designed (using the simulation programme "GFUN" at the Rutherford Lab., see ref.9) in such a way that the field variation in the volume of interest was kept as small as possible and even at its boundaries did not exceed 25% of the central value. In the following paragraphs, the method will be described with which the magnetic field was measured and a description will be given of the method of polynomial-evaluation used to parameter ise it.

2.3.1. Measurements of the magnetic field.

Xf.i The three components of the field were measured with Hall-probes in an assembly that was mechanically driven through the field; this measuring gear was developed at CERN (ref.10) and installed with the help of D.Lehm. The assembly consisted of IS Hall probes, for measurement of three f ie Id-components in four equidistant points at the same time, mounted on á 'temperature controlled arm and attached to a chariot which was driven mechanically along a support bar. The movement of the assembly was automated along the axis of the support bar, and either manual or automatic in the other two dimensions depending OH the gear used; the one-dimensional gear has automated movement along-just one axis,

10 whereas with the three-dimensional gear a given volume could be measured without manual intervention. Both gears were interfaced to a Hewlett Packard 2100 computer programmed to control the positioning of the probe-assembly nnd to read the Hall voltages across the probes; these were record':.1 on magnetic tape. In'addition, the programme continuously monitored cne state of the probes, i,e the Hall-current and temperature of t It a assembly. In the case of measurements of the field in a user-spec i f ied volume or box (3-dim. gear) or along a line (l-dim. year) the programme controlled and monitored the position of tha assembly. The error in the measurements was mainly caused by the inaccuracy of i the alignment of the Hall probes with respect to the magnet coordinate system; this alignment was accurate to within 4mrad.

BEAM (ORIGIN OF FIELD - MEASUREMENTS)

fig.2.3. Scetch [top view) o& magnet thawing d 6ild boie*

The procedure of automated measurement was as follows. After defining the origin of measurements, which in our case was the point (.v ,y, 2) = <1 . 860,0.960,0.380) (all values in meters, in the mngnet•coordiunle system as in fig.5.3), and giving a suitable ro'rcnnnd to the computer, the chariot with the assembly was driven through the magnet. Its position was defined by counting holes, machined in the support bar at 2cm distance, with sensors supported by the chariot. At n given crid point where measurements had to take place, the position of the chariot was fixed and after suitable delay to allow the probe-assembly to settle, the Hall voltages were scanned and recorded on tape together with the coordinates of the Crid piiinl. The chariot was thereafter released, and moved on to the H UCX t RT 1 d PO int . Wli p n tlie measurement of a complete box had finished, the magnetic t.-ip» wes analysed off-line using a programme developed at CERN 11 •• f . 1 I ) . In this programme the Hall probe voltages of each r Í -ň] - • ľ r nt of' Hie field were collected for one set of measurements; tl"- iniliiiRs were converted from microvolts to Gauss using the known

U ca I i brat ion-curve of each probe for a given Hall current and a complete map was produced throughout the volume of the box measured, taking into consideration the geometry of the Hall probes and the grid points where the field was measured. The experimental error of the values in these maps nevar exceeded 0.5%, which includes the error in the measurement of the calibration curves.

In ref.12 a detailed review is given of all the measurements performed. In total, 8 measurements were made at different values of magnet current in order to cover the full range of the magnetic field from zero to about 15 KGauss (central field value); in addition, 3 extra measurements were made in order to investigate the fringing field on the side of the incoming beam and the field in one of the side-gaps of the magnet. Table 2.1 gives a list of all measured maps; the corresponding boxes are sketched iu fig.a.3 (only box no.4 is not displayed; this box is roughly the sum of boxes 1 and 3). The main (z°) component of the field at the origin, in Table 2.1, was measured with a NMR-probe, the current is the current in the field coils and DVM is the voltnp.e measured with a digital voltmeter across a resistor of 75MJL in series with the coils.

Table 2.1: Rev-tew of, HeJLd mexuwieminZi

box + dimensions (in m) x y z map B (origin) DVM - current no. of point from to from to from to (KGauss) (tnV) (A) measured

1.86 -2.10 0.96 -0.66 0.38 -0.38 1 -9.471 150.0 2000 37520

2 -7.902 119.0 1587

3 -5.306 77.8 1038

4 -8.774 135.0 1800

2 0.18 -0.18 1.44 1.02 0.38 -0.38 5 same value as map 1-4 1120

3 -3.82 -4.30 1.20 -0.66 0.30 -0.38 6 +9.471 -150.0 -2000 5184

•i ii 7 +5.308 -77.8 -1038 it

4 1.86 -2.94 0.96 -0.66 0.38 -0.38 8 +12.102 -221.0 -2950 45360

9 +13.387 -262.5 -3500

10 +10.713 -180.0 *2400

11 +14.493 -300.0 -4000 The results of the measurements at three central field values, the third of which (5.31KG) is close to the value used in our experiment which was 5.095KG, are summarised in figs.2.4,2.5,2.6 and 2.7. Figures 2.4-2.6 are plots of isofield-1ines in the central plane

ISOFIELDLINES 1,5.to.20,30,«0,50,75,90 PCT CENTR.( 1.86, 0.96) 1.68

0.56 .

4.20 x (m)

fig.2.4. OmicAon úo&ieldtineA ctntncJL piano. [z=o] Bzl0) = 14.S KGcuiAi (&£ne 1=1% o\ cen&ual value, etc.)

ISOFIELDLINES 1.5.10.20.30.40.50.75.90 PCT CENTR.(1.86,0.96) 1.68

1.12 .

0.56.

0.84 1.68 2.52 3.36 x(m)

2'5' OmicAon itoiieJtdJUnu cen&uxl plane. [z*o) 82(0)»9.47 KQcuui [lini 1=1% oi centAal value etc.) ISOFIELDL1NES i,5.10.20,30,40,50,75,90 PCT CENTR.t 1,86,0.96)

0.84 1.68 2,52 3136 x( m)

fig.2.6. OmicAbn ii l cen&ial pplane (z-o) 11* & tZ 82(0)=5.31 KGauAA [line. 1*1* o& cznt/iaZ value, etc.)

Fig.2.7 is a plot of B as function of the magnet current and shunt voltage. The dotted line in this figure represents an extrapolation of the linear first part of the curve, i.e. without noticeable saturation.

8.3.2. Parameter!sat ion of the field,

A polynomial model of the field was chosen according to refs.13 and 14. In this mode], three harmonic (legendrr:) polynomials are taken for the f i e Id-components, ench in x, y, and i. It can be shown that, if one takes terms with sums of powers less than or equal to

N, the total number of independent coefficients is etjual to (Nt-C) -1 (see also ref.15) due to the constraints imposed by Maxwell's equations for a stationary magnetic iieJd

div B = 0 (2.1)

curl B = 0 (2.2)

The harmonic polynomials, thus limited in rv [>iii?ion, were fillrd li> the measured field values from a u uut be i c í i-.->inlr. within a Certain volume. Fur thcrmore , the order of' Hie {• •> I ynom i n I s wns limited to 3 in order to obtain a fast evaluation of the po I ynnrn a 1 - coe f f i Ľ i ľ.n t s

Í4 and of the field-components from those coefficients; a lower order was taken whenever possible. In this way, the number of coefficients used for parameterisation could be kept relatively small.

mV(SHUNT) 90 150 210 270

1000 2000 3000 4000 AMP

fie-2.7. Tk& magnetic hieli oi OmicAon (iee te.x.t)

For a given measured fieldmap, the procedure of párametcrisat ion was as follows. Firstly, the map was divided into smaller volumes or boxes, the size of which was chosen to give reasonable speed of evaluation of the coefficients and good overall accuracy. The latter was defined by requiring the total RMS residual of the three components at the measured points to be no more than 50 Gauss for each of the small boxes. The lowest order polynomial was then fitted to the field values of the grid-points within each box, using a linear least squares fitting routine which also assured sufficient smoothness between the individual boxes. Only if the RMS residual was larger than 50 Gauss, a higher order fit was attempted. After each box had been párameterised, the coefficients together with the order were written inside an array.

By means of this parameter i sat ion, an array with total length of the order of 30000 words was obtained; while large, this array could easily be k^pl in core during the execution of the off-line programs. Reduction of this number, e.g. by fitting only a certain part of the measured map ( defined by a particular experimental

15 geometry) or by exploiting symmetries in the magnetic field, were not attempted. However, a reduction of the time of evaluation of the field-components from the coefficients was obtained by multiplying coefficients by certain constants when they always appear in that form in the polynomial expressions, and by optimising tfie routines used for this evaluation.

Details of the polynomial fitting can be found in ref.12; in general, the nominal maximum of 50 Gauss for the accuracy was exceeded at only a small number of points (about 8!< of the total), while the order of fit in the centre of the magnet was usually not larger than two. At the points where the field was measured this was compared with the values obtained from the polynomial expansions. A Gaussian distribution was found centered around zero, with FWHM of 8-9 Gauss for all three field-components. Selecting only the central volume of the ma'gnet, wi th |z| í 0.26m, reduces this FWHM to 6 Gauss in the case of the parameterisation of the third fieldmap.

The results of both the measurements of the magnetic field of OMICRON and the párame téri sa t ion are in agreement with the predictions from the design-program (see above). For example in the third fieldmap it is observed that at the pole edges the value of the z-component is about SO" less than the central field value; naturally, the field falls off more rapidly at greater saturation (compare figs.2.4, 2.5, and 2.6 ). Also, the field as dependent on current can be párame ter ised relatively easily to a good accuracy; again, towards the higher field values the parameterisut ion becomes more difficult (in the sense of requiring higher order polynomials and an increasing number of boxes). The field applied in our experiment deviated very little from the field measured in the third map. Since we are well within the linear part of the field-curve (see fig.2.7), the field used could be derived from this map by linear scaling. For other experiments at higher field values, a suitable interpolation between measured maps would have to be made, whereafter the párame ter i sa t i on may be performed as above.

16 References :

1. The feasability and desirability of constructing a large aperture magnetic spectrometer (OMICRON) for use at the synchrocyclotron, Omicron Working Party, PHU1-74/41 (20-6-1974) 2. A proposal for a large acceptance magnetic spectrometer for uss at the synchrocyclotron, Omicron Working Party, PHUI-74/57 (5-12-1974)

3. Initial' programme for the Omicron spectrometer. The Omicron Collaboration, PHI11-/S/11 (30-4-1975)

4. o + - A determination of the branching ratio for IT —e-e , The Omicron Collaboration, PHlll-75/15 (20-6-1975) 5. Addendum to PHUI-75/15, J.D.Davies and N.W.Tanner, PHUI-75/15/Add. (3-6-1977)

6. Analysis of test runs of October 9-14 (B-pipe) and October 29 - November 2 (C-pipe), 1979, G.Kernel, CERN-Omicron report (3-6-1981)

7. B.W.A1lardyce et al, Proc. 7th Int. Conf. on cyclotrons (Birkhauser, Basel 1975) p.287

8. o The choice of the beam trajectory- for f-*2et W.van Doesburg and G.Kernel, CERN-Omicron report (39-2-1980) 9. W.Trowbridge, J.Simkin, Rutherford Lab. Internal report (1975)

10. A system for measuring magnetic fields, J.Adams, D.Runolfsson, CERN NP-OHG 74/2 (1974)

It. Magnet measurement magtape processing, J.Schinzel, CERN HP76-8/2 (revised version, 5-5-1977)

12. Measurements and processing of the magnetic field in the Omicron spectrometer, W.van Doesburg, Omicron note (CERN) 0N-B1/3

13. M.Metcalf and M.Regier, J.Comp.Phys.11 no.2 (Febr.1973)

14. H.Wind. J.Comp.Phys.2 no.3 (Febr.1968)

15. A polynomial model of a magnetic field, W.van Doesburg, CERN-Omicron report (April 1979)

Í7 CHAPTER 3. THEORETICAL NUMMARY AMD DESIGN OF THE EXPERIMENT.

During past years there has been considerable interest in the decay processes of neutral pseudoscalar mesons into lepton pairs. Processes such as

K° •*• y"V (3.1)

T) •* Ii+W~ (3.2) have been studied both experimentally and theoretically, and various theoretical models have been constructed to account for the observed widths of these decays. Some of those models assume t lie existence of neutral currents, resulting in rather high values for the decay widths. The process which we are studying, the decay

ir° •+ e+e" (3.3)

is of particular interest as a probe of the if - vertex, and as a potential source of information on possible non-electromagnetic interactions between electrons and hadrons. In the following paragraphs, a brief summary will be made of the theoretical models mentioned above, and their implications for the branching ratio of process (3.3) will be given. The few experimental values that have been obtained so far will be given in addition to the theoretical predictions, and thereafter the choice of the configuration of our experiment will be explained.

o 3.1. The decay modes of the IT

The neutral pion is a relatively short lived particle with a -IB mean life of (0.828± 0.057)*10 sec (see ref.l, Particle Data Group).

The normal electromagnetic decay modes of the TT are given below together with the respective partial decay fractions (see ref.l). The decay mode that occurs most frequently is

TT° + YY (98.85 ±0.05%) (3.4)

furthermore we have

18 + - (1.15 + 0.05%) (3,5) « e a decay mode, first pointed out by Dalitz (ref.2) and hence called Single Dalitz Pair (SDP)-decay, which is the internal conversion of one of the photons from (3.4). When both photons convert internally, we obtain the decay mode

+ + 3 ïï° -, e e"e e" (3.32 x 10~ %) (3.6)

called Double Dalitz Pair (DDP)-decay. The branching ratio B of the decay (3.3), which we are looking for, may now be defined as the decay rate of this rare process with respect to the decay rate of (3.4)

B = i- eV) (3.7)

In fig.3.1 the lowest order Feynman-diagrams for the above processes, including the rare decay mode via the conventional electromagnetic interactions, are given.

single dalitz pair

'"•!*• double dalitz pair (it0-* c +«-> V

fig. 3.1. fzynman fu.ctun.zi o i ir° decay modu

The expression for the width of the decay (3.3) must contain the

19 Z 2 factor <* (m /m ) , where <* is the fine-structure constant and m e o e o and m are the electron and ff mass, respectively. On account of the o 2 factor (m /m ) titis leads to a very small value, which may be e o o explained by the fact that the spin 0 of the vr forces the decay I leptons to have the same helicity • The factor just mentioned is therefore sometimes called the helicity-suppression factor. In its general form, the matrix element for the rare decay rate (see e.g. ref.3) contains a complex amplitude; the imaginary part (or absorptive part) of this amplitude is given using the unitarity relation. Assuming that the (physically allowed) two-photon intermediate state dominates the unitarity sum, a lower limit of the imaginary part of the amplitude and hence a lower limit for B can be calculated (see ref.4, and below). This so-called unitarity limit or lower bound B is found to be u

B Bu - 4.75 x 10" (3.8)

The actual decay rate may be larger due to the real (or dispersive) ; part of the amplitude, the size of which will depend on the coupling >' of the photons to the neutra! pion. Various models have been made to describe the real part of the decay amplitude, and they can be roughly divided into three classes. In the first class, an assumption is made of an ad-hoc form-factor that appears in the decay amplitude (models of Orell or Berman & Geffen); in the second class the model assumes some form of vector meson dominance (models of Sehgal or Quigg & Jackson) or intermediate nucleon-antinucleon state (Pratap & Smith). The third class, finally, contains the various models based on some non-electromagnetic type of interaction (models of Pati 4 Salam or Herczeg). The main features of these models will be briefly "'; discussed in the next paragraph.

3.2. Various models for the pion form-factor. • '•

• ;'/.

o The unknown structure of the tr - vertex can be expressed by a form-factor which is taken into the decay amplitude. One of the : 2 ; first models by Drell (ref.5) contains a form-factor F(q ), depending only on q = q + q where q /q are the fourvmomenta of + - + the positron and the electron. This form-factor is written as a dispersion integral, where one includes two-photon states with total

20 2 2 2 mass q » xm up to x < M , where «represents a cut-off in units of o o m (m is 1T -mass). o o For three cut-off masses the value of B is calculated, namely JH = 13.9, ,« = 6.95, and /» = 1, corresponding to twice and once the o proton-mass and exactly the TT mass; the results, going up to about 5 times the unitarily limit, are listed in Table 3.1.

lu the more detailed model of Berman and Geffen (ref.B) the - - _--" ..-'•_-- o general form of the matrix element for the ir decaying into two photons of four-momenta K and K is used, which contains the " - ;- -/- - •- ' l -;'-. 2 2 z ' • ,2...... -."" .. .; ; __ o ^_ form-factor r (K , K , (K -+K ) ). For a rea 1 it , the constraint 1 2 i J2 - -" ' :'Z}F./i^:-~- ---- 2 2 ; - -- "- :~~ '-' 2 (K +K ) = m is valid; normalisation is such that r*(O,O,m ) = l. 1 2 o o For the SDP decay mode (3.5) this function is only dependent on the o 2 2 four-momentum of the virtual photon and the tf mass, i.e. P(K ,0,m ) 1 o 2 2 and can therefore be written as V (x) with x = K /m . In the 1 o kinematically allowed region for the variable x

2m /m < x < 1 (3.9) e o - -

which is also the physical region for this process l~(x) is written as an approximation as

T(x) - 1 -+. ax (3.10)

where a is a real constant, which is called the slope parameter, (Note, that taking V as unity is equivalent to excluding any o electromagnetic structure of the IT .) o + - . r For the rare decay Tf —e e , the form-factor becomes dependent on 2 2 the two virtual photon masses K and K , with the constraint of 1 2 o o K =q -K with q = four-momentum of the IT , and the TT -mass; we can 2 o 1 o 2 2 2 then write f(lC , (q -K) ,m ). o o ŕ 21 Beman & Geffen suggest an approximation for I in its simplest form as a function symmetric in the two photon variables

2 2 2 2 ,(qo-K) ,m^) = A /(A -K - (3.11)

Z Z when A » m , with A a cut-off mass parameter related to the slope o 2 Z parameter as A =m /a, o The branching ratio can now be calculated as

2 B = 2(arae/mo) |N| (3.12)

where N is a complex quantity with its imaginary part independent of the cut-otf, and its real part dependent on it. The unitarity limit (3.B) is reproduced taking Re N = 0. Calculations of B for various values of the cut-off are listed in Table 3.1.

In the two models just described there is no clear physical interpretation of the cut-off parameter. In the model of Quigg and Jackson, however, the masses of vector mesons are taken to dominate tbs real part of the decay amplitude (ref.7). This model is a vector-dominance model (VDM) of electromagnetic couplings; here it o is assumed that there are no direct coupl ings of the xt to a photon, but that all photon couplings occur via intermediate vector-mesons (see fig.3.2).

fig.3.2. Fiynman-dingiam showing the. ve.ctot dominance model

22 r 2 Z Z The above general form-factor V(K ,K. ,m ) then becomes proportional i 2 o 2 2 2 2-1 to I(m +K )

4m2 r n (3.13) 2a2

which compares to (3.12); now, X and Y are proportional to the dispersive and absorptive part of the transition matrix-element for the rare decay. Again, the imaginary part, is independent of the model chosen for the form-factor and depends only on the o o + - on-mass-she 11 amplitudes for iT^lry and TT —e e . The value of Y is

m + \/mz - 4m 2 O VO e 2m (3.14) e

and substitution of Y in (3.13) while setting X to zero, immediately reproduces the unitarity limit (3.8). The value of X is calculated in this model according to a two-vec tor-meson intermediate state and depends on the physical mass of the vector meson taken. In Table 3.1, two values of B are given calculated with the VDIil; both are slightly larger than the unitarity limit. Quigg and Jackson have also made calculations using Sehgal's model (ref.8), where only one of the two photon couplings occurs via an intermediate vector meson. o + - In this model, values for the branching ratio of the decay K —M jK L appear to be of the same order as the values»obtained from the VDM for this process, suggesting similar behaviour with respect to the o + - decay if-e e .

Fratap and Smith (ref.9) propose yet another model for the form-factor where higher mass states are included in the form of a nucleon-antinuclcon loop (see fig.3.3). When they take a proton-antiproton intermediate state, they obtain a (relatively) large value for B, as listed in Table 3.1.

X. i k • 23 X

fig.3.3. Fee/nmon-dtagiama showing nň-loop h decay

Now, let us come to the category of possible non-electromagnetic interactions between electrons and hadrons. This category includes the neutral current interactions such as sketched in fig.3.4a, predicted by unified theories of the weak and electromagnetic interactions (for a review, see ref.10); then, there is a model based on a type of interaction between leptons and quarks mediated by heavy bosons as in fig.3.4b (see refs.il and 12). A general discussion is given in ref.13 on electrons having a hadronic core, where a superposition of hadronic states H (see fig.3.4c) mediates i o between the electrons and the1T .

„) neutral intarm. boson

lapto-quark boson

«o H, c> direct elactron- hadron coupling

fig.3.4. FetpuMft-dtag/unié contrUbuting to thz decay w° • e*e" Figures 3.4b and 3.4c are examples of direct electron-hadron coupling. Neither of these models gives a definite number for B; the indications are that the neutral current interactions do not contribute significantly to the real part of the decay amplitude, but that direct electron-hadron couplings might result in a rather high value for the branching ratio. In the paper of Herczeg (ref.3), an amplitude originating from a neutral current interaction which is allowed to violate CP-invariance is also included; again, the contribution from this amplitude is estimated to be small compared to the unitarity limit. However, Herczeg estimates interference from an amplitude due to a CPT-violating neutral current to result in a value for B lower than B by more than 4OX. u

In Table 3.1 the main features - relevant to our experiment - from the various models presented above are listed.

3.3. Experimental numbers, and comparison to theory.

The experimental numbers on the branching ratio that were available prior to the start of our experiment are added to Table 3.1. The first number is an upper limit for B, deduced from the 1961 data of Samios' bubble chamber experiment (ref.14) by Davies et a! (see ref.13). The second number comes from the 1976 experiment of Fischer et al (ref.15). This was a counter experiment set up to . + study the K decay (ref.16); as a by-product it produced data on the o + - o rare decay 1ľ—e e , the IT being produced by in-flight decay of the + + o kaon K —1T1T ; this was the first time events from this rare decay were claimed. From about 6 events they calculated the value for B with 90% confidence to be

B - 2.23+2'4 x 10"7 <3.15) -1.1

Comparing this value to the predictions from the various theoretical models, one would conclude that the observed branching ratio fits o within the framework of electromagnetic interactions where the IT e.m. form-factor is governed by a cut-off or vector meson mass, as in the models of Berman ft Geffen or Quigg & Jackson. In the same experiment, Fischer et al determined the slope parameter deiined by (3.10), from single Dalitz pair decays; the value they extracted (ref.17) is a = 0.11+0.03 (3.16)

and, since the slope parameter is related to the cut-off mass by .,

ES

^ 2 2 o A = m /a, a cut-off mass of roughly 3 times the V mass would o result. This would then lead to a branching ratio about 3 times below their experimental value. Resuming we conclude that on the basis of the results of the above experiment no preference for any of the theoretical models can be given.

In order to establish a significant value for B, we aimed in our experiment (ref.18) at obtaining accurate data on 200-300 events o + - if—e e . By detecting SDP-decays at the same time we would also be

able to obtain an accurate value for the slope parameter of the TT e.m. form-factor. In the next paragraph, the basic design of our experiment to achieve this goal will be described. Another experiment for determining the value of B was proposed at Los Alamos by the group of Mischke (ref.19). After several experimental runs, a preliminary analysis showed (ref.20) a tendency towards Fischer's results; however, no final results have been reported upto now.

o + • 3.4. The design of the experiment of TT—e e with Omicron.

The basic requirements for an experiment searching for the o branching ratio B are: sufficiently high TT -flux, freedom from kinematically indistinguishable background and sufficient resolution in order to calculate the invariant mass of the leptons to within a few percent. Burkhardt et al (ref.21) have examined these requirements in great detail; they concluded that the charge-exchange reaction

TT (3.17)

in the AC1232) region offers the best opportunity. We will now briefly discuss the main arguments for this choice, assuming that o the requirements for fl" -flux and resolution can be met (which is the case in our experimental set-up).

Two important sources of background to reaction (3.3) have to be considered, the first of which is the SDP-decay (3.5). Since the branching ratio for the SDP-decay is considerably higher than B, this process poses a background to the pure leptoni c mode? when the ii-. photon is soft. However, the main contribution in this process comes from high energy photons (see ref. 22), which means

the e e pair has a small opening angle and invariant mass.!

The invariant mass x of the e e pair is, as usual, given by

2 2 x = (E+ + E_) - (p*+ + p-J* with E ,E and p" ,p the energy and momentum of the positron and + - + electron; this can be written as

2 2 X " 2E+E_ + 2m - 2p+p_ cos i|i (3.18) where V is the opening angle between the outgoing leptons. Neglecting the electron mass then gives

2 2 x = 4p+P_ Bin iJi/2 (3.19)

with an error<0,OIK. (Note: the invariant mass x expressed in units o of T mass gives the variable x from 3.9ff). The (cinematica 1 ly allowed region for the invariant mass of single Dalitz pairs is, using (3.9)

2m < x < m (3.20) e - - o

and demanding the invariant mass to be within a small region around o the IT mass (x=m for a single lepton pair) it appears that this o source of background will depend strongly on the invariant mass-resolution that is experimentally obtained (see ref.4 of ch.2). The second source of background is due to the fact that, for each arbitrary process in which a neutral pion is created, an accompanying virtual photon production process can take place. The + - background from these photons decaying into e e pairs, the so-called internal conversion pairs, is kinematically indistinguishable from the rare-decay process, assuming that the spins of the leptons are not detected (otherwise leptons from pion decay, having identical helicity, would be distinguishable from those from a virtual photon). Although in our case the cross section for internal conversion pair.*

TT+p + e+e+n (3.21)

* using natural units with h=c=l

27

«^.,;:^Wľ.--.T.sv,--TO-t,-.T^^^ is relatively small (see ref.22) and, in addition, only pairs from heavy virtual photons in the tail of the distribution of reaction (3.21) can contribute to the background (virtual photon mass around m ), the branching ratio B is very low and the signal-to-noise ratio o R, defined as

a(ïï p ••• vr°n •*• e e n) R - (3.22) a (IT p •* "y" -•een)

might easily become so small that events from the rare decay would disappear into the background.

180

9cm( DEGREES^

fig.3.5. Angula/i dlitfuJbutloni o& photo-emliiion (ir~p -»• Y«) and chcuigi ixchange. (ir"p -*-nO at T 'ÍBO tíe.V

The experimental lay-out was therefore chosen to give an optimal value for R. When we consider reaction (3.17) at rest, the Panofsky i ratio given by a(ir p •+• ir n) P = (3.23) O(TT~ p •*• y n ) has a value of Pcíl.5 (see e.g. ref,£3), which gives a value of Re: 1/30 at the unitarity limit. In the A(1232) region however (170

As a result of these considerations, a lay-out was chosen as sketched in fig.3.6. Here a beam of 190 MeV TT particles, analysed by mul t iwire proportional chambers, is incident on a 10 cm long o liquid H target where 25Í is converted to TT with reaction (3.17). 2 o At forward angles, where R has its optimal values, the 1T momentum varies slowly with angle and is close to the momentum of the ó incident TT (300 MeV/c). The decay leptons, isotropic in the tT rest frame, are thrown forward in the laboratory frame; the arrangement of fig.3.6 accepts only the forward region, with lepton momenta roughly in the range 165+55 MeV/c. For these momenta the opening 4 - O angle f of the e e pair falls in a narrow band V =50±2 ; the mul t iwire proportional chamber immediately downstream of the target

is designed to accept electrons with angle relative to the 1T beam o up to 60 .

Later, using extensive Monte Carlo simulation, the lay-out of our experiment was adjusted to give maximum geometrical acceptance in the detection of the single lepton pairs (see ch.4.2).

29 Tl~ SPENT BEAM

MWPC'S4

rt~( 300MeV/c)

fig.3.6. Vtiign o^ ir° •* e*z~ the. ÖMICRÖW Ape.c£n.omvte>i

Invariant mass-spectrum and background

o + - The 1T —e e «vents have to be identified as a small peak in the invariant mass-spectrum at x=m , standing on a background of o internal conversion pairs. At x C m , many single Dalitz pairs will o also be visible. According to (3.20), the SDF-spectrum ends at exactly x=m when a finite resolution is not taken into account, in o which case these pairs should give a negligible contribution in the range of interest. In fig.3.7 the predicted spectrum of + - e e -invariant mass x (calculated from the momenta p and p and the opening angle y .according to 3.19) is given for a I'/, resolution,

30 with various cuts on the summed energy p +p with respect to the

o •fl" -energy E namely: o

(a) no restriction (b) E -dEÍ p +P é E +dE with dE/E=4.50!< o + - o (c) E -dE £ p +p í E +dE with dE/E=l. 82X. o + o

If the cut is placed at dE/E less than 15Í, the SDP contribution becomes almost invisible; in this case, the SDP-spectra do not interfere much in the determination of B,

However, the internal conversion pairs from (3,21) do interfere, since the kinematica1ly allowed range for the invariant mass is

2me < x < nia - mn (3.24)

where m and n are the masses of the ^-resonance and the neutron. £ n A useful parameter is the energy partition y, defined as

y=(p,-p)/p (3.25)

p is the momentum of mass x; internal pairs are distributed o 2 as (l'y ) (see ref.22), whereas single lepton pairs are distributed independently of y. Th

31 15 t Z \ ' \ I CALCULATED \ °l SINGLE DALITZ PAIRS < 10 \ I a) p +P unrestricted I * ' b) p +p within 4.50o/o of Í , c) p +p_within 1.aoD/fi o( U] + V LJ \.n~p-*-y"n-»e+e n v \ QĹ UJ CD - -n ~*eTe .--•--;o. Z 0 50 100 150 200 250 INVARIANT MASS X ( MeV)

fig.3.7, invcuUant mm, iptct/um Uee t&xt)

Some other sources of background, which have not yet been mentioned, are briefly discussed below. (t) Double Dalitz Pairs: if geometrically accepted, they can be effectively suppressed by a reasonable (p +p ) cut in the invariant + mass spectrum (see e.g. ref.18).

(2) tf P elastic scattering: the high cross section for this reaction

generates a large number of secondary pairs of (if.p). When measures are taken to identify the protons in geometrically accepted events (see eh.4) there should be no contribution whatsoever to the invariant mass spectrum. This reaction could also be used as a monitor during data taking. + - (3) radiative capture iC P—jfn — e e n: these so-called externally + - converted e e pairs (from a real photon) could contribute to the invariant mass-spectrum. However, the opening angle between the electron and positron is very small since the leptons originate from a real photon, and they are easily recognised with respect to the o + - I large opening angle of pairs froia iT — e e (see above). The various sources of background, in particular SDP-decay and if p elastic scattering, contribute of course enormously to the trigger rate; therefore, some means of reduction of the trigger rate and pre-select ion of the data had to be considered (see ch.5). Table 3.1: Branching latio vcutueA Uee -text)

rot0 source cut-off or vector meson mass - eV) (in units of neutral pion-mass) r(w° •* YY) unitarity ("B^ 4.75 ., 10"8

Dreli 1,0 3 It

It II 6,95 12

13.9 II It 22 Berman & Geffen 3.16 6.7 It n 9.8 5.7 tt

Quigg & Jackson 5.7 (p) 6.4 II

•i 7.6 (i|)) 6.1 II

Pratap 6 Smith 6.95 (p) 14 II direct electron- hadron » B

CPT-violating neutr.current «B

Experimental values;

Samios < 1200 " (90Z C.L.)

Fischer +24 22.3-11 (90Z C.L.)

33 Raferencea

1. Review of particle properties. Particle Data Group, Rev. Mod. Phys. vol.52 no.2 (April 1980)

2. R.H.Dalitz, Proc.Phys.Soc.(London) A64(1951)6B7

3. P.Herczeg, Phys.Rev,D Vol.16 no.3 (1977) 712

4. D.A.Geffen and B.-L.Young, Phys.Rev.Lett. 15 no.7 (1965) 316

5. S.D.Drell, Nuov.Cim. vol,11 no.5 (1959) 693

6. S.M.Berman and D.A.Geffen, Nuov.Cim. vol.18 no.6 (1960) 4416

7. C.Quigg and J.D.Jackson, Lawrence Radiation Laboratory Report no. UCRL-18487, (1968, unpublished)

8. L.M.Sehgal, Nuov.Cim. 45 (1966) 785

9. M.Praiap and J.Smith, Phys.Rev.D voj 5 no.8 (1972) 2020

10. M.A.Beg and A.Sirlin, Ann.Rev.Nuc1.Sci.24 (1974) 379

11. A.Soni, Phys.Rev.Lett. 52B no.3 (1974) 332

12. J.C.Pati and A.Sal am, Phys.Rev.Lett. 32 no.19 (1974) 1083

13. J.D.Davies, J.G.Guy and R.K.P.Zia, Nuov.Cim. 24A no3. (1974) 324

14. N.P.Samios, Phys.Rev. 121 (1961) 275

15. J.Fischer et al (Geneva-Saclay collaboration), Phys.Lett. 73B no.3 (1976) 364

í 34 i i 16. L.Rosselet et al. Phys.Rev.D 15 no.3 (1977) 574

17. J.Fischer et al (Geneva-Saclay collaboration), Phys.Lett. 73B no.3 (1978) 359

18. o + - A determination of the branching ratio for tT— e e , The Omicron Collaboration, proposal CERN/SCC-77/28 19. J.S.Frank, C.M.Hoffman, R.E.Mischke, R.O.Werbeck, Lampf proposal no.222, Los Alamos (unpublished)

20. R.E.Mischke, private conununicat ion (ti-4-1978)

21. H.Burkhardt, R.K.P.Zia and J.D.Davies, J.Phys. A7 (1974) 40 - - • -_ ^ ^ ^ ^ ^-;-^ .-., . _ 22. N.M.Kroll and W.Wadá, Phys.Rev.98 no.9 (1953) 1355

23. 7 Intermediate energy nuclear physics, Lock ft " Measday ~ (Methuen & Co., London)

35 CHAPTER 4. THE EXPERIMENTAL ARRANGEMENT.

4.1. Introduction.

This chapter contains a description of the apparatus used in the OMICRON-spectrometer (see ch.S) during the 1980 experiments, First a general view on the arrangement within the spectrometer will be given. Then a description of the detectors used to ascertain the presence of particles and to< locate their tracks will follow, Finally some remarks will be made about equipment we used in addition to that just mentioned; here the survey equipment for precision measurement of the position of our detectors will be presented.

V • I I OMICRON-magnet B = 0.5 T«slo central beam "JURA-side'; trajectory

s,. beam hodoscope — — fc X

/ SP - counters—• SH+V Liq. H TARGET platform ľ "SAĽEVE-side" ELECTRON HODOSCOPE He-bags

M.W. PC.

ZTTA DRIFT CHAMBERS

Layout, e+e~

36 4.2. General sct-UP.

Using the C-pipe beam and subsequent configuration as described in chapter 2.2, the experimental arrangement of the spectrometer was as shown in fig.4.1.

The beam entered the spectrometer via a 200mm thick lead collimator, positioned immediately after the last quadrupole lens of the beam line (LG4); the dimensions of this collimator, 150 x 200mm, corresponded to the diameter of the beam tube * 250mm. This was done to suppress background due to particles emerging at large angles, In the spectrometer, the beam passed through the following

scintillation counters: SI or beam hodoscope BH (during the 1980 runs usually SI), S2 or S3, before reaching the target (see Table 4.1 for dimensions of the oounters). The beam was designed such that a focus was obtained at the entrance of the target (ref.l); at counter S2 the FWHM of the beam was about 40mm, whereas at the entrance of the spectrometer the FWHM was of the order of 60mm. The beam was defined on the target by means of a circular scintillation counter S2, positioned just in front of the target; the space around S2 was covered by a rectangular counter S3, which bad a round hole in the middle for fitting in S2 (see fig.4.2). In the electronics, counter S3 was used in ant i - coincidence in order to eliminate events originating from particles in the beam-halo interacting in the target walls (see ch.5.2.1). Multiwire proportional chambers (MWPC's) (see ch.4.3.1) Cl to C4 were used to record the tracks of the incoming particles.

The target, from which secondary particles such as electrons and positrons emerge, contained liquified H at a temperature of 2 o 20 K (see ref.2). An aluminium target vessel contained the cylindrically shaped target flask filled with H , with a diameter 2 of 50mm and a length of about 110mm (see fig.4.3).

I * constructed at the workshop of the Free University, Amsterdam t . 37

í Table 4.1: ScÁntiUation counter, dimzniioni [mm]

Scintillator counter width diam. height thickness number of (material NE102A) , strips

SI 200 200 3

BH+ (beam hodoscope) 25 200 3 8 hor.+ 8 vert.

S2 46 3

S3 725 hole 200 6 50 SH+ (Salève electr.hod.) 1136 100 8 8 hor.

SV+ (Salève electr.hod.) 147 or 137 820 10 8 vert.

SP+ (Salève paddle) 300 400 3 2

JH+ (Jura electr.hod.) 1136 100 8 8 hor.

JV (Jura electr.hod.) 147 or 137 820 10 8 hor.

+ dimension•• s given per strip

3 n Light guides

Jura -track

Beam-track

Salcve-track

fig.A.2. Con^iguAcuUon o j itintMivtoU S2.S3

The secondary particles were detected on both sides of the central beam trajectory in the so-called Jura- and Sal eve-arms of the spectrometer, corresponding to the left and right hand side (resp.) with respect to the incoming beam. Both arms shared one MWPC (C40), and further consisted of three drift chambers each (see ch. 4.3.2) and a hodoscope of scintillation counters. These electron-hodoscopes contained 8 horizontal and 8 vertical strips, amply covering the surface of the outer drift chambers. The drift chambers were positioned inside the spectrometer in order o + - to obtain a maximum acceptance for events If—e e ; the plane of the Jura-drift chambers was parallel to the X-axis, while that of the Saleve-drift chambers was tilted with respect to the X-axis by 15 degrees. In addition, two scinti Ilators covering the first two vertical strips of the Saleve hodoscope wers mounted just in front of it, in order to obtain an identification of the protons from IT - p elastic scattering^ on the Saleve side (this was done by means of pulseheight discrimination, see ch. 5.2.4); these scinti1lators were called the Salsve paddle, or SP-counters.

The hodoscopes and counter SI were mounted inside the magnet at a fixed position; all signals from the scintillation strips including those from S2 and S3 were led to their respective photomultipliers outside the magnetic field via perspex lightguides.

39

Äfi^ - beam direction (x-axis)

target f lask with liq.H,

C40 mylar entrance foil

fig.4.3. Taageť aaembly [dunzmioiu in mm)

How«\ f, the assembly of S3 and S3 and their light guides could be moved in and out of the magnet through one of the side gaps, a location jig providing an accurately reproducible position of the assembly inside the spectrometer. Also the target vessel, mounted on a long arm, could be moved in- and outwards through the gap on the other side; again a location jig secured correct positioning of the target inside the magnet. All the chambers and location jigs were rigidly mounted on a large aluminium baseplate, furnished with several airbearihgs. Thus it became possible to slide the base with all that was on it out of the •••f- magnet onto a platform adjoining the lower pole face (the so-called dummy-pole), e.g. for repair jobs or surveying of the chamber positions (ch.4.4.1). Inside the spectrometer the base was located by precision dowels relative to the magnetic pole.

40 4.3. Wire detectors.

4.3.1. Multiwire proportional chambers (MWPC).

In the experiment, the detectors Cl - C4 and one of the detectors in the secondary arms are of this type (sen ref.3 for a detailed description; as an example, in fig.4.4 the construction of chamber Cl is sketched). M.WPC's consist of, planes of evenly spaced parallel wires hold between planes of aluminium foil, from which they are insulated. When a negative high tension of a few kilovolts is applied t., the foils and the system is filled with a suitable gas it becomes an array of proportional counters of which the foils are common cathodes and the wires individual, anodes. An ionising 'par t i cle traversing the system is detected by one or two wires closest to its trajectory. Their signals therefore furnish one coordinate in the plane of the chamber. A second set of parallel wires in a neighbouring cell determines the position of the hit in the plane; additional planes at other angles serve to reso'vc ambigu, ties *vh.n there are several hits within the sensitive time of the chamber, which is typically about 50ns for a wire spacing of 1mm.

The choice of MWPC's was determined by their ability to operate 6 -1 in particle fluxes of the order of the incoming.beam (^10 sec ); their dimensions could be kept small in accordance with the size of the beam, whereas the resolution could be of the order of 0.5mm, as required by the experiment. However, one MWPC of larger dimensions had to be made especially for this experiment (C40), since this chamber was used to determine the trajectories of secondary particles. In all cases the condition that the resolution of the detector should be of the same order as the error due to multiple scattering was fulfilled. The hardware parameters of the MWPC's are given in Table 4.2. For the gas composition, the classic "magic" mixture was taken, which contains 7054 argon, 275Í isobutane, 0.4'/, freon, and 2.6% me thy lal (see ref.4). The high voltages were applied between the anode wires and the cathodes, according to the various plateaus, where efficiencies were measured to be in the range of 90-97%. The negative high voltage on the cathodes, aluminium foils of iO-um thickness, was set to values from -3.50 to -3.60 KVolt. Using an on-line computer-procedure, the above mentioned efficiencies were calculated in the following way (see also ref.5). In order to compute the efficiency of plane i<£ ), two adjacent i planes j and k were selected (usually j,k=i + 1, i -1) ; if these planes had one hit each the value of counter M was incremented by one. jk

41 7 nnm vetresite - frame

Mylar window (6u) A Al • foil (cathode, lOn ) A Vertical anode-wires (0 = ion) A AI - foil ( 10H) A í I.Z Inclined anode • wires A Al -foil ( 10 |i) A Horizontal anode-wires (0 = 10w> A Al - foil ( 10n) A Mylar window (6u)

BEAM

fig.4.4. Oiote-ievbion o& chamb&i Cl (anode utOiii Ofj gold-plated tung&ten, 160 in each plane)

If al the same time one hit was recorded in plane i, another counter N was incremented; now the efficiency is given by fc. =N /M *100ľ<. jk i jk jk (Note: in this manner efficiencies were calculated for n whole plane and not for individual wires.) A single hit cluster on the adjacent planes, where not one but a small group of neighbouring anode wires produced simultaneous output pulses, was also taken into account in this calculation; the ratio of single hits to hit clusters was in our experiment of the order of 3:1, which was normal for this type of detector and acceptable for the experiment.

The resolution (rms deviation) was calculated from the reconstructed tracks in the analysis programs; the value obtained was of the order of 400ynm, to be multiplied by the wire spacing in millimeters, for all chambers.

42 Table 4.2Í MblVC - data.

MWPC plane wires dimensions (mm ) dimensions wire chamber used spacing (mm) in exp.

Cl 1 horiz. 160x160 same 1 2 inclined II M 3 vert. If 11 1

C2 1 horiz. 128x128 same 1 2 vert. II ti 1

C3 1 horiz. 128x128 same i- i M 2 vert. II l

C4 1 inclined 128x128 same V2 2 inclined M tt \j2 3 horiz. tr i? 1 4 vert. ii II 1

Ľ40 1 inclined 544x544 384x384 2 ':' 2 inclined II 11 2

• -_ 3 hori;:. 384x384 256x256 2 f 4 vert. n 384x384 2 + . wires rotated -45° with respect to pos. y-axis

++ . [ wires rotated +45° with respect to pos. y-axis

43 ŕ. 4.3.g. Adjustable field drift chambers (AFDC).

The drift chambers used in the Omicron spectrometer were of the adjustable field type (see reis.6 and 7; for a sketch of the construction, see figs.4.5 and 4.6). The mode of operation of these chambers can be understood by reference to fig.4.6. Each plane is divided into a number of drift cells. Each cell contains one or two anode wires held at positive high tension which act as proportional counters. The cathode wires are .at negative potentials decreasing from a maximum at the extremes of the cell towards zero at its centre. The cathode wires therefore produce a region of an approximately uniform electric field (the drift field) between the "field-shaping" wire and the anode. An ionising particle traversing the plane of the chamber leaves a column of ionisatiou, and the free electrons are driven towards the drift field. The distance of the hit from the anode is then given by

X,. - X = ƒ v ft)dt 0 where v(t> is the driftvelocity and t the drift time of the d electrons from the position x of the hit to that of the anode x . h a ŕ- The choice of the adjustable field drift chambers • was decided by the need to operate the chambers in a magnetic field parallel to one set of anode or sense wires. In this case the drifting electrons are subject to. a Lorentz force, which has to be compensated by tilting the electric field created by the cathode or field wires (see refs.3 and 7). Thus an additional component of the electric field opposite to the Lorentz force was introduced; in this experiment the value for the tilt angle B was chosen according to tan 9 P 1/3, appropriate for the applied magnetic field of B = 0.5 Tesla. In each cell we used two adjacent sense wires, placed 500/um apart, in order to resolve the left-right ambiguity with a minimum of planes (ref.7).

44 Mylar window (8 M) Aluminised mylar (1O|i) 3mm 6 Cathode wires Vertical sense wires'* * 3 + fie Id- shaping wires" 3 Cathode wiros+

Al - mylar - Al ( 13 n)

Cathode wires Horizontal sense wires.* * 3 + field • shaping wires* 3 Cathode wires*

6 mylar (10 (O 3 Mylar window ( 8 u )

fig.4.5. Oio44-4ec£ion o j dnÁ^tchombeA. (• = 01Ú0iim Cu-Be tai&e, •• = 0 lQ\m goti-ptouted tungitin uúJ)

cathode wires anodic wire-couple ( -HT) (+HT) 1 2 26

field- ' shaping wire (-HT) 26 2 1 50 mm cell

25 mm half-cell M 25mm half-cell

•4 fig.4.6. Oion-Azction o^ ceil I no tUt angle.)

45 The drifl-times were measured with reference to the electronics trigger (see ch.5.4).

Various parameters of the drift chambers are listed in Table 4.3; here the abbreviations used fo~ the AFDC's correspond to the drawing in fig.4.1. All the measured values given in the table are typical, and given for the actual experimental situation, i.e. with magnetic field and tilted electric field. The gas mixture was composed of 50H ethane and 50Jť argon; the values for the applied high voltages were of the order of 2.1 KV for the sense wires and -3.3 KV for the cathode wires (across one cell) and field-shaping wires. With the aid of W, Lourens and C.W.E.van Eijk, at the University of Technology in Delft a voltage distribution system was developed for applying proper voltages to the AFDC's and monitoring their leak-currents . Also a system of noise-suppression at the input of the preamplifiers for the sense wire-signals was developed. This was an essential step which ensured a correct functioning of the drift chambers since it allowed us to work with low discrimination bias.

Table 4.3: V/uft ckcmbeA clata (604 •t., 4ee ( -•

dimension drift efficiency plane cell length no. of no. of o velocity V of plane (%) (ram) cells wires (mm) Q (nsec) (Um/nsec

JD3 vert.wires 50 13 26 650 51.5 699 93 hor. wires 50 13 26 650 51.3 699 94

JD41 vert.wires 50 17 34 850 51.6 700 96 hor. wires 50 13 26 650 51.9 703 96

JD42 hor. wires 50 13 26 o50 51.2 703 98 vert.wires 50 17 34 850 51.0 705 97

SD3 vert.wires 50 13 26 650 50.2 704 96 hor. wires 50 13 26 650 51.5 706 97

97 SD41 vert.wires 50 17 34 850 51.5 705 ,!T. í\ hor. wires 50 13 26 650 51.8 705 97

V- SD42 hor. wires 50 13 26 650 50.4 705 98 vert.wires 50 17 34 850 50.8 705 97

46 The values for the efficiencies have been determined (with a rigs deviation of appro*. IX) using an on-line computer procedure (see also ref.5), as in the case 01' the MWFC's. Here the procedure was as follows: in order to compute the efficiency of wire n in plane i (£. ), again two adjacent planes j and k were selected. If ni thes R planes had one hit each, a predicted coordinate in plane i was calculated on the basis of a straight line truck from plane j to plane k, and the value of counter M was incremented by one. Only jk if there was one hit in a region in plane i centered around this predicted coordinate, another counter N was incremented, and the j k efficiency was then again Given by £ = N /M * 1OQX, The region ni jk jk around the predicted coordinate was taken suitably large in order to compensate for the neglect of the curvature of the track and to allow for the intrinsic resolution of the planes. In this way the efficiencies of all wires could be calculated separately; in the table, however, average efficiencies per plane are given.

The drift velocity v and the time-offset parameter t o o (indicating the end of the drift time spectrum; see ch.5,4) were determined by A.G.Zephat using the track reconstruction method as presented in ref.8, based on a principle described in refs.9 and 10. The value of v was determined to an accuracy of IX (nns deviation), o the value of t had a rms-deviation of 2 nsec (see ref.ll). o These values were determined from a separate set of measurements, that were done in the following way. The electronic equipment was changed such that a coincidence between a signal from the Jura-side hodoscope, i.e. the recording of a particle in both any vertical and horizontal strip, and a signal from the Saleve-side hodoscope sufficed to trigger the data acquisition. Since this particular excercise was done with all equipment as under normal running conditions but without any incoming beam, these Irip.ncrs represented cosmic rays passing through the apparatus of the secondary arms over a wide range of angles. These events -1 occurred at a rate of about 1 sec ; it appeared that the energy of the cosmic rays was sufficiently high for their track in the magnetic field to be very well approximated by a parabola, which greatly facilitated the analysis. The cosmic ray-measurements have been performed at various occasions durinp *llc 19P0 runs. Since the tracks passed over a wide range of anples through the secondary arms of the spectrometer, the drift chnmbets were irradiated uniformly; as an average, several hours of measuring-time proved tc be adequate to build-up the statistics necessary for obtaining accurate numbers for v and t per plane. o o In addition, usinr; the track rerous t rue t ion method, small corrections to the measured positions of the ADrC's could be determined. The time distance relation was found to be linear within the experimental error, confirming that the application ~f the

47 method of tilting the electric field was performed correctly.

The resolution (rms deviation), obtained from the reconstructed tracks of cosmic rays in the analysis programs, was for all drift chambers of the order of 300yum.

If a track incident on a chamber is not perpendicular to the «ire plane of that chamber, the coordinate obtained from the drifttime will be too small since the drifttime corresponds to the shortest distance from a sense-wire to the incident track and not from its centre of gravity. In this case, the coordinate must be corrected; in the analysis program (see ch.6) such corrections were made according to the method given in ref.12 (see this reference for a detailed discussion).

4.4. Additional equipment.

4.4.1. The survey rig.

As mentioned before (ch.4.2), the base on which all the chambers were mounted could be slid out of the spectrometer onto the dummy pole, where it was dowel led into position. A survey rig was designed to move across the dummy pole, in order to measure the positions of the chambers with respect to the base. Once these positions were known, the absolute positions of the chambers wi'thin the spectrometer could easily be obtained using the known relation between the position of the base inside and outside the spectrometer.

The survey rig consisted of a video-camera with a fixed focus, capable of moving in three dimensions. A mechanical arrangement using precision dial gauges ensured an accurate readout of the three coordinates of the camera. The camera was positioned such that a good focus was obtained on one of the fiducial marks on the chambers, and the dial gauges were read. On each chamber two fiducial marks were placed at fixed positions with respect to the positions of the wires in the chambers; in this way the position of each wire relative to the base could be determined. The requirement that the uncertainty in the position of a wire should be small compared to the resolution was satisfactory; on average, the positions of wires were determined to an accuracy of about 50yum. 4.4.2. Helium-hags anf* background reduction.

In order to obtain the required accuracy of our results, the multiple scattering should not contribute more to the experimental error than the resolution of the detec tors. This~could be achieved by replacing the air between the detectors by helium, using he 1ium- bags . These are bags made of mylar foiI continuously flushed with helium (radiation length about 20 times larger than in air). The He-pressure within a bag was just over 1 atm. One such bag was employed in the beam line, from the end of the vacuum pipe up to the last quadropole lens (see ch.2,.2). Within the spectrometer we used helium-bags in the spaces between the multiwire chambers Cl to C4 (see fig.4.1). Another bag filled the space between the two inner drift chambers (JD3 and SD3) ond C40 (see ch.4.O. The helium-bags between chambers Cl to C4 were constructed in the form of the bellows of an accordion; in this way the bags could be moved --into position very easi.ly after the mounting of the chambers on the base was finished and could be inflated subsequently. Before employing the individual helium-bags, we planned to use one large helium-bag or helium-box, in which the whole apparatus was embedded. However, this arrangement made it difficult to comply with the CERN safety rules which required the gas composition in various parts of the apparatus to be monitored continuously to detect any escape of highly explosive components of the detector gas. It also proved to be very difficult Eo fill the box in a reasonable time after an intervention without creating a dynamic overpressure which would endanger the chambers. We therefore had to adopt the above system of small bags, which functioned satisfactorily.

To conclude this section, two provisions made to suppress background should be mentioned. Firstly, a brass plate of about 15mm thickness was placed alongside clumbers Cl and C4 on the Jura-side, to protect the Jura dri f t-chambers from incident muons originating at shallow angles from decaying pions in the beam. .. Secondly, a 2mm thick aluminium plate was introduced between the horizontal and the vertical strips of the Saleve electron hodoscope. This was done in order to slow down the protons from inelastic iTp- scattering; these protons were of higher momentum than those produced by fTp- elastic scattering, and appeared everywhere in the Saleve hodoscope strips. The additional absorber stopped some of these protons and so reduced the number of triggers. Other protons were able to cause trigGers but could be distinguished from positrons in the analysis by the pulse size in the scintillators.

49 References

1. o The choice of the beam trajectory for TT —• 2e, W.van Doesburg and G.Kernel, CERN-Omicron report (29.02.19B0)

2. J.D.Davies and R.Gregory, private communicat ion (CERN) 1980

3. E.Chiavassa, S.Costa, G.Dellacasa, M.Gallic, A.Musso, M.Panighini, K.Bos, W.van Doesbure, A.Stanovnik, and D.Vranie, N.I.M. 156(1978)187

4. R.Bouclier, G.Charpak, Z .Dimcovski , G.Fischer, F.Sauli, G.Coignet, and G.Flugge, NIM 88(1970)149

5. A.G.Zephat, Omicron note (CERN) 0N-81

6. I.Charpak, F.Sauli, and W.Duinker, N.l.M. 108(1973)413

7. A.Breskin, G.Charpak, B.Babioud, F.Sauli, N.Trautner-, W.Duinker and G.Schultz, N1M119(1974)9

8. G.Dellacasa, M.Gallio, A.Musso, M.Rapetti, A.G.Zephat, N.Mirfakhrai, S.M.Playfer and E.G.Michae1 i s, N.l.M. 176(1980)363

9. H.G.Twijnstra, ACCMOR Report no. 15, University of Amsterdam, Zeeman Laboratory (1977)

10. W.Spiérenburg, ACCMOR Report no.24, NIKHEF-H (1978)

11. o Drift-parameters for the tí -experiment from IB.08.80 till 29.10.80, A.G.Zephat, CERN-Omicron report (Jan. 1980).

12. A.Breskin, G.Charpak, F.Sauli, M.Atkinson and G.Schultz, N.l.M. 124(1975)189

50 CHAPTER 5. ELECTRONIC EQUIPMENT AND DATA AQUISITION.

5.1. General set-up.

The output signals of all detectors (scintillation counters, multiwire proportional and drift chambers) were transferred to the data taking system, a lay-out of which is shown in fig.5.1. In this system, the N1M-electronics played a central part; triggers wore formed from the scintiUator signals, and relevant information was passed on to pattern units, ADC's and TDC's ,

SCINTILLATION MULT I WIRE DRIFT COUNTERS CHAMBERS CHAMBERS

NIM strobe RMH ELECTRONICS SYSTEM

target

~l C CC ui a A 5 o u DTD < < ň SYSTEM M stop O o Is A 10 C L Tí BORER INTERFACE

HP 21 MX 1600 bpi ,-Jy. COMPUTER GD 45 ips 9 tracks

fie.5.1. Layout o á data-taking

Furthermore, the NIM-electronics gave a gate-signal to the readout system of the MWFC's (the "RMH-syst em") and of the AFDC's (the "fiTD-system"). Finally, it provided a trigger to the LAM-grader,

51 which was the sign for the computer to commence readout.

In our experiment we used a Hewlett Packard HP21 MX minicomputer with 80 K memory, of which 38 K directly addressable, and standard peripheral equipment. Transfer of data to the computer was performed with CAMAC, via a Borer series 2200 interface. In this way, we were able to use existing CAMAC software facilities, supported by CERN (ref.l). In total, six CAMAC crates were used, five of which contained the DTD-readout system; the sixth crate was filled with (CAMAC) sealers, ADC's, TDC's and pattern units; as well as the LAM-grader. In addition, the last crate contained the MWPC-interface used for communication with the RMH-system, the functioning of which is independent of CAMAC,

In the following sections we will elaborate on the various parts of our data-taking equipment. In addition, we will present a method used for preprocessing of the data, and finally a description of the data acquisition (DAQ) system will be given.

5.2. The NIM-electronics.

In this section, an outline is given of the NIM-electronics as used in our experiment; a block schematic is shown in fig.5.2. Here the output signals from the scinti 1 la tors, all (except the beam hodoscope counters) having a 2" EMI photomult i piicr (type EMI 9813 K.ÜJ and equipped with a CERN standard base (type 4238., see ref.2), were generating the logic necessary to recognize signals from good events among a variety of signals. Three basic coincidences can be distinguished, from which the final coincidences were derived, namely: (a) the beam coincidence A(BM), indicating an incoming particle; (b) the Jura-coincidence A(JHV), indicating a secondary particle on the Jura side of the spectrometer; (c) the Sa leve-coincidence A(SHV), indicating a secondary particle on the Sal eve. side of the spectrometer.

5.2.1. Beam logic.

The signals of both the vertical and horizontal beam-hodoscope strips, which were equipped with 3/4 " bialkali photomult i p Iier of the type EMI 9826 A and a specially designed base (see ref.3), went via a discriminator (LRS type 620) into a logic OR (LRS type 429). With the two outputs thus obtained, O(BH) and 0(BV), a coincidence A(BHV) was formed indicating a beam particle in at least one horizontal and one vertical strip. The signals from scinti 1 la tors SI, S2, and S3 were fed into updating discriminators (LRS type 623), whereafter a coincidence A(BM) was formed (using a LRS type 465 coincidence unit) between SI, S2, S3 and A(BHV) in order to establish a beam particle on to' tire liquid H • target. 2 ^— (GCJ 1SP1 J v ") l^rrrfg iMa i^rrffi

DISC) ATÍSP1! AT(SP2) LFO LFO LFO LFO PUČU

ADC»-! • ADC

SCALER FO(BM)

PRE SCALER P.u e » SCALER

A ' AND ( COINCIDENCE) O OR D DISCRIMINATOP FO LOGIC FAN-OUT FO LINEAR FAN-OUT PS PULSE SHAPER 1,2 ms TU TIMING UNIT TU AT: ATTENUATOR TU 20 ns M . LENGTH OF OUTPUT PULSE 50nsL Is PS PS LAM 1 ^ PS GRADER PS ' SCALES P.U. 6 ADC P U.o.p INHIBITS J OUT GATE GATE GATE DTD STOP (PROMPT) BORER -• TDC START RE5ET

In fig.5.2. Block ichemcuUc otf NIM zZzc.tA.onia> {deZayi not ihouin] The pulse coining from S3 was shaped to a width of 20ns because this pulse, corresponding to a particle in the beam halo, was used as a veto. Occasionally, the gas-cherenkov counter was used to determine electrons in the beam, and is therefore included in the block schematic. Under normal running conditions this detector was not in position (see ch.2.2).

5.2.2. Jura- and Saleve-side loeie.

In order to obtain a signal indicating a particle on the Jura-side, a coincidence requirement was made between the horizontal and vertical strips of the Jura hodoscope. Via a linear fan-out (LRS type 428 A) and a discriminator (LRS type 620) the pulses from the horizontal strips were fed into a logic OR (LRS type 4?,9), the output of which was used as a gate to the coincidence units A(JHV), LRS strobed coincidence type 370, The pulses* from the vertical strips were, again via linear fan-out and discriminator, input to these coincidence units. The gate was fixed in time by adjusting the delays between the photomultiplier-output of the horizontal strips and the linear . fan.-out with respect to the signals of one of the vertical strips. I With this gate as a time reference (8 nsec width), the signal going to A(JHV) from each vertical strip (20 nsec width) was timed-in such that the period of the gate fell in the middle of the signal. I The eight output signals of the coincidence units were fed into a • logic OR circuit O(J), LRS type 429; the cables from A(JHV) to this OR circuit were of different length, in order to correct for the difference in transit time (of the order of several nanoseconds) between electrons travailing from the target to tha upstream and downstream end of the hodoscope.

Via two linear fan-in circuits 0(JV) and O(JH), LRS type 127, the signals from the vertical and horizontal strips respectively • were taken to ADC's, to permit pulseheight-discriininat ion of protons > from electrons in the analysis. Furthermore, each signal from horizontal and vertical strips was '•'& applied to a time digitising device (DTD, see ch.5.4). This made it '", possible to identify the hodoscope strips which had furnished the "; trigger signal and to distinguish them from those struck by stray ,: particles during the sens i t i ve 'time of the drift chambers. -"\ C- This time is given by the maximum drift time across the cells :';: and is about 500ns. A flux of stray particles equal to about Z01Í of •/ the beam striking the target passed through the Jura-side drift ƒ;; chambers. The time-informat ion from the hodoscope strips struck by Vj these strays permitted in certain cases the identification of their -'•? hits in the drift chambers after which they could be eliminated from i the analysis. . ;Ï

54 With the signals of the Saleve-side hodoscope, a logic was used similar to the one described above.

5.2.3. Further logic.

The outputs from the logic OR circuits 0(J) and 0(S) were put into a coincidence unit (CERN type N6237) in order to obtain a signa' A(JS) corresponding to a hit in both the Jura and Saleve arm of the trigger system. This pulse A(JS) and the beam trigger A(BM) constituted the initial trigger A(ee). using the coincidence unit LBS 465.

A considerable reduction of this trigger was obtained by applying a veto signal from the "central plane" hodoscope strips. This signal was obtained by forming a coincidence A(JS45) between a signal from one of the two middle (= 4th and 5th) horizontal strips on the Saleve-sidc and a similar signal corresponding to the Jura-side (via OR circuits 0(S45) and 0(J45), LRS type 429). The veto signal represented, apart from a small number of good triggers, + - a large background due to coplanar e e -triggers in the mid-plane caused by electrons in the incoming beam. The main trigger for the experiment A(ee45) was the initial trigger A(ee), put into coincidence (LRS type 465) with the veto signal just mentioned.

5.2.4. Final trieeer and subseouent logic.

In addition to the signal A(ee45) three other signals were used to constitute the final trigger A(TR).

Firstly, in order to monitor the incoming beam and initial ,.- > tr i gger- ra te, the beam trigger A(BM) and the initial trigger A(ee) .-.I were scaled down by known factors and, via OR circuits LRS 429 A, included in the final trigger. ,'">'. Secondly, a trigger representing events from TTp elastic scattering '£ was formed and, again via OR circuits and scaled down as above, " .'. combined with the main trigger as a monitor to the detection system * and for later normalization of the Dalitz pair spectrum.

| The TTp-elaslic trigger A(ifp) was obtained in the following ].l ;}" way. The signals from the SP -counters covering the region of the : t first two Saleve vertical strips (see ch.4.2) were used as an ..' ; identification of protons on the Saleve-side. The large pulses from h protons in SP1 and sr? were selected using a sequence of an I i;. attenuator and a discriminator, after which the signals were ••':' JO combined in a logic OR circuit O(SP). The elastic scatters detected ~

55 o by the system have a very large opening angle of about 110 , and in our experimental arrangement only the upstream ends of the electron-hodoscopes contained such secondary particles. Therefore, only the first two Jura vertical strips were selected (via OR circuit O(JV1E), LRS type 429) to go to the A(fTp) coincidence unit (LRS type 465). Here they were combined with the beam trigger A(BM) arvd the (ant i-coincident) Saleve proton- si gnal O(SP). The A(iT p) signal was further used as a veto for the initial trigger A(ee).

Having thus formed the final trigger A(TR), this signal was used to produce the necessary gates for pattern units, ADC's and TDC's as wel] as a gate for the multiwire- and drift chamber readout systems, as indicated in fig.5.2, The time reference for the TDC's and DTD's, deteriorated on account of the jitter from the various levels of coincidence, was reshaped with a 5ns wide pulse from counter S2. Obviously, the final trigger was also used to provide a NIM-level to the LAM-grader, as a signal to start the data acquisition. The output of the LAM-grader, i.e. the computer busy-signal, was used to prevent further output of A(TR) during readout of data, and was also taken to inhibit some of the CAMAC sealers.

5.2.5. Pattern units. ADC's TDC's. and sealers.

In order to facilitate the analysis of the dala, signals from the various triggers A(BM), A(fl"p), A(ee), A(ee45) and from counter S3 were taken to separate inputs of a pattern unit labeled (, . Further pattern units (labeled<* and P) were used to identify the horizontal and vertical strips of the beam-hodoscope.

For pulse height analysis, signals from S2, the Saleve counters SP1 and SP2 and all Jura and Saleve hodoscope strips were taken to input channels of an ADC (LRS type 2219 A) via linear OR circuits. In addition, two time spectra were recorded with a TDC (LRS type 2226 A); the stop signals came from pulse-shaping circuits PS(J) and PS(S) of the Jura- and Sa leve-hodoscope, while the (common) start. was provided through the final trigger. This was done to perns i t electron-proton identification using the time of flight of the secondary particles.

CAMAC-sealers were used (LRS type 2551/2552 and SEN type 2S2024) to collect the following signals: counters SI, S3, S3, output from coincidence-units MBM), A(JS), A(JSICO, A(ee), A(TTp), A(ee45) and A(TR)., as well as signals from the Jura- and Saleve-hodoscopes taken from PS(J) and PS(S), and finally the individual signals of the horizontal strips on Jura- and Saleye-sidc taken from O(JH2) and O(SH2).

56 Table 5,1: Typical counting fiatu duKing 1980 HUM {Í&C ]

Counting rate

A(BM) "i. 10 x 106

6 SI 2..25 x I0

6 S2 1,.36 x 10

6 S3 0.69 x ÍO

PS(J) = Jura 6 hodoscope

PS(S) = SalSve g hodoscope

A(JS) 2.1 x 103

A(ee) 319

A(ee45) 75

A(itp) 1A

A(TR) 7A

If •ŕ I 87 A 100 Hz signal was also recorded in the sealers; once with (n ) 100 and once without (N ) the inhibit from the LAM-grader. This way too the dead time of the computer could be calculated from X B <1 - n /N )• ÍOOX. 100 100

5.2.B. Tripger rates.

Table 5,1 shows typical rates of both individual counters and coincidence units during the runs of August • November 1980. Most of the time we had to operate at a rather low value of extracted beam, due to a defect in the synchrocyclotron. During the 19B0 runs, the beam-hodoscope signals were not used in the coincidence A(BM) due to problems arising from a bad transmission of light to the phot omul t i pi i ers . Therefore, t lie coincidence A(BM) only contained the information from SI, SC, and S3.

with the A(TR) rate of 74 per second, the computer dnad t ime appeared to be about IB", which was partially « .used by the software pre-se I ec t ion being operative (see ch,5.5.2).

5.3. The MWPC readout.

For the readout of the MWPC's, the so-called RMH-system was used, developed at CERN (see ref.4 for a detailed description). In this system, there is one preamplifier and amplifier for each wire. The preamplifier cards, each with 32 channels, are mounted either directly on the chambers or on a support close to them. They are connected to the wires by flexible leads to allow a very high versatility in the chamber positioning. From the preamplifiers, the signals were sent via about 100m long 32-twisted-pair cables to the amplifiers, the receiver-memory-hybrid (RM11) module!:. Here, after amplification, the signals are stored into memory if a gati? has been generated by the N1M-electron ics . Each RMH-module has 32 channels with a hybrid circuit having an amp!ifier-discriminatcr for each channel, a flag switch, a monitor "ť-, output giving real time signals, and a strobe input. In n (special) RMH crate a maximum of 22 modules can be housed, together with a crate encoder and a control unit, The latter contains amongst others a common strobe input, the use of which we preferred to strobing the RMH modules individually.

Figure 5.3 shows the lay-out of the RMH-system which w«s used in our experiment; four RMH crates were used filled >v i It li 7 1 Ri.'H modules, which is equivalent to a total of 2272 wires' tt,rrrs[ onUug to the regions of interest of the

58 CRATE ENCODER TWISTED PAIR | CONTROL UNIT CABLES

r i i i i i i i i • STROBE „..1... 22 RMH MODULES INPUT -4\ (704 WIRES) o 1 I I I I I I I 1 RMH CRATE 1 terminated

\\\ i i i i n M MWPC T PRINTED CIRCUIT 00 BOARDS I I I I 1 I I I I I I RMH CRATE 2

\\\ i i i i i i i r

i i i i i i i i i i i 00 RMH CRATE 3 I í I I I I I I I I I D I I I I I I I I I I I RMH CRATE 4

SYSTEM ENCODER MWPC INTERFACE

CAMAC CRATE

TO FAST DECISION LOGIC

fig.5.3. Trie RMH madoiLt it/itm

59

a&T;^^ ,, A signal of 75 nsec duration was used as a strobe to all crates, after which the stored information became available for readout. This is performed by the crate encoders, who are connected to a branch, controlled by the System Encoder (SE) that receives the coded hit channel patterns. Communication of the SE with CAMAC was obtained by using the MWPC-interface, connected to the SE via an internal output bus; an extra front panel data output-connector on the SE provided fast access to data when required.

Special care had to be taken to ensure that the RMH-system prpperly re-reads the data after preprocessing, i.e. after reading with the front panel output only. Furthermore, a special configuration of the RMH modules within the crates had to be used for use with the hardware preprocessor (see ch.5.5.1).

5.4. The AFDC readout.

The readout system used for the (adjustable field) drift' chambers is the DTO-system, developed at CERN by Engster and Verwey (refs.S and 6), see figure 5.4. . * The pulses from the sense wire of an AFDC were taken from the Lemo connector on the printed circuit board, (see chapter 4). These signals were led via appox. 7 m long (50.fi.) cables to a preamplifier-discriminator of the type CERN N4190. These preamplifiers are modular (16 channels) and drive 5'ÓJl coaxial cables to the drift-time-di gi Users (DTD), type 215. Each of these modules has four time measuring channels for a maximum of 16 inputs, with a time resolution of 2 nsec and a time range set to 768 hsec. .The input signals were taken as the start of time measurements; the stop was the experimental event-trigger, applied via a DTD controller type 211.

The sequence of operations was as follows: after being initialised by the data acquisition program, the DTD controller provided control (enable) and clock signals to the DTD modules via various fan-outs. From that moment on, the DTD modules were accepting start signals originating from the sense wires of the AFDC's; after a stop signal from the NIM-electronics, the modules were ready to be read out. In the time-spectra thus' obtained the time-offset (t ) could be o recognised, corresponding to zero drifttime of a particle at the sense wire of a cell, and a range of approx. 500 nsec corresponding to a half-eel 1-length of 25 mm at approx. 50 Mm/nsec dri f t-velocity I (see ch.4.3.2). ' All DTD modules were contained in five CAMAC crates, together with the DTD controller; they were directly accessible 'to'the data acquisition and/or monitor program. , In our case, all modules were read out sequentially in a single

60 block-transfer of data, in order to keep the duration of data-transfer as short as possible.

INPUT CH. 50 R LEMO OUTPUT CH. CABLES i i \ 1 1 f> r—i v — PREAMPLIFIERS 4190 — 16 CH, ( NIM )

T AFDC I I I DTD CONTROLLER terminated FAN-OUTS 1 T r STOP CAMAC IN CRATE DTD CONTROLLER MODULES CLOCK ENABLE D STOP OUT J I CAMAC CRATE 1 f

DTD MODULES

D J I CAMAC CRATE 2

TO HP 21 MX

fig.5.A. The VTV leadowt ttjitm

61

^ '/.-• S.5. Preprocessing of the data.

B , -1 At the highest beam intensity of about 3*10 particles sec , the event rate was about ISO final triggers per second. At this rate, we suffered from a substantial computer dead-time of the order of 3054; furthermore, every 13-20 minutes a magnetic tape would have been filled with data. In order to reduce the rate of events offered to the computer we looked for a method of fast inspection of the data available through our normal trigger.

A solution was found in using a hardware preprocessor, originally designed by Pizer et al

In chapter 5.5.1 the above hardware preprocessor will be presented. Unfortunately, due to defects in the electronics, the FOL was not available for data-taking during the 1980 experimental runs. A temporary alternative was found by implementing a software version of the FDL into the data acquisition program; this will be explained in chapter 5,5.2.

5.5.1. The hardware FDL.

5.5.1.1. Principle of operation.

The principle of operation of the FDL can best be understood with the help of figure 5.5. Here a type of event is shown that frequently occurred at the higher beam intensities: tracks originating from an interaction point (labelled 1, in, lb) and n simultaneous beamtrack without interaction in the target vessel (labelled 2). In this picture, the planes Al to A4 of ibn post-target chamber CIO have three hits each, while tin; planes 'BI to B4 of the pre-target chamber C4 have two. When the hit pattern is read in from the RMH-syst em, the pnipose of the FDL is firstly to eliminate non-interact ing hanm tr.ir.ks (track 2), and secondly to look for nn acceptable opening migle between the tracks corresponding to the remaining hits (tracks la + lb). The first aim is achieved by the function of the PTS (rropnn«Me Track Selector), the second by the function of the ACli (Aiilhmrtic Control Unit), while communication with the RMH-sys tem i's established via the SU (Swi t clung Uni t) .

62 C 40 -planes

C4- planes

L J J Bi B? BJ B«

Ál-. A2 A3

fig.5.5. Simplified pictufiz o í poteible üiackt, [it

r From RMH

Event/in Reset Busy Accept PTS Reject PTS

Switching Programmable Arithmetic Control unit track control card selector unit I

FDL-crate

fig.5.6. Layout o£ tin fait decision iugi

63 The logic operates on one set of planes at the time, containing one post-target and one pre-target chamber plane, i.e. Al + Bl, AS + B2, etc. For each set a special ACCEPT-counter is incremented if a hit pattern was found according to the two criteria mentioned above. If at any time the value of this counter exceeds a pre-set value, a NIM-signal (final ACCEPT) is obtained; if after all logic operations no final ACCEPT has emerged, a final REJECT is supplied that can be used to reset the equipment to a new experimental trigger. In fig.5.B a layout of the FDL is shown; here also the control card is shown which has no logic but just monitoring functions. All modules are contained in a separate crate.

It has to be kept in mind that the FDL operates on single wire hits as obtained from the RMH-system; no clusters of hits are recogni sed.

5.5.1.2. The Switching Unit (SU)

This unit maintains the necessary communication with the RM-H-system and controls the logic sequence. When an external trigger (event/in) is given to the FDL, it starts reading in the hit patterns from the system encoder corresponding to the first set of planes Al+Bl. In the RMH-system a new plane is indicated by setting the flag switch in the first RMH module of that plane; this flag is transmitted as the upper bit in the first (16-bit) data word of that plane. The SU passes the data on to the PTS via two separate channels and switches its output from one channel to the other upon recognition of this flag bit. After one set of planes has been completed, the transfer of data is stopped. Now the SU waits for the logic of the PTS and ACU to finish, and resumes its operation on a new set of planes until all 4 sets have been read. Evidently, for a correct functioning of the logic the organization within the RMH crates of the modules corresponding to the planes of C4 and C40 has to be in agreement with the order in which these planes are read out by the SU (see fig.5.6).

5.5.1.3. The Programmable Track Selector (PTS).

The PTS contains a Random Acess Memory of 1024 words of 20 bits. This memory is loaded via CAMAC with previously obtained values indicating which regions in a B-plane correspond to hits in an A-plane in the case of a beamtrack. The memory words are split in two parts; the first 10 bits are used to define the lower limit, and the second 10 bits to define the upper limit of these regions. The logic of the PTS addresses the memory location corresponding to each hit in the A-plane, and compares sequentially if any of the B-plane hits fall with.in the range defined by the relevant upper and lower limits. If this condition is fulfilled, the hit from the A-plane is eliminated; all other hits are accepted as output to the ACU.

64 Loading of the memory was done in a separate (short) run, where only beomtracks were selected and a correlation was made between the individual wires of C40 and C4. Loading of actual values into the memory locations is performed with a specially designed CAMAC-module type 212 (decision write unit).

5.5.1.4. The Arithmetic Control Unit (ACU).

The ACU receives good post target chamber (C40) words from the PTS and stores the words for one plane in the input buffers. It then goes through all possible combinations of two words and compares the difference of these words (which correspond to the projected distance between the two hits) with a pre-loaded value, relevant to that plane. If the difference is greater than the stored number, i.e. the separation of the two tracks is greater than the chosen value, the ACCEPT-counter is incremented. The 4 values for the minimum opening angle in each plane were chosen well below the val.ues obtained from our Monte-Carlo o + - calculations for the process TT — e e in our experimental arrangement, and were set to the following numbers; for the 1st and 2nd inclined plane, the 3rd horizontal and 4th vertical plane the values were 5, 6, 7, and 8 respectively. These numbers represent a hi t-separát ion in terms of numbers of wires of C40, which corresponds to a separation of 10, IS, 14, and 16 mm respectively. The value for the minimum number of ACCEPT-signaIs out of the total of 4 planes was preset to 2. This means that an event that had secondary' (non-beam) tracks with an opening angle greater than the pre-loaded value in at least two out of four planes was accepted to trigger the data-taking system. The low number. (2) was chosen to allow for inefficiencies in chambers C4 and C40.

5.5.2. The software preselection.

In order to reduce the number of bad events being fully accepted into the data-taking system and subsequently being written to' tape, a preselection in the data was made during the 1980 runs on the basis of the hit patterns of the multiwire chambers. The preselection was done in analogy with the hardware FDL. However, to obtain exactly the same functioning as the hardware would have meant introducing a considerable amount of dead time. Therefore only the function of the ACU was reproduced in the software. The data-taking system was activated in the normal way by the event trigger A(TR), and the information from the RMH-system was read out. An HP-assembler routine quickly inspected these data words, and decided whether or not this was a good event. If so, the rest of the data was read out (DTD's, sealers, etc.); if not, the internal buffers were reset and the event was rejected (see also fig.5.7). In the latter case, a counter was incremented in order to monitor the rate of rejection.

'\

65 Tlie criteria for rejecting an event were the following: (a) the total number of words in the MWPC data buffer exceeds 50; (b) the total number of data words in Cl - C* exceeds 32; (c) the total number of data words in any C40-plane exceeds 10; (d) the condition of opening angle in two out of four planes of C40 is not fulfilled. The last criterion is equivalent to the criterion of the ACU. This criterion proved to be the most effective one of all, effectuating the rejection of about G5'4 of the events. In addition, a rejection of about 5JÍ of the events was obtained through the other criteria. In this way, we obtained a total reduction in the number of events of about 70'i; ihe computer dead time introduced by this method of preselection was of the order of 5'<4. The rate of writing data to magnetic tape was considerably reduced so that one tape was filled every 60 minutes.

5.6. The data acquisition (DAC).a.nd monitor pro g rajnu

In figure G.7 a block diagram is given of the on-1 ire pr>>p,i-nm which was used for data acquisition and monitoring of the experiment, ^ The data acquisition routines, written in HP: assnmb 1 er * contained all the necessary functions for data transfer vith the organisation of data buffers within the computer core, the transfer of data to magnetic tape and finally the code for preselection of the data. The monitor piogram, written in Fortran, contained routines for the determination of efficiencies of chambers, histogramming and other utilities used to keep track of the essential parameters of the experiment during data-taking. For a detailed description of the functions of the monitor program, sec ref.8. As stated before, in the DAQ we used the existing software that w,-»s developed at CERN (ref.l). Also in the monitor program good use was made of several existing facilities for histogramming etc. (ref.9).

When the on-line prop.ram had been loaded into the core of the computer, the monitor became automatically active and initialised all parameters either by their default values or by values obtained from the user. At this stage, the program communicated frequently with the user. After this initialisation the user would usually start the data-taking, which action then caused the DAQ to take over control. However, the user could intervene at a suitable stage, e.g. to end the data-taking or to obtain some information on chamber performance, sealer readings etc. A small sample of the data was copied automatically into the buffers of the monitor program in order to analyse events when the computer was not busy with the transfer of data from CAMAC and/or onto magnetic tape. At all time highest priority was given to the PAQ and subsequent transfer to tape; an option existed, however, to change this priori ty. , '

66 DAQ MONITOR INITIALISE PROGRAM INITI ALI SE

BEGIN OF NEW EVENT BEGIN Or ( LAM ) NEW Rui. ~ RESET yes

READOUT ( DMA) RMH- SYSTEM

PRESELECTOR

accept reject sample

READOUT ( DMA) sqmpie PU. ADC, TDC

READOUT ( DMA). sample DTD- SYSTEM

1

I READOUT sample (DMA) SCALERS ANALYSE EVENT

T + END-OF -EVEN FILL HISTOGRAMS REACHED sample END OF RUN ?

yes

DAQ STOP PRINT RUN L. STATISTICS + HISTOGRAMS

BUFFER FULL? NEW RUN? yes no no TRANSFER TO END MAGN.TAPE L. 67

4 i g • 5.7. Bťivfe diat\\m o if tlw cn-iinc ptegtam {the dcttvd Witicttf fniť supaïatei tiw mututd ,-5*1 I'm the PAO) ^ The transfer of data was performed with the use of the DMA (Direct Memory Access) -channels of the HP computer. These were used for both the transfer of data from CAMAC and the transfer of data to tape; these actions could take place simultaneously, as indicated in figure 5.7. In order to save computer time and to reduce the amount of information per event on magnetic tape, the sealers were not read out at each event but only once every N times, N to be specified by the user (by default, N = 50). Taking data in the fashion described we filled one tape of experimental data in less than 20 minutes without the use of a preprocessing device and in dne hour when using the software preselection,

r

68 References

1. General-purpose CAMAC software for HP 2100 series computers, E.M.Rimmer, CERN - OD 1978.14.

2. Photomultiplier base type 4238, provisional specifications, P.Duteil, CERN -EP 1979.02.05.

3. P.Duieil, private communication (1978),

4. J.B.Lindsay, C.Millerin, J.C.Tarle, H.Verwey and H.Wendier, N.I.M. 156(1978)329.

5. C.Engster and H.Verwey, CERN - EP 1976.04.15

6. J.C.Tarle and H.Verwey, CERN - NP 1975.09.26.

7. I.Pizer, J.Lindsay and G.Delava1 lade, N.I.M. 156(1978)335.

P.. A.G.Zephat, Omicron note (CERN) ON-81.

9. HP BCS data acquisition system (draft), E.M.Rimmer, February 1978.

i

69 CHT . THE OFFLINE DATA ANALYSIS.,

6.1. Introduction.

The data written on magi.jtic tape were analysed using a chain of Fortran programmes, which carried out data reduction and full event reconstruction necessary to obtain all possible information about the events of interest. The analysis chain, shown in fig.6.1, can be divided into four parts. In the first part, the raw data from the Hewlett Packard computer (see ch,5) are examined using a pattern recognition algorithm in order to associate signals from the wire detectors with groups corresponding to particle tracks. Pattern recognition is performed for the three arms of the spectrometer separately, i.e. for beam particles, particles entering the Jura hodoscope and particles entering the Saleve hodoscope (see fig.4.1). If tracks are identified, the corresponding digitisings are labelled and a preliminary estimate of event parameters is produced. The second part of the analysis chain selects events that might be of interest, in order to avoid the full reconstruction and subsequent long computing time for all the events that are passed on by the pattern recognition code. Then, event reconstruction is performed on the selected events and all necessary information is-obtained using the full accuracy available from the field-map coefficients (see ch.2). In the third part of the analysis chain a test is performed if an acceptable vertex can be achieved in the liquid hydrogen target, using one track in each arm of the spectrometer. The fourth part, finally, is a programme that reads the data summary tapes produced by the event reconstruction code. A variety of constraints can be imposed to give the final spectra.

In this chapter the mnin features of the above programmes will be described, and details about their performance will be given. In addition the Monte Carlo programme used to simulate events will be briefly described. The first part of the analysis (pattern recognition) was performed at Birmingham university by S.M.Playfer, using the computer facility ". of the Rutherford Laboratory. All the other programmes were run at ,> + -. the Free University for the analysis of e e - events, using the '•-*; Cyber system of SARA-Amsterdam. I

6.2. The finding of tracks. í

As sketched in fig.B.I, the raw data from the magnetic tapes are read in by the pattern recognition programme together with an input buffer containing all the information on detector and target positions (see ch.4.4.1) and dri ftveloc i t i es (soe ch.4.3.C). Uric the main decoding of all digitisings t.ikes place. Coordinates in the spectrometer are calculated from the digitisings.

70 INPUT BUFFER INPUT DETECTOR FROM HP-DATA POSITIONS TAPE ETC

PRINCIPAL DECODING

POINTERS TO LIGITlSINGS PATTERN T RECOGNITION + ESTIMATE ON MOMEN A (CIRCLE FIT ) AND OPENING ANGLE

SELECTION OF EVENTS

i _£ ESTIMATE OF TRACK -PARAMETERS WITH CIRCLE FIT i ESTIM ) r OUTPUT BUFFER + ALL ANALYSIS PARAMETERS ti T SINGLE ( LEAST MOMENTA z SQUARES ) FIT DATA SUMMARY o PROCEDURE OF ALL TAPE ( SINFIT ) TRACKS u (+ ERRORS) cc IMPOSING OF t- CONSTRAINTS (OPENING ANGLE ETC.) O ESTIMATE OF VERTEX O POSITION WITH UJ STRAIGHT LINES CC ( VERLIN ) FINAL SPECTRA T

UJ > LEAST SQUARES FIT VERTEX OF VERTEX POINT PARAMETERS ( VERTEX) * ( + ERRORS)

fig.6.1. Block diagiam oft analyiii chain 71

u< ,s—.• ÍK KiSšs^ In the case of drift chambers signals on the same wire separated by not more than 4ns (so-called "ghost"-signaIs) or signals on neighbouring wires due to cross-talk are removed. The hodoscope information from the DTD's (see ch.5.2.2) is decoded into a strip number and a time (in nsec), and a time window is used 'to select prompt trigger signals.

Now, for each spectrometer arm an attempt is made to associate signals from the four chambers with curved tracks of charged particles in the magnetic field. In principle this pattern recognition is a well known procedure; however, as there is a low redundancy of the wire detector information, it is non-trivial in our case. The algorithm used is described in detail in ref.l; here we will summarise it. To find a track from the signals of four chambers a combination of three hits in vertical-wire planes is chosen, giving three times a set of coordinates in x and y (see e.g. fig.2.3 for the magnet coordinate system; fig.4.1 may be used as a reference to the various detectors and counters). Using a constant (average) field value, the radius and centre of a circle is calculated to fit these coordinates and the requirement is imposed that the circle must intersect the correct scintillation counter at the edge of the spectrometer (SI for the beam arm and the vertical hodoscope strips for the secondary arms). If this requirement is met an attempt is made to find a signal in the remaining vertical wire plane no further than lcm away from the prediction of the circle-intersect ion with this plane. The circle is also required to intersect a volume surrounding the target (lcm away from the geometrical target boundaries). When three or four vertical wire signals have been found to form a circle, with the right intersection properties, a search is made for horizontal wire chamber information using basically the same technique as above of comparing intersections with actual hits. Finally it is checked that the track intersects the horizontal hodoscope strips in the case of secondaries. The above procedure loops over all possible signal combinations of hits in vertical and in horizontal wire planes. In the case of a cluster of hits from neighbouring wires the cluster centroid is taken as a single coordinate.

If at lea.it three hits from vertical and two from horizontal wire planes have been found to'form a good track, a check is made with respect to the inclined wire planes of C4 or C40 again using the circles to intersect these planes. The following final conditions are imposed on the acceptance of a track: a minimum of seven signals is required of which at least ; ""•-•: three. ,">ust be hits in vertical wire planes, two in horizontal and : Npne in ^ň ïücl ined-wire p Lane. To._en_sure_correct recognition of the ,' . track neer the vertex it is further required that at Ieast~three :Í signals have been found from the four planes of each of C4 or C40. i I Events not satisfying these conditions are rejected; rejection i also occurs when more than four tracks have been found in one í spectrometer arm. In Table 6.1. the rejection rates are listed; \ about 5-lOri of the events are rejected immediately because of errors

72 in the input buffer such as a complete absence of digitisings in one spectrometer arm or a buffer overflow. In about 5'A of all cases too many beam tracks are found; the other rejected events are due to drift-chamber insufficiencies (=absence of digitisings).

Table 6.1: Rejection in paüttWA izcogmUion Uee te.xt)

specification rejection rate decoding (buffer errors, 5 - 10 % no or too many digitisings)

more than 4 beam tracks found "\J 5 %

Jura insufficiencies •*» 20 %

Salëve insufficiencies ^ 45 %

total rejection rate *> 75-802

Triggers lacking sufficient drift chamber information may be caused by a particle of the beam-halo striking the Jura counters in random coincidence with a signal from the Saleve hodoscope, or by a iT~p bremsstrahlung event of large momentum transfer. Many events without tracks in the Jura drift chambers originate from beam-electrons undergoing bremsstrahlung in or around the target where the Saleve hodoscope is then triggered by the photon. All in all, about 20-25% of all events are passed on by the pattern recognition to the output buffer; estimates obtained from the circle-fit procedure of momenta and opening angle between secondary particles are added to the output buffer for each event, together with the pointers to all digitisings belonging to identified tracks. The efficiency of the pattern recognition programme in the case of + - simulated e e -events is about 75%.

6.3. Selection of event» for final analvsi».

The output buffers from the pattern recognition were inspected by the event recognition programme before proceeding to analysis and a selection of the data was made which greatly reduced the aaount of computing time. • - First of all, the e e triggers were identified from pattern unit

73 £ (see ch.5,2.5; in this unit, the pattern was defined by the experimental trigger condition). Then the ADC spectra from the Saleve hodoseope strips were examined; proton signals were clearly separated from the others, and using + - this information Í0-15X of the "e e " triggers could be rejected.

For the remaining events, a window for the summed momentum of the outgoing particles was defined as well as a window for the opening angle between them. These windows were taken rather large since the estimates for momenta and opening angle are based on circle fits and are therefore not very accurate. The summed momentum was taken between 200 and 370 MeV/c, and the opening angle between o o o + - 34 and 83 (for the process TT —*- e e the summed m^memtum and o opening angle are expected to lie around 330 MeV/c and 50 , respectively). As a result, many small opening angle pairs were rejected (if not already having been rejected on-line by the preprocessor, see ch,5.5). Finally, only those events were accepted that had only one track in each arm (called 1,1,1-events), This fraction of (1,1,1)-events was + - on average 7Q'A of the e e triggers. * * In total, about B'A of the data obtained from the pattern recognition programme was passed on to the event reconstruction code.

6.4. The event reconstruction.

Reconstruction of the events selected from the output of the pattern recognition programme was performed in order to improve the accuracy on the momenta approximated by the circle fit (see above), and to obtain accurate information on vertex position and opening angle. The former is done by a single fit procedure of each track in a given arm of the spectrometer to the chamber digitisings • ([procedure SINFIT), the latter by fitting all three tracks to a [. common vertex inside the target (procedure VERTFIT). The event ,.; reconstruction code may therefore be divided into two parts according to these two procedures (see again fig.6.1). To obtain full accuracy, stepwise integration through the field (using its f parameter!sa t ion as described in ch.2) was performed. Any charged : particle passing through a magnetic field B can be described by the T equa t i on _,. •'•- |£ = qv x í I where p, Tand q are momentum, velocity and charge of the particle. • In simple cases this equation can be explicitly solved, but in : general where B is an arbitrary function of the coordinates there is ; no analytical solution. An approximation technique has to be used, : and in our case the Runge-Kutta integration technique has been chosen since it offers high accuracy for a relatively small amount í of computing time for each step (see refs.2 and 3). - '7

74 B .4.1. Th e SINFIT procedure.

A particle travelling in the Omicron field is specified ; seven párame ter-vec tor containing the position of the parti .: (x.y.z), its direction in the form of three direction cosines •.-• , >: a , a ), and the absolute value of its momentum (p). The n-j to the outer dimensions of the target. Tracing is done away t th" target boundary by step integration through the field, wL : L lie changes in the track parameters due to the step size an-i the variation of the field are calculated over the length of a sttrp During the tracing intersections of the track with each detr tcr plane are calculated, leading to a set of predicted coordinate; in those planes. These can be compared to the coordinates derived trom the actual digitisings to give a residual deviation reflecting the quality of the initial track parameters at the target boundary plane. Both beam particles and secondaries are traced out from the target, i.e. upstream for beam particles and downstream for secondaries. The size of the step during tracing through helium (He-bags) is 5cm; for dense materials such as plastic se int i 11 a tors a smaller step size of lnun is chosen to avoid inaccurate calculation. ; Energy loss was taken into account at each integration step, . using range/momentum tables to look up the change in momentum for a given step size in a given material.

)' The track parameters at the target boundary planes are now optimised by minimising the sum of squares of the residual deviations at the wire chamber planes. Here, a least squares method ; developed at CERN (ref.4) was used. The track parameters employed in ; this method are five independent quantities, namely two coordinates • (x or y. z), two direction angles (©with respect to positive z-axis, JP with respect to positive x-axis) and the inverse momentum (1/p), which parameters can easily be derived from the parameter-vector described above. First the track is traced using : the original set of independent parameters, then small variations ^ are applied to each of the parameters in turn whereupon tracing is I repeated. A derivative matrix is obtained containing the changes in E residual deviation at the detector planes divided by the variation t in the independent parameter. Using this matrix and a weight matrix r containing the chamber resolutions, modifications to the five |« parameters are calculated in order to minimise the squares of the ť residual deviations, as required.

75 fig.6.2. Rzc.onitfui.cXzd beam momentum di&t>UbwUon

Table 6.2: ReAolu£ioru> obtained jiom analy&ii

resolution from analysis program (%)

beam-momentum 2.4 Jura-secondary momentum 1.7 Salève-secondary momentum 2.2 opening angle 1.7

76 Multiple scattering due to electromagnetic interactions with the material along a given track is a random effect which cannot be included directly in the step integration procedure. As the errors involved are of the same order as the chamber resolutions it has to be taken into account; here we have followed the method as given in ref.4. One calculates the deviations of the trajectory on a given plane (i) caused by all proceeding planes ( i -1, i-2,etc.) taking account of the path length between those planes. These deviations can be interpreted as a spatial error at plane (i) and hence a deterioration of the resolution of that chamber plane. As there is no correlation between the errors due to the chamber resolutions and those due to the chamber multiple scattering, the two effects are additive and one formally modifies the weight matrix used in SINFIT by adding the matrix of the calculated deviations on all planes. If the trajectory intersects NP wire planes (where NP has an upper limit of 11 for beam tracks and 10 for secondary tracks), the weight matrix has the dimension NP x NP.

A chisquare parameter representing the goodness of the fit can be calculated from"ths vector of residuals with components d at the wire chamber planes (i=i to NP) and the weight matrix with components w as i j

= (> d w d )/NDF ľ i ij J where NDF is the number of degrees of freedom (NDF = NP-5). Of course, the least squares fit can be iterated using the modified track values as input for new tracing. In practice it was found that one iteration was already sufficient for a good fit.

From SINFIT final values for the parameter-vec tor at the target boundary planes were obtained, leading to optimal values for the momenta of all three particles. The value of the beam momentum at the entry of the Omicron magnet can be derived from the beam momentum at the target boundary by tracing backwards; fig.6.2. shows the distribution of the beam momentum at the entry from all analysed events. The distribution has a mean at 297.5 MeV/c and a FWHM. of 5JÍ, in agreement with the value obtained previously (see ch.2.2). A good estimate of the resolution with which the momenta of beam and secondary particles are determined can be derived from the distribution of the rms-deviations obtained in SINFIT. These rms-deviations aie obtained from the matrix of variances of the fitted parameters, which matrix is calculated from the above described derivative and weight matrices (for details, see ref.4). The results are listed in Table 6.2. For the beam particles the resolution given in this table is larger than the resolution obtained from SINFIT as in fig.6.2, since we had to correct this last number for the chisquare distribution not being peaked around one; systematic errors due to incorrect MWFC-pos i t ions could account for this effect. The measurements of the MWFC-pos i t i ons with the

77 survey rig were checked by a fit procedure to tlie beam trajectories (see ref.1) . One may notice that, for the momenta of the secondary particle, the resolution on the Saleve side is larger, which may be explained by the fact that the lever-arm at this side of the spectrometer is o smaller due to the angle of 15 between the long axis of the Saleve drift chambers and the x-axis.

6.4.2. The reconstruction of the vertex.

Now the target boundary planes served their purpose; by means of the párame ter-vee tor nt such a plane all the information from the track was transferred to the last part of the analysis chain, called the vertex reconstruction. Here it was attempted to reconstruct the vertex position using the information from each of the three tracks at their respective target boundaries, constraining the tracks to fit to a common vertex. Since the target boundary planes correspond to the outer boundaries of the actual target, vertices are reconstructed for good events as well as for background events originating from the" aluminium and mylar walls around the hydrogen (see f ig,4.3).

The procedure of the vertex reconstruction is as follows. At first, an estimate of the vertex position is made by extrapolating each track from the target boundary as a straight line, using the target boundary parameters as obtained from SINFIT (procedure VERL1N). Here the estimated vertex position is defined as the point where the sum of the squares of the distances from that point to the lines is a minimum. A weight factor according to the chisquare value of each track from SINFIT is included in this procedure; the vertex point will therefore fit best to that track which is most reliable. After having obtained the estimated vertex position a 15 párameter-vec tor is set-up containing the properties of the event, namely the vertex position itself (x ,y ,z ), the direction cosines VVV (a , a , a ) for each of the three tracks and the three track x y z momenta in analogy with the pa rámeter-vec tor defined above. The párameter-vec tor is subject to a least squares fitting procedure (VERTEX), similar to the one described in the previous section. Each track is traced from the estimated vertex position to the appropriate target boundary plane, where residual deviations are defined on comparison with the correspond i rig values obtained in SINFIT. For each track five parameters are varied, namely the vertex coordinates (x ,y ,z ) and the angles o and ,' ; the momentum, being vvv well defined after SINFIT,, is not varied. By minimising IE residual deviations (x or y, T.and for each track & and f) an optimisation of the 9 free variables (x,y,,z and 9 , y for eacli track) is made. Again. a weight matrix con t a i in I he c ortecti ons for the effect of multiple scattering in the target !Ihydrogcn 4 walls); nlso included in i.lie i: weight matrix are f he chisquare values for t lie individual tracks

78 from S1NF1T. It is found that two iterations are sufficient for convergence of the fit.

F.-om the vertex parameters thus obtained, the opening angle between the outgoing pair was determined. As in the previous section, an estimate of the resolution of the opening angle could be derived from the distribution of rms-deviat ions for the angles 6 and y of the secondaries. The value obtained is listed in Table 6.2. On average, the position of the vertex could be determined to within about lmm.

E'-'ents were rejected either by the S1NFIT procedure or by the vertex reconstruction section for various reasons. The main cause of rejection in S1NF1T was thnt a track had no proper intersection with a target boundary plane; in VERTF1T events were rejected mainly because an estimated vertex position could not be found within the target bounds. Summarising the event reconstruction, about 25-305* of the data passed on by the selection code (see ch.6.4) were completely accepted.

For all accepted events information containing the original data-buffer together with the information from the event reconstruction was written to a data summary tape.

6.5. Production of final spectra.

Using the information available on the data summary tapes, final spectra were produced under various conditions. While special conditions will be discussed in the next chapter, the general conditions under which all the spectra (including fig.6.2) have been filled are given below. First of all, new target boundaries were defined such that events from the aluminium and mylar walls around the hydrogen were completely eliminated from the spectra (see fig.4.3). Secondly, the selection criteria on summed momentum and opening angle as given in ch.6.3. were once again imposed, in order to take account of the differences between the estimated parameters from pattern recognition and the final parameters from event reconstruction. Finally, a cut in the chisquare distribution of the vertex 2 reconstruction with *£ •£ » was applied in order to remove those events from the spectra that had badly defined vertices. Where the second constraint had only a minor effect on the spectra, the first and last criteria removed quite some events, evenly distributej. over the invariant mass scale, indicating a large amount of background and ill-defined events (about 40'/. of all the events on the data summary tapes).

79 B.B. The Monte Carlo programme.

To obtain information on geometric acceptance functions for the particles at the various detectors a Monte Carlo technique was used, based on a general purpose simulation programme developed at CERN (ref.5). Here events are generated randomly according to specified kinematics and cross sections, while realistic effects such as multiple scattering, energy loss and particle decay can be included. For a sufficiently large number of events valid acceptance parameters are obtained. Since digitisings are set up whenever a particle track intersects a detector, an output buffer can be produced similar to a real data buffer and the analysis programme can be used to reconstruct the simulated event. Thus, the analysis programme can be checked and an estimate of the experimental resolutions can be obtained from a comparison of generated with reconstructed parameters.

The generation of an event starts with defining a beam particle with the usual parameter-vector (x,y,z,a ,a ,a ,p), see ch.6.4.1. If x y z one is only interested in acceptance functions a so-called pencil beam is sufficient, single-valued in all parameters and starting from a specified point upstream of the target. This method we used at the design stage of the experiment, optimising the acceptance by suitable positioning of the detectors. With the initial parameter-vector as starting value, the particle is tracked through the spectrometer using the- Runge-Kutta step integration procedure as above (ch.6.4) while the intersections with detectors are recorded and digitisings are calculated using the known positions of the detectors. The beam particles are tracked upto the target bounds; from there the path length inside the hydrogen is calculated and interaction points (vertices) are chosen uniformly along that path. Now, after transforming into the centre-of-mass system of the interacting particles, the secondary particles are generated for the defined reaction according to its (differential) cross section, specified in ° tabulated form. For the react.i'bn IT p —•• TT n the secondary pion is generated according to the. angular distribution from fig.3.5. Secondary particles may be specified to decay, as in the case of the neutral pion. After generating the decay particles uniformly over the available phase space transformation back into the laboratory system takes place. Hereafter, all secondaries are tracked through the spectrometer (except for neutral secondaries, which are ignored after the vertex) and intersections with the various chamber planes are again recorded. If a particle is stopped or its track misses a detector, the evont is rejected.

At each integration step multiple scattering and energy loss are taken into account. Energy loss is calculated using the ra ige/momentum tables as above (ch.6.4.1). Multiple Coulomb scattering, being a random effect, can be treated quite well within

80 the framework of the Monte Carlo technique. A; each step a rms-scattering angle is calculated from the thickness and radiation length of the material present and the momentum of the particle. The actual scattering angle is then generated randomly in a normal distribution with a standard deviation given by this rms-angle (see e.g. ref.6). A trigger condition is imposed as to the acceptance of the whole event by requiring hits in a horizontal and vertical hodoscope strip in both secondary arms of the spectrometer.

The Monte Carlo programme was mainly used for adjusting the o + - experimental set-up to give a maximum acceptance for ir —• e e and for debugging of the analysis programme. + - The geometrical acceptance of our experiment for e e -pajrs was determined to be '1.5X for the region of invariant mass around the o TT -mnss.

81 References

1. S.M.Playfer, Ph.D. thesis Birmingham University, to be published.

2. N.B.S. Handbook procedure 25.5.10

3. D.Frame, private communication (1978) ;\ 4. A split field magnet geometry fit program : NICOLE, M.Metcalf and M.Regier, CERN yellow report 73-2 (7-2-73)

5. The. 0M1CR0N simulation programme, D. Frame and M.Gallio, CERN-Omicron report (Jan,1977)

6. J.D.Jackson, Classical Electrodynamics, John Wiley & Sons, New York, 1975

82 CHAPTER 7. FIRST RESULTS AND DISCUSSION.

o + - In 1980 the experiment on if —*- e e was performed during about 140 shifts of 8 hours each, and as a result on 210 magnetic tapes data were recorded. In total, 176 tapes were analysed; the other tapes contained data from test runs or were unanalysable. Results from this analysis will be discussed below.

The general conditions for filling these spectra will be recapitulated from ch.6.5. Firstly, events from the aluminium and mylar walls of the target were eliminated by defining target boundaries according to the actual volume of the hydrogen (see fig.4.3). Secondly, all events from the tail of the chisquare distribution of the vertex reconstruction were disregarded by demanding this chisquare value to be less than 4, which means that events with ill-defined vertex parameters were eliminated. Thirdly, constraints were imposed as to the summed momentum of the secondaries and the opening angle between them.

7.1. The invariant mass soectrum.

The invariant mass x can be calculated directly from the momenta of the secondary particles (p and p ) and their opening angle (^) at the vertex, using the relation

^j sin 4>/2 (7.1.) obtained from eq.(3.19). o The invariant mass x will be given in units of theTľ mass (134.9B3 MeV, see e.g. Review of Particle Properties, Farticle Data Group 1980).

The error in the invariant mass can be calculated from the errors obtained in the case of the momenta of the secondary particles and their opening angle, as listed in Table 6.2. U has to be remembered that these are errors obtained from the least squares fitting procedures in the analysis; evidently, systematical errors are in no way included in these error estimates. We nave calculated a value of 2.65Í for the invariant mass-resolution using the values of Table 6.2.

84 As no calibration of the mass scale was available we tried to extract information on this subject from the data, before proceeding to plot final spectra. For this purpose we looked at the energy difference E defined as

AE = (E + E _ + E ) - (E E ) (7.2) n i P in the case of events with high invariant mass. For events with a single lepton pair originating from either a neutral pion or an internally converted gamma the kinematic properties of the recoil neutron are fixed by the parameters of in- and out-going charged particles at the vertex. To make sure that no events from single Dalitz pair-decay would be interfering, the energy difference was determined for events with calculated invariant mass above 145 MeV, allowing for the finite resolution and a possible mass-scale calibration error.

fig.7.1. EneAgy dl^eJiznce. fan. invaniarvt maii above 14S MeV

85 Figure 7.1 shows the distribution for the energy differences thus obtained. When a gaussian curve is fitted to the spectrum, a rms-deviati on of about 8.5 MeV is obtained (FWHM of 20 MeV), which is consistent with the single track resolutions obtained previously (see Table 6.2). The peak is not centered around zero, but has a mean deviation of 10 MeV (this result is reproduced when determining the energy difference in the same manner with a higher invariant mass threshold). As the beam energy is veil reproduced as compared to the value known from the pion channel parameters and the proton (rest-)energy is fixed, we concluded that a systematic error had occurred leading to values for the calculated momenta of secondary particles that are too high. This of course means that also the values for the invariant mass are too high, and we have to correct the invariant mass-scale. What could have caused this systematic error is at this moment not understood. As we have yet no reason to believe that the analysis programmes would produce such a systematic error, we suspect an error in the measured/assumed position of chamber C40 relative to the drift chambers to be an explanation, since the determination of the parameters of the secondary particles is very sensitive to this.

400

300

2 8 u. o 200 CĽ ÜJ (D 3

100 .

O Q4 0.8 1.2 1.6 í X (MeV/134.96)

fig.7.2. tnva/iiant man without additionaZ conitsuUnté

86 We decided to correct the invariant mass-scale according to the shift of AE=10 MeV as in fig.7.1. All the following spectra have been produced using this re-defined mass scale.

In fig.7.S we show the full invariant mass spectrum, without having applied constraints additional to those listed above. We see a spectrum consisting of a broad peak of single Dalitz pairs, cut off at a low mass value due to the constraints imposed by the experimental set-up and the selection procedure (ch.6.3) with a long tail of internal conversion pairs for x>l. At x=l one expects to o + - see a small peak due to events from TT —•- e e . As seen from this figure, no such peak is clearly visible. Now we want to impose more severe constraints on this spectrum, restricting the summed momentum of events to a range around the expected summed momentum for the rare decay (330 MeV/c) and by requiring the opening angle to be close to the expected opening o angle of about 50 . By imposing such constraints we admit only a small portion of the single Dalitz pairs to the final spectrum. The opening angle between secondaries is thus required to be larger than o 40 , while the summed momentum of the secondaries is allowed to deviate from the expected 330 MeV/c by respectively 20,30,40,50,60, and 70 MeV/c. In figs.7.3-7.8 the invariant mass plot is given under these restrictions. In all these figures a few channels around x=l stand out; the constraint of the minimum opening angle does not affect o this particular region of invariant mass (a cut at 40 is noticeable up to about x=0.76, as we may learn from a comparison of figs.7.5 and 7.6 to figs.7.9 and 7.10, which are identical spectra but for the opening angle cut).

Furthermore it can been seen that the channel contents in the region of x=l -hardly depend on the summed momentum cut chosen, and therefore practically all these events can be regarded as genuine events from the rare decay process together with events from the background of internal conversion pairs and some single Oalitz pairs, smeared out even above x=l by the effect of the resolution. The contribution B from single Dalitz pairs to the branching ratio d B in the mass range around x=l has in fact been estimated by Burkhardt et al (ref.21 of ch.3). For a mass range m ± dE this o contribution is given by

5 (Ei 3ir m o I ?; and if we now take dE according to our experimental mass-resolution

| we find about 0.6*10 for this contribution to the branching ratio. SUMMED MOMENTUM SUMMED MOMENTUM 30 SUMMED MOMENTUM 20 + 20 MeV ±30 MeV ±40 MeV fig.7,3. fig.7.4. fig.7.5. 25 10

15 I 20 10 15

10

i u. O O CC u SUMMED MOMENTUM SUMMED MOMENTUM SUMMED MOMENTUM m ± 50 MeV 80 + 70 MeV 2 ±60 MeV fig.7.6. fig.7.7. fig.7.8. 60. 30

60

20 40 40

10 20 20

r,. 1 I I 0.4 0.8 1.2 1.6 0.4 0.8 1.2 1.6 0.4 0.8 1.2 1.6 X( MeV/134.96)

f igs.7.3-7.8. Xnvaiiant man utith opening ati^fi' > 40 and vaiioui uumed meniť ti rum cut i

88 120 SUMMED MOMENTUM SUMMED MOMENTUM 80 + 40 M«V ±50 M«V

fig,7.9. I] fig.7,10. 90 60 \ zi- O U 60 & 40 u ľ In CO S 30 i 20 \

0 Q4 0.8 12 1.6 0 0.4 0.8 1.2 1.6 X (MeV/134.96)

figs.7.9-7.10. moS4 ulithcut aiigt'c cuf

Also at higher invariant mass (around x=1.25) one high channel is visible, presumably due to statistical fluctuation in the spectrum of internal conversion pairs. In general, the channels containing internal conversion pairs at high invariant mass -contain considerably fewer counts than expected; we will return to this subject below.

7.2. The branching ratio B.

The region of the bump around x=l in the invariant mass spectra is about 4 channels wide (1 channel in x is 0.02) consistent with the obtained resolution of Z.B'A. First we want to make an initial rough estimate of the value for the branching ratio B. By approximative extrapolation of the high mass tail of the spectrum we

89 can make an estimate of the internal conversion background in this region; after subtraction of this background we are left with the total of 12 counts. B can be calculated from the relation

N. da. a. x. e, f. B = 12 (7.3)

11 where N — 5.10 the total number of pions incident on the target, d

7 B % 2.IO~ (7.4)

which is of course very approximative, especially since the invariant mass-resolution has been disregarded. The left hand side. of (7.3) should in fact also contain a factor due to the efficiency of the event reconstruction programmes (good events wrongly rejected) and a factor due to the efficiency of the detecting system, both of which would increase the value of (7.4).

A better way of obtaining a number for the branching ratio B is to compare the experimental spectra in f igs.7.3-7.10 to a simulated invariant mass spectrum where the Dalitz pair spectrum has been generated using the formulae given in Kroll & Wada (ref.22 of ch.3) o + - and events from 1T—>. e e have been superimposed on this spectrum, folding in (in both cases) the invariant mass - resolution of 2.6%. Taking again a region of 4 channels around x=l (labelled I, with x=0.9B-l.06), this , region is compared to various regions in the Dalitz pair spectrum namely region II with x=0.94-0.98, region 111 with x=0.92-0.9B and region IV with x=0.90-0.98. The comparison is made both in the case of the experimental spectra and in the case of the simulated spectra, generated for values of the branching ratio B -7 from 2.5 to 5.0 in units of 10 When we calculate the channel-contents of the Oalitz pair spectrum for high invariant mass using the approximative relation (7.3), where B is now replaced by a factor according to the region of the Dalitz pair mass chosen, it is found that the experimental channe1 - contents are reproduced reasonably well. This gives us confidence that comparing the region around x=l to part of the Dalitz pair spectrum at high invariant mass is a justified undertaking.

90 Table 7.1: Ratio* fciom expeifrnentaŕ

experimental ratios ratio of region I (0,98 - 1.06) fig.7.5 fig.7.6 fig.7.7 fig.7.8 ft*.. with respect to AE =40 AE = 50 AE =60 AE = 70 no region H 1.22 1.00 1.00 1.20 v.

Table 7.2: Ratio* jKom Qine/uited

generated ratios for B in units 10~7 ratio of region I (0.98 - 1.06) 2.5 3.0 3.5 4.0 4.5 5.0 with respect to

region II 0.98 1.11 1.23 1.34 1.45 1.53 (0.94 - 0.98)

region III 0.45 0.52 0.59 0.66 0.7? 0.78 (0.92 - 0.98)

region IV 0.23 0.27 0.31 0.34 0.38 0.41 (0.90 - 0.98)

91

-.„, . ,t , Table 7.1 gives a summary of the ratios of the contents of region I over the contents of the other regions (after subtraction of background by extrapolating the high mass tail of the spectrum, as above) which values were calculated for the spectra from figs.7.5-7.8. In Table 7.2 the values from the generated spectra are given. If a summed momentum cut of a certain value is taken, one can calculate the position in invariant mass where this cut starts to have effect. The narrow window in summed momentum that was applied for figs.7,3 and 7.4 al.ready affected part of the high mass region around x=l, and therefore the above method of comparing regions would give unrealistic results'. For the figures 7.5-7.8 ratios have been calculated for the regions untouched by the respective summed momentum cuts. In addition, the same ratios have been calculated from the invariant mass spectrum without the extra constraints (fig.7,8).

By comparing Tables 7.1 and 7.2, we see that the rntios from the experimentally obtained spectra are we 11 covered by the ratios -7 generated for values of B in the range 2.5-3.5, in units 10 . If we choose a different region than the region I taken above, slightly different ratios are obtained but the result leads to the same conclusion. Only if one chooses region I to be sma11er, i.e? corresponding to a better mass -resoluti on, the experimental ratios -7 show a tendency towards a smaller value of B of the order of 2.10 Therefore, under the restrictions mentioned in detail above, in particular the uncertainty introduced by the experimental correction to the mass scale as given in ch.7.1, we conclude the order of magnitude of B to be

-7 (7.5)

and, taking into account statistical deviations only, we find for the value of B

B = (3 + 1) 10 (7.B)

which covers the crude estimate of (7.4) found previously. It also covers the result of Fischer's experiment, and indicates no significant deviation from theoretical calculations based on an o electromagnetic decay of their with its form-factor governed by a il cut-off or vector meson mass parameter (see ch.3.3). 7.3. Closing remarks.

The value for B given in (7.6) is not conclusive. It is obtained after the first analysis of the data taken during the 1980 experiments. During 1981 about twice as many data were collected compared to 1980 and considerable improvement in statistics is to be expected. The first analysis of the 1980 experimental data which is presented here suffers from the lack of a calibration of the invariant mass-scale. A confirmation of the shift in the mass-scale is wanted, together with an explanation of its cause(s). A careful analysis of TT •p elastic scattering events, also recorded during the 1980 experiments, is one way of obtaining this information. These events have well defined kinematical properties and can therefore serve to obtain direct experimental data for the error-limits in opening angle and secondary momentum, which in this work were obtained from a statistical analysis. In the 19B1 experimental runs conditions were improved considerably compared to 1980. Various tests were performed to check the positions of the wire detectors, while also the positioning and the measurement of positions were much improved. In addition, a thin mylar foil was put at an accurately defined place just after the target in order to have a fixed reference when reconstructing events from TT- p elastic scattering.

As already remarked in the previous section there is a disagreement between the expected number of internally converted pairs at high invariant mass and the number experimentally obtained. Calculating the number of conversion pairs e.g. for the region 1.1-1.3 in x, using the total cross section for IT + p—)f+n (see Burkhardt et al, ref.21 of ch.3) and the internal conversion coefficient as given in the paper of Kroll ft Wada (ref.22 of ch.3), we obtain appoximatively 40 counts for this region. In this calculation the angular distribution function (see fig.3.5) and the geometrical acceptance for these pairs have been taken into account. Experimentally we observe about 15 counts in this region of invariant mass, as can be seen in figs.7.3 and following. Notwithstanding the fact that we did not take the efficiency of the analysis programmes into account in the calculation, we have a discrepancy which cannot be well accounted for. The signal to noise ratio of rare decay events to internal conversion pairs thus appears to be much better than predicted (see the argument in ch.3.4), and a careful investigation using simulated events of internally converted pairs is required to provide a check of this predicted value. In addition, a theoretical inquiry into the accuracy of the Kroll & Wada formulae mentioned above seems appropriate, since these authors employed a model that did not contain details on the internal structure of the particles concerned. Normalisation of the events from the rare decay on the spectrum of internal conversion pairs cannot take place when the above matter has not received attention.

93 SUMMARY

In this thesis the first results of measurements on the rare

decay of the neutral pion IT —- e e are described. These measurements were performed in a collaboration at the European Organisation for Nuclear Research (CERN) in Geneva, using t h ^ OM1CRON spectrometer.

A negative pion beam of T=190 MeV produced neutral pions via o the charge exchange reaction IT p—iTn in a liquid hydrogen target placed inside this spectrometer. The tracks of the incoming pions and any decay leptons emerging from the target were localized using multiwire proportional and drift chamber detectors. In the analysis, the momentum of a particle was then obtained from the curvature of its track and the values of the magnetic field along that track. The magnetic field was accurately measured throughout the volume of the spectrometer.

Having obtained the momenta of one incoming and two outgoing particles, the events of interest were selected by requiring a common vertex position of these three particles inside the target. At the vertex the opening angle between the secondary particles was determined, and the invariant mass could then be calculated from this opening angle and the two momenta of the secondary particle.

Background events from Tľ -p elastic or inelastic scattering processes were identified either on-line or in the off-line analysis and were excluded from the final spectre.

Here the first results from the analysis of the data taken during the 1980 runs are presented; considerable statistical improvement may be expected from the analysis of the 1981 runs, where about twice as many data were collected. A systematic error was found during the analysis of the 1980 data, causing a shift in the energy scale of the invariant mass spectrum. It is most probable that this error was caused by an error in the position of one of the detectors; a correction of the energy scale could be deduced from the analysis of events with high invariant H mass.

94

i^ In the invariant mass spectrum, tht spectrum caused^ by events o + - originating from Single Dalitz Pair decay (TT —.- e e ) can be recognised. In addition the background due ,to conversion pairs from + - the reaction TT p—e e n (via an internally converted photon) is seen. o Around the IT - mass there is evidence of events from the rare decay in the form of a small peak, standing on the background of internal conversion pairs and the tail of the Single Dalitz Pair spectrum smeared out by the experimental resolution. The invariant mass resolution obtained is S.65Í.

o By means of a comparison of the region around the TT - mass to a region in the Single Dalitz Pair spectrum, a value of the branching ratio B for the rare decay with respect to the usual decay o -7 TT — yjf is deduced to be (3±1) * 10 This value is consistent with theoretical calculations based on an electromagnetic decay of the neutral pion with its form-factor Roverned by a cut-off or vector meson mass-parameter.

At high invariant mass, a discrepancy is found between the expected spectrum of internally converted pairs and the experimentally observed numbers.

i "••"-;

95

&ť./azžCFä^a?,^reaB«z?gif=e^Y^^ SAMENVATTING

In dit proefschrift worden de eerste resultaten beschreven van o + - netingen gedaan aan het zeldzame vervalsproces ir—*• e e . Deze metingen werden in samenwerkingsverband gedaan bij de Europese Organisatie voor Kernonderzoek (CE.R.N.) te Geneve, gebruik makend van de zg. OM1CRON spectrometer.

In deze spectrometer was een doelwit met vloeibaar waterstof o geplantst, waarin met de reactie ir p—iTn de neutrale .pionen werden geproduceerd bij een pionenergie van 190 MeV, De banen van de deeltjes in de inkomende bundel van negatieve pionen en van de uitgaande leptonen afkomstig van het vervalsproces werden vastgelegd door middel van dradenkamers. In de analyse werd het impuls van een deeltje verkregen uit de kromming van zijn baan en de waarden van het magneetveld daarlangs. He.*.magneetveld werd in het gehele volume van de spectrometer nauwkeurig gemeten.

Wanneer op deze wijze de impulsen van het inkomende en de twee uitgaande deeltjes verkregen waren, werden de interessante gebeurtenissen uitgeselecteerd door het opleggen van de eis dat de drie deeltjes uit een gemeenschappelijk vertex-punt binnenin het doelwit moeten komen. Bij deze vertex werd dan de openingshoek bepaald tussen de twe* uitgaande deeltjes en de invariante massa kon vervolgens berekend v/orden uit de openingshoek en de waarden van het impuls van de twee uitgaande deeltjes. Achtergrond ten gevolge van TT p - elastische en inelastische verstrooiing werd in de electronics van het meetsysteem of in de analyse-programma's geïdentificeerd en niet tot de uiteindelijke spectra toegelaten.

Hier worden de eerste resultaten gepresenteerd van de analyse van de meetgegevens uil de experimenten gedurende Í980. Een aanzienlijke winst in statistiek mag op grond van de analyse van meetgegevens uit 1981 vrorden verwacht aangezien in 1981 -nog eens tweemaal zoveel meetgegevens werden verzameld. Er werd een systematische fout gevonden gedurende de analyse van de meetgegevens van 1980, die een verschuiving van de energiesehaa1 veroorzaakte in het invariante massa-spectrum. De meest waarschijnlijke reden hiervoor is een fout in de plaats van een der i detectoren; een correctie van de energieschaa1 kon echter afgeleid worden uit de analyse van de gebeurtenissen met een hoge invariante massa.

96 In het invariante massa-spectrum kan men het spectrum herkennen van zg. Single Dalitz Pair gebeurtenissen (d.w.z. gebeurtenissen ten o + • gevolge van het verval TT —• e e ) benevens achtergrond door +• - conversie-paren uit de reactie TT p— e e n waarbij deze paren ontstaan via een intern geconverteerd foton. o In een gebied rond de massa van het TT vinden vrij gebeurtenissen terug van het zeldzame vervalsproces in de vorm van ecin kleine piek, die op een achtergrond staat van conversieparen en de staar': van het spectrum van de Single Dalitz Pairs dat door de experimentele resolutie wordt uitgesmeerd. Deze resolutie bedraagt Z.B'A.

o Door een vergelijking van het gebied rond de massa van het TT met een gebied uit,het Single Dalitz Pair spectrum wordt een waarde voor de zg. vertakkingsverhouding van het zeldzame verval, gedefinieerd in verhouding tot het meest gebruikelijke verval o -7 "^ —tV , afgeleid en een waarde van (3±1) • 10 wordt verkregen. Deze waarde is consistent met theoretische berekeningen gebaseerd op een electromagnetisch verval van het ongeladen pion waarbij žijn vormfactor bepaald wordt door een (vector meson) massa parameter. Het te verwachten spectrum van conversieparen bij hoge invariante massa is niet geheel in overeenstemming met de experimenteel gevonden waarden.

97 Contents Page

CHAPTER 1. INTRODUCTION AND SURVEY. 2 1.1. Introductory remarks. 2 1.2. Survey of this thesis. 3 1.3. Acknowledgement. 4

CHAPTER 2. THE OMICRON SPECTROMETER. B 2.1. General review. ' 6 * 2.2. Beam configuration, 9 2.3. The magnetic field of the OMICRON magnet. 10 2.3.1. Measurements of the magnetic field. 10 2.3.2. Parameterisation of the field. 14

CHAPTER 3. THEORETICAL SUMMARY AND DESIGN OF THE 18 EXPERIMENT. o 18 3.1. The decay modes of the V . 3.2. Various models for the pion form-factor. 20 3.3. Experimental numbers, and comparison to 25 theory. o + - '26 : 3.4. The design of the experiment of TT -~e e with Omicron. 3.5. Invariant mass-spectrum and background. 30 CHAPTER 4. THE EXPERIMENTAL ARRANGEMENT. 36 ; 4.1. Introduction. 36 4.2. General set-up. 37 4.3. Wire detectors. 41 4.3.1. Multiwire proportional chambers (MWPC). 41 4.3.2. Adjustable field drift chambers (AFDC). 44 4.4. Additional equipment. 48 4.4.1. The survey rig. 48 4.4.2. Helium-bags and background reduction. 49

CHAPTER 5. ELECTRONIC EQUIPMENT AND DATA 51 AQUIS1TION. ' 5.1. General set-up. 51 5.2. The NIM-electronics. 52 • 5.2.1. Beam logic. 52 i 5.2.2. Jura- and Sal eve-side logic. 54 I 5.2.3. Further logic. 55 !' 5.2.4. Final trigger and subsequent logic. 55 \ 5.2.5. Pattern units, ADC's TDC's, and sealers. 56 i 5.2.6. Trigger rates. 58 [ 5.3. The MWPC readout. 58 ; 5.4. The AFDC readout. 60 ' 5.5. Preprocessing of the data. • 62 : 5.5.1. The hardware FDL. 62 í 5.5.1.1. Principle of operation. 62 I 5.5.1.2. The Switching Unit (SU). 64

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5.5.1.3. The Programmable Track Selector 64 (PTS). 5.5.1.4. The Arithmetic Control Unit (ACU). 65 .5.2. The software preselection. 65 ,6. The data acquisition (DAC) and monitor 66 program.

CHAPTER 6. THE OFFLINE DATA ANALYSIS. 70 6.1. Introduct ion. 70 6,2. The finding of tracks. 70 6 .3. Selection of events for final analysis, 73 6 .4, The event reconstruction. 74 6 .4 1. The S1NF1T procedure. 75 6 .4 2. The reconstruction of the vertex. 78 6 .5 Production of final spectra. 79 6.6 The Monte Carlo programme. 80 CHAPTER 7. FIRST RESULTS AND DISCUSSION. 84 7.1. The invariant mass spectrum. 84 7.2. The branching ratio B. 89 7.3. Closing remarks. 93

SUMMARY 94

SAMENVATTING 96

II Table of Contents

* e+e-

ACADEMISCH PROEFSCHRIFT

ter verkrijging van de graad van doctor in de wiskunde en natuurwetenschappen aan de Vrjje Universiteit te Amsterdam, op gezag van de rector magnificus dr. H. Verheul, hoogleraar in de faculteit der wiskunde en natuurwetenschappen, in het openbaar te verdedigen op vrijdag 4 december 198! te 13.30 uur in het hoofdgebouw der universiteit,

De Boelelaan 1105

door

WILLEM VAN DOESBURG

. geboren te Amsterdam ; H Serv'Impri | AMSTERDAM 1981

v'. -• '-'-'^-5-^-^ï^fe'Wii3i5^ Promotor : Prof. dr. H. Verheul Coreferenten : Dr. N W. Tanner Dr.E.G.Michaelis

I

ÜÉ-

Sï.' STELLINGEN

1. Bij het onderricht in de natuurkunde binnen het voortgezet onderwijs dient een inleidende systematische behandeling van elementaire deeltjes als bestanddelen van de materie aan de orde te komen. 2. De aanduiding door Herczeg** van het in het pionverval optredende neutrale intermediaire deeltje met Z° is misleidend. *) P. Here zeg, Phys.Rev. D16 no.3 (1977) 712 3. De door Konijn et al " gemeten absorptiebreedtes van het 3d-niveau van pionisch 2M Bi en85'l87Re wijken duidelijk af van de theoretische voorspel- lingen. Deze afwijking wordt gestaafd door metingen aan absorptiebreedtes van ls-,2p-,3p- en 3d-niveaus van pionisch "Na, 7sAs,'l0Pd en^Ta23*.» Deze resultaten wijzen erop dat de absorptie in het optische potentiaal model niet goed wordt beschreven. 1) J.Konijn et al., Nucl.Phys, A326 (1979) 401 en Nucl.Phys. A360 (1981) 187 2) AľOlin et al., Nucl.Phys. A312 (1978) 361 _r 3) R.Abela et al., Z.für Phys.A282 (1977) 93 4) M.Leon et al.v Phys.Rev.Lett.37(1976) 1135 5) C.Batty et al., Nucl.Phys. A355 (1981) 383 4. Bij de discussie van hun metingen aan muon geïnduceerde splijting van uraankernen hadden Johansson et al.** in plaats van een af schatting te geven van de kans op stralingsloze overgangen in238U deze kans d.m.v. een eenvoudige Y~Y coincidentiemeting kunnen bepalen. *) T.Johansson et al., Phys.Lett. 97B (1980) 29 5. Het is te betreuren dat de geregelde veranderingen in het systeem ter aanwending van het rekentuig bij SARA slechts af en toe geen consequen- ties voor de gebruiker hebben. 6. Bij de bepaling van het hartvolume d.m.v. echografie kunnen nu waarden worden verkregen die even nauwkeurig zijn als de waarden* verkregen met behulp van ciné-angiografie, zodat voor de bepaling van het hartvolume hartcatheterisatie niet langer noodzakelijk is. 7. In de geneeskundige diagnostiek wordt dikwijls gebruik gemaakt van radio- actieve stoffen. In sommige gevallen kan van dit gebruik worden afgezien door toepassing van de methode van nucleaire magnetische resonantie (NMR), waarbij de patiënt in een sterk magneetveld moet worden geplaatst. Dat deze laatste methode zeer veel minder risico's met zich brengt dan de eerste is een uitspraak die vaak wordt aangetroffen. Het is echter zeer de vraag wat de fysiologische effecten van sterke magneetvelden zijn: onderzoek hiernaar is dan ook dringend gewenst. 8. Bij de referenties naar publicaties over het naast elkaar bestaan van toestan- den met verschillende kerndeformatie in het massagebied A- 100 wordt in het Jaarverslag van de afdeling Natuurkunde van de Universiteit van Uppsala" het onderzoek van de Vrije Universiteit2> ten onrechte niet vermeld, 1) Annual report 1980, Tandem accelerator Laboratory and Nuclear Physics division, Institute of Physics, University of Uppsala 2) J.Bron et al., Nucl.Phys. A318 (1979) 335 9. Resultaten van recent onderzoek wijzen erop dat de kunst der wichelroede niet als toverkunst mag worden afgedaan.

Stellingen behorende bij het proefschrift van Willem van Doesburg, 4 december 1981.