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Nuclear Physics B134 (1978) 365-391 © North-Holland Pubhshmg Company

SYSTEMATIC STUDY OF K n PRODUCTION IN THE REACTION K±p--> K~ n±p TECHNIQUE AND MEASUREMENTS AT 10 GeV/c R BALDI, T. BOHRINGER, P A DORSAZ, V HUNGERBf3HLER, M N KIENZLE-FOCACCI, M MARTIN, A MERMOUD, C NEF and P. SIEGRIST Umverstty o] Geneva, Switzerland and CERN, Geneva, Swttzerland Rece:ved 4 November 1977

A two-arm spectrometer for simple event topologaes is described Its mare characteristics are (1) large sohd-angle acceptance for the forward emitted parhcles, owing to the absence of magnetic-momentum analysts, (u) hlgh-resoluhon tlme-of-fhght measurement of the recod proton, m the momentum-transfer range 0 05 < Itl < 1 (GeV/c)2, (111)high datataking rate and onqme pattern recogmtlon The apparatus has been used for a systematic study of the K~rsystem produced m the reaclaon K±p ~ K~lr-+pat 10 GeV/c We present the results m terms of spherical harmomc moments of the KTrdecay angular dtstnbutlon

1 Introduction The aim of this expenment is the detailed investigation of Kn production m the reaction K±p --" K°zr±p

wRh K ° -~ n+rr -

(1)

We have built a spectrometer with the object of obtaining h:gh statistics m this channel as well as m other channels with similar topologies In this first of two papers we describe the apparatus, its performance, and the method of analysis, in detail We then present our results m terms of moments of the KTr decay angular chstnbutlon m the t-channel hehclty frame, which we determine both as a function of Kn mass and of m o m e n t u m transfer t In the second paper [1 ] we then study the phys:cal :mphcataons. In particular, we perform an amphtude analysis of KTr production through the K*(890) and K*(1420) mass regxon and d:scuss the exchange mechanism responsible for production of these resonances

365

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R BaMl et al / Kn productlon

2. The spectrometer The spectrometer has been designed to measure events signed by a slow recoil proton at large laboratory angle and 1 V ° + 1 charged track m the forward dIrecnon This topology corresponds to the reactions K-+p --, (Ks°n+)p,

K ° ~ 7r+rr- '

K+p ~ ( A p ) p ,

X ~ ~n "+ ,

K - p --* ( A ~ ) p ,

A -* p~r-,

n+p_~ K soK ± p,

K~ --* n+n - ,

pp -+ A K + p ,

A --* w r - ,

~ p -+ ~ ( - p ,

A--, ~ +

(2)

The spectrometer lS capable of operating in an unseparated beam of either polarity and of recording simultaneously K-, lr-, and p-induced reacnons As the mare a m o f the experiment is kaon physics, incident K's are gwen priority over zr's and p's, m order to accept these comparanvely rare events with small dead-tame loss this as achieved by a two-level trigger an conjuncnon with a buffer memory The lr- and p-reduced triggers are then recorded as by-products, with a lower priority Other topologies are also obtained as by-products, corresponding, for example, to the reacnons K-+p ~ K-+K+K-p, K+p ~ K-+KOK~p

with both K ° -> 7r+zr-

(3)

2 1 Prmclple o f the spectrometer The apparatus consists of the following parts (fig 1) (i) a beam spectrometer, to measure identity, direction and momentum of the incident particle, (u) a recoil proton arm to identify the recoil proton, and to measure the direction and m o m e n t u m , (nl) a forward arm to measure the dlrecnons of the forward emitted pamcles No magnet Is used and therefore the forward-pamcle momenta are not measured The kinematics can be completely reconstructed for events with one forward track and a seen V ° (2C fit, reactions (2)), three forward tracks, or one forward track and two seen V°'s (both 1 C fits, reactions (3)) In addition to the kinematical constralnts there are geometrical constraints, such as the requirement of a mimmum separation between producnon and decay vertex of the V °, or coplananty of the V ° decay ~ t h the production vertex

R Baldt et al / Kn productzon

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2 2 Beam and target The experiment has been operating m the d31 beam at the CERN PS At a momentum of 10 GeV/c, and wath a momentum bite of-+ 1 4% for the posltxve beam and +2 4% for the negative beam, the intensity was typically 2 4 × 106 posltwe particles, and 0.35 X 10 6 negative particles per 420 ms burst at the experimental target The beam momentum is measured by making use of an intermediate horizontal focus with a chromaticity of 5 mm/% Ap/p Two scintillation hodoscopes H o and H i , wath 6 vertical overlapping elements each, record the position of the trajectory near the lntermedxate focus The momentum measurement is calibrated by closing the momentum sht to 0 1% and moving it across a band of-+l 5% As an example, fig 2 gives the distrlbutxon of hits in H o and Hi, for a narrow slit centred at Po - 1% Po and Po + 1% The momentum resolution, deduced from such cahbratlons, is Ap/p = 0 2% The direction of the incident particle IS measured by four hodoscopes HI to H4, two of them with horizontal and two with vertical elements, before the hydrogen target The angular resolution of the incident track is -+0 54 mrad, mainly due to the element size and geometry of the hodoscopes Four threshold ~erenkov counters CI to C4 are used for parUcle identification two 3 m counters, filled with hydrogen at 7 5 atm, are sensltve to plons, and two 1 m counters, filled with lsobutane at 6 5 atm, are sensmve to plons and kaons The beam composition K/Tr/p is 1 9%/97%/1.1% for negatwe polarity, and 2 1%/25%/73% for positive polarity, at a primary beam energy of 26 GeV/c The contamination of the K

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R Baldl et al / K~rproduction

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sample, owing to Inefficiencies, dead-time, accidentals and 8-rays, :s neghglble for the negatwe beam, and amounts to 2% by plons and 4% by protons in the posmve beam The beam is focused on a 53 cm long hquxd-hydrogen target of 4 cm diameter The beam size at the focus is 20 mm horizontally and 24 mm vertically (FWHM) The beam is pos:tloned close to the s:de wall of the target, in order to reduce multiple scattering of the recoil proton, which traverses on the average 1 cm of llqmd hydrogen The target vacuum vessel has a carefully designed geometry, with thin mylar windows on the side of the proton arm (250 tam), and the forward arm (500 tam) 2 3 Forward arm, multtwlre proporttonal chambers The forward arm consists of four multlwlre proportxonal chambers (MWPC), each with two perpendicular sense wire planes The first chamber downstream from the target has a fiducml area of 512 × 512 mm 2, while that of the three following chambers is 1280 X 1280 mm 2 The first and third chamber measure horizontal (x) and vertxcal (z) coordinates, the second and fourth chamber are rotated by 15 ° (u-o coordinates), in order to remove ambiguities The forward arm accepts tracks up to about 33 ° with respect to the beam axis The construction parameters are the following sense wires have diameter 20 tam and spacmg 2 mm For each sense-ware plane there is a separate set of two high-voltage planes, made of 50/am wires w:th spacing 1 mm. The high-voltage gap of 6 m m is kept constant b y support wxres and spacers The gas used is the "magic" mixture, consisting of 79% argon, 14% lsobutane, 0.3% Low intensity

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370

R Baldt et al / KTr production

freon 13B1 and 7% methylal The chambers are operated at about - 4 0 0 0 V The readout o f all wires xs in parallel each wire is connected to a preamphfier mounted on the chamber frame The signals then travel through 60 m long twisted pairs to line receivers, followed by one-shot delays and flip-flop memories The angular resolution, due to the geometrical accuracy of the MWPCs, is about -+0 3 mrad Multiple scattering In hydrogen, air, and the MWPCs (Z/Zra d = 0 0073) dominates for tracks slower than 4 GeV/c The MWPC efficiency depends on particle flux Outside the beam and supportwire regions, the efficiency was 95 to 98% In the beam region, for a flux density of the order of 106 partlcles/cm2s typical for the posltwe beam, the efficiency drops to about 60% (fig 3) The inefficiency is hmlted to the region where the flux is high and does not extend to the whole length of the sense wires going through the beam It is therefore related to a space-charge effect rather than to electromcs dead-time The support hnes of the sense-wire planes are fixed at a potential of - 1 0 0 0 V They produce an inefficiency of about 50% in a 4 mm wide band We observed no loss of efficiency due to the support wires of the high-voltage planes 2 4 R e c o t l proton arm, tzme-of-fltght counter

The recod proton arm consists of a large time-of-flight scintillator (T) for the momentum determination, a range system of scintillators and absorbers for proton lden-MMx= 90 ~00M e

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R Baldt et al / KTr production

371

tlficatlon, and of three MWPCs identical to the ones used in the forward arm for direction measurements (the range system xs not used in the analysis of the 2C channels (2)) The axis of the proton arm is at 59 5 ° with respect to the beam The geometry of the proton arm determines essentially the acceptance m K~ mass (fig 4) Tune of fl~ght is measured between a start counter S m the beam line in front of the target, and the stop counter T of dimensions 150 X 150 cm 2, at a distance of 1 9 m from the target Both S and T counters are each viewed by 4 photomultlphers, gwmg 4 independent tune-of-flight measurements The start and stop s~gnals are fed, on the one hand, into a commercml t~me-dxgltlzer circuit, on the other hand, their pulse height is also recorded in ADCs The four time-of-flight measurements are then averaged, and a correction depending on the average pulse height in the S and T counters is apphed These corrections have been determined empmcally using elastic events. The proton time of fhght is then obtained after correction for the distance between the S counter and the interaction vertex, and finally the proton momentum at the production vertex is deduced from the time of flight, taking into account the energy loss along the proton path The tune resolution has been measured m the production set-up using elastic events. From incident momentum and recod angle the expected time of flight can be calculated and compared with the measured value Alternatwely, the incident and forward

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372

R Baldt et al / Kn productton

tracks can be used to predict the time of flight of the recod particle, which is compared with the measured value F r o m these distributions we can then derive the time resolution, shown in fig 5, wtuch is found to depend on proton m o m e n t u m A typical value Is 200 ps at p = 500 MeV/c, corresponding to a momentum resolution of 2% The MWPCs in the proton arm are of the same construction as those In the forward arm. However, a less expensive readout system is used As one expects only one particle in the proton arm, it is possible to encode 256 consecutive sense wires into 16 groups of 16 wires each Each sense-wire signal is then fed into two electromc channels one channel gives the number of the group, the second gives the wire number wathln the group The number o f electronics channels required is thus reduced by a factor of eight At low rate (less than a few kHz) and for single tracks, the efficiency of this system is the same as for parallel readout. It drops, however, with increasing accidental rate In the chambers, as it is difficult to remove ambiguities due to multltracks m one segment of 256 wires It is mainly for this reason that the efficiency per track of the MWPCs In the proton arm drops to about 70% m the haghest intensity runs The accuracy of the recoil proton direction is determined primarily by the multiple scattenng m hydrogen and air The average amount of material traversed is L/Lra d = 0 005, corresponding to an angular resolution of 4 3 mrad for 500 MeV/c protons

3. Trigger and data aquisition system The trigger and data-acquisition system (fig 6) consists o f the following parts (a) A first-level trigger, derived from the scintdlatlon and ~erenkov counter signals, avaalable after 600 ns It generates gates for the hodoscope and time-of-flight signals, and a strobe for the MWPCs. (b) Memories prlot to transfer They are CAMAC ADCs, TDCs, pattern units and scalers. The MWPCs have two memories a parallel memory on each wire, followed by one CAMAC compatible coding unit per MWPC plane These gwe m 2 to 3/as the number of wire clusters, their coordinate and size (c) A second-level trigger It is derived from the information of the beam hodoscopes, and o f the MWPC coding units, and initializes the transfer to the computer (d) A PDP 11/45 for data acquisition and partial event processing between bursts (e) An IBM 1800 for tape writing and on-hne checking of the whole equipment IBM 1800 and PDP 11/45 are linked through a CAMAC buffer memory. 3 1 The first-level trigger

The first-level trigger condition is M=B

C T SAT A ,

where B is the coincidence of the beam telescope counters (B = BoBI BaAoS I S 2 $3S4)

373

R Baldz et al /Klr productton

9) Trigger togJc counter ~ = 1 f~rst-[evel [ ~ _ mformatton - trigger

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Ao is an anh-halo counter and S, are the four time-of-flight start signals The ~erenkov-comcldence C Identifies the beam particle C = C 1 C2C3C 4 for a¢r, C1C2C3C-4 for a K, and CIC2C3C 4 for a p The 7r and p signals can be prescaled before the first-level trigger T is a coincidence of the four tlme-of-fhght stop signals In order to reduce the tame jitter due to the large counter size, the time average of pairs of photomultlphers looking at opposite sides of the counter are used T = (T13 average) • (T24 average) The resulting time jitter is less than 2 ns and allows rejection of/3 = 1 particles.

374

R Baldt et al / K~rproductton

SAT is a threshold on the sum o f the amplitudes of the four stop signals, to remove rmnimum ionizing particles m the proton arm A = AI A2 is an anti-beam telescope with rough m o m e n t u m analysis downstream from the target It rejects non-interacting beam particles without suppressing interaction products emitted in the beam region with a lower m o m e n t u m 3 2 The second-level trigger

The second-level trigger N is a coincidence o f four flip-flop outputs, each corresponding to a specific condition N=M-H

F P,

where M is the first-level trigger, H is a condition on the beam hodoscopes requiring at least one hit m each of the hodoscopes HI to H4 F is a condition on the number o f forward tracks For each plane of the forward MWPCs, a lower and upper limit on the number of clusters can be set, as well as lower and upper limits on the total number of clusters in all x-u and z-v planes The F reJection IS overridden for kaon- and antiproton-lnduced events P is a condition on the MWPCs in the proton arm, requiring at least one hit in two x- and In two z-planes This is the minimum condition for the reconstruction of a proton track If not all the conditions are met, the event is rejected and the whole electronics reset 3 3 PDP 11/45 and IBM 1800

If the second-level decision is yes, transfer to the PDP 11/45 starts The following data blocks are transferred successively (a) Scalers, pattern units, ADCs and TDCs (28 16-bit words), (b) MWPC coding units (64 words) The total transfer time is about 370/as The events are first stored In the 24K memory of the PDP 11/45, at a maximum rate o f 225 events per burst The transfer o f 225 events gwes a dead-time of about 20% for a 400 ms burst This represents too high a loss for the relatively rare kaon-mduced events To avoid this loss, plon- or proton-induced triggers are inhibited while an event is being transferred to the PDP 11/45. The rare kaon- or antlproton-lnduced events, however, are Inhibited only for the time necessary for transferring the first data block, 1 e for about 100/as After this time, the first block is reset, and a new event can again be accepted. It wall be stored in the first block normally, and In the parallel flip-flop memories of the MWPCs, waiting for the coding units to be liberated. The resulting dead-time for such lugh-pnorlty events IS thus reduced to a few per cent In the 2.2 to 2 4 s between bursts, the PDP does a partial processing of all events It consists o f pattern recognition and track reconstruction in the forward MWPCs, of

R Baldt et al /Klr productton

375

decoding the information of the matrix read-out of the proton chambers, and of checking the hodscope signals. Events with more than one track in the last four hodoscope planes are rejected. Also events where the proton track cannot be reconstructed because of ambiguities m the matrix readout are rejected The track reconstruction in the forward arm is the main part of the one-hne processing For an average of about 3 reconstructed tracks/ event, this requires about 10 ms/event As forward track reconstruction is a major part of the complete geometrical event reconstruction, we have been able to reduce the off-line processing by approximately a factor of two As soon as the events are processed by the PDP, they are transferred wa a 256word CAMAC buffer memory to the IBM 1800, used for tape writing and for technical checks The techmcal momtorlng is performed by a samphng program, consisting of five overlays which are running cychcally Each has a specific task analysis of the detectors in the beam hne (hodoscopes, ~erenkov counters, spot size, etc.), the forward MWPCs (distribution of hats, efficiency, etc ), the proton MWPCs, the time-offlight system (TDC and ADC dxstrlbuhons), and the results of the reconstruction by the PDP (track parameters, ×2) The results in the form of histograms are displayed continuously

4 Data analysis 4 1 Event zdenttficatlon

Events corresponding to the reaction (1) are Identified by their geometry and kinematics The geometry cuts select candidates with the correct topology (1) a successfully reconstructed smgle track in the proton arm due to a recoil particle, and (u) a (1 charged + seen V °) topology m the forward arm. The V°-decay vertex must be at least 27 mm downstream from the production vertex We allow for the possxbthty of one additional accidental track. Next, we use momentum conservation to calculate the unmeasured momentum magnitudes of the three forward particles. We then calculate the two kinematic constramts of the reaction, which can be chosen as the overall energy balance AE of the reaction 3

AE = Emc + mp - Erecoa - ~ E, t=l

(4)

(where E~ are the forward particle energies) and the effective mass of the V ° These two constraints must be satisfied within wide hmlts IAEI < 20 MeV and 450 5% The successfully fitted events are further required to have forward momentum p > 300 MeV/c Thas cut eliminates events suffenng from large multiple

R Baldt et al / K~r production

376

scattering m the target Finally we reqmre Mrrp > 1 4 GeV m order to remove a small background due to excitation of the target nucleon m K+-p ~ K ° A ~ + Note that this reacUon Is already suppressed by the spectrometer geometry and by the requirement of a single track in the proton detector The resulting sample contains 46 450 events corresponding to the K+p -+ K°n+p reaction, and 17 960 events in the K - p ~ K°Tr-p channel

4 2 Background The quahty of the sample can be demonstrated by displaying the distribution of the kmematlcal constraints zlE and MKO, calculated with the unfitted quanmies only (fig 7). Interpolation of the tails of the MKO distribution under the K ° mass peak gwes a background of about 2%. Alternat]vely, we can estimate the amount of background by mspectmg the shape of the P(X 2) dlstnbutxon The excess of events at small P(X2) is also of the order of 2% The most hkely source of background IS the reacUon K+p ~ K°zr-+7r°p,

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R BaMI et al /Klr production

377

w:th a n o m add:txon to the (1 charged + seen V °) topology Tins reactmn is dlffraclave and has a large cross sect:on We have estimated the expected contammatxon of the data by tins channel using a Monte Carlo program We find a value winch :s indeed consistent w~th the observed one 4 3 Resolutions The energy balance is satisfied to +3 5 MeV Tins small value is due to the fact that any inaccuracy in the incident momentum ~s carried over into inaccuracies of the absolute momenta of the forward pamcles The energy balance is lnsensmve, in first order, to the resulting shaft m longatudlnal momentum The K ° mass resolutmn is -+7 MeV These widths are in good agreement w:th Monte Carlo calculations incorporating the resolutions of the individual detectors. The resohatmn in Krr mass is mass dependent at the mass of the K*(890), K*(1420) and K*(1780) resonances, It is -+7, 8 5, and 10 MeV, respectwely The t resolutmn depends essent:ally on the accuracy of the time-of-flight measurement typ:cal values are +-0 005 at t = - 0 1 (GeV/c) 2 and -+0 02 at t = - 0 . 4 (GeV/c) 2 We monitor the stabfl:ty of the system by continuously recording elast:c events during the data-taking penods 4 4 Acceptance The acceptance for production of a KTr system as a funclaon of mass and momentum transfer is essentially determined by the proton arm, whale the acceptance as a funct:on of decay angles is given by the forward arm The Kn mass acceptance extends from threshold up to about 2 4 GeV at an lncxdent momentum of 10 GeV/c (fig 4) The azimuthal aperture of the recoil detector hmlts the overall acceptance to a maximum of 17% This does, of course, not mtroduce any bias in the Kn decay angular dlstnbutlon. The absence of a momentum-analysing magnet allows a large forward solid angle of 0 3 sr The forward arm acceptance is hmxted only by the size of the MWPCs, and by chamber lneffic:ency m the beam region We have done detailed acceptance calculations by the Monte Carlo method, m order to present the data in corrected form, normalized to the production cross-seclaon. In particular, the calculatmn takes into account (a) the geometry of the e n m e set-up, (b) the efficiency of the MWPCs, (c) absorption and decay of the incoming kaon, and of the outgoing pxons, mchadmg the energy dependence. In addition, the Monte Carlo program mchades the effects of the cuts on kinematic variables to remove background, as dascussed above (d) forward particle momentum p > 300 MeV/c, (e) np effective mass Mnp > 1 4 GeV

378

R Baldt et al / KTrproductlon

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m the Gottfrled-Jackson frame

The Monte Carlo program generates events for fixed values of the production variables MK~r and t, as a function of the Kn decay angles (cos 0, 4~) m the GottfnedJackson frame The acceptance Is obtained stmply from the ratio of events accepted by the apparatus to events generated, as a function of the four kxnematlcal variables As an example, we show xn fig 8 the (cos 0, q~)-acceptance of the K*(890) (0 84
The Monte Carlo acceptance calculation (subsect 4 4) accounts for efficlencaes depending on the configuration of each event In order to obtain absolute cross sections we have to correct, m addition, for the following configuration-independent effects

(1) incident particle Identification (11) hodoscope efficiency

Efficiency K + beam

K - beam

094 0 83

10 0 90

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R Baldt et a l / Klr productton

(111) dead-time losses (iv) efficiency of time-of-fhght system (v) accidentals in beam antlcounters A1, A2 (v0 track reconstruction efficiency proton arm forward arm (vu) cuts on event geometry (Vlll) cuts on event kinematics

0.96 0.88 0 92

0 99 0 95 0 98

0 0 0 0

0 75 0 94 0 93 0.93

67 87 93 93

To determine the normahzatlon of the data, we have selected two independent samples of parncularly homogeneous quahty for each beam polarity. We obtain consistent results and estimate the systematic error of the cross-section scale to be about 10% Correctmg finally for the branching ratio B(K ° -~ K ° ~ lr+Tr- ) = 0 344, we obtain the following sensltmty of the experiment (in the K*(890) region) 329 measured events//Jb for K+p ~ K°Tr+p, 138 measured events//lb for K - p ~ K°Tr-p

5 The measurements 0 ± Here we present our data on the reactions K + - p ~ Ksn p at 10 GeV/c incident momentum Fig 9 shows the K~Tr± mass spectra in the full range of momentum transfer t accepted in this experiment, 0.05 < It] < 1 0 (GeV/c) 2 The sohd-hne histograms show the uncorrected data, wlule the points with error bars represent the spectra after correction for the acceptance of the spectrometer The spectra are clearly dominated by production of the K*(890) and K*(1420) resonances above a very low level of non-resonant background. The high statistics allows the determination of the spherical harmomcs moments of the Kn decay angular distribution as a function of KTr mass and as a function of t m the mass regions corresponding to K*(890) and K*(1420) production, both for the K + and K - Induced reachons

5 1 Deterrnmatton of the moments In a given bm of production variables M, t we expand the KTr decay angular distribution I(0, ~) as

I(0, ~) = N ~

(ym) ym(o ' ~5),

(6)

J,m

where N is the number of events (or the cross section) in the M, t b m considered The spherical harmomcs moments (Yfl) are obtained by reversion

N ( y M ) =f I(o, ~) Yy(O, ,) d ~

(7)

R Baldt et a l / Kn productton

380 20000

0

*

a) K ' p ~ Ks~ p

15000 4-

=E

10000

÷

BA

+

5000

08

10

12

I/-* 16 M (K° Tt') (GeV)

18

20

22

20

2z

8000 b) K - p ~ K°~-p 6000

+ ÷

4000 laJ

o8

)o

12

1~, 16 M ( K % ) (GeV)

18

Fig 9 (a) Ksrr 0 + and (b) K ~ n - effectwe mass spectrum, for 0 05 < Itl < 1 (GeV/c) 2 The spectrum is shown before (histogram) and after (points with error bars) acceptance correction A constant factor of 5 8, due to the aztmuthal aperture of the proton detector, is not included m the correction

In this analysis, we t a k e 0, q~ to b e t h e angles o f t h e K ° m t h e t - c h a n n e l h e l l m t y f r a m e ( G o t t f r l e d - J a c k s o n f r a m e ) In this r e f e r e n c e f r a m e , p a n t y c o n s e r v a t i o n m t h e p r o d u c t i o n process l m p h e s t h e s y m m e t r y

(8)

I(0, c~) = I(O, 27r - (p) , or in t e r m s o f t h e m o m e n t s

(yiM)

= (_ 1)M(yM)

and

( I m yM) = 0

(9)

R BaMt et a l / Kn productton

381

This property allows one to rewrite 1(0, ~) in the form

I(O, q~) = N

~

3,M>>O

eli< Re Yy) Re yM(o, dp),

(10)

with eMj={ 1 2

f°rM=0 for M 4=0 ,

where the sum now extends over positive values of M only For ease of notation, we will omit from now on the Re sign in front of yM The measured angular distribution ~'(0, ~) is distorted by the acceptance of the spectrometer A (0, $)

"[(0, 4)) = A(O, c~) l(O, d~)

(11)

The measured moments (~}u) of the distributionS(0, ~) are related to the true moments (YM) of I(0, ~) by a set of linear equations

J',M'>/O

Ass, (Y~ )

(12)

The correlation coefficients A MM' are determined by the acceptance function A (0, qS) m the following way

Ays¥'=f Yy(O,¢) A(O,¢) YM'(0,qS)da,

(13)

and they can be calculated by the Monte Carlo method. We note that the number of equations (12) is determined by the complexity of the shape of the acceptance, while the number of unknown moments depends on how many waves are present in the reaction We found that the acceptance is well represented by a set of moments with 0 ~
5 2 The moments as a function o f mass We calculate the moments N ( Y f l ) of the angular distribution of the K ° in the t-channel hehclty (GottfnedJackson) frame Figs 10 to 13 show the mass dependence of the moments, in the t interval 0 1 < I t l < 0 4 (GeV/c) 2 In this restricted range we expect the different amplitudes to have slmdar t dependence The normahzatlon IS such that N(Y~o ) = do/dM, 1.e. the cross section within this t range. The moments in figs. 10, 11 have been obtained from a fit with Jmax = 4 and Mma x = 2 to the set of equations (12) A good fit is obtained in the mass region up to 1 6 GeV without the introduction of any higher moments into the fit We further search for moments with higher M or J by fitting all terms up to Jmax = 4, Mmax = 4,

R Baldl et al / Kn productton

382

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1.6

R Baldt et al /K~rproductzon 20

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Fzg 11 The moments N< yM) of the K!2n- decay angular dzstnbut]on as a functzon o f K~r mass, m the t interval 0 1 < I t I< 0 4 (GeV/c)

384

R Baldl et al / Kn productton

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Krc- m(L.~ (GeV) Fig 12 The higher momentsM = 3, 4 and J = 5, 6 for K0*r+ as a function of mass, xn the t interval 0 1 < Itl< 04 (GeV/c)2

and up to Jmax = 6, Mmax = 2, respectwely The moments with M = 3 and 4, shown m figs. 12, 13, are negligible compared to the dominant moments, implying that the K*(1420) is predominantly produced with hellclty X = 0, 1 and that X = 2 is negligible Also the moments J = 5 and 6 do not show any significant signal (figs. 12, 13) The lower moments are stable wxth respect to the particular choice of Jmax and Mmax We conclude that S-, P-, and D-waves with hehclty zero and one suffice to describe the data in the mass range up to 1.6 GeV The moments in the higher mass region 1 5 < M < 2 2 GeV have been published previously [2] They give clear evidence for production of the K*(1780) resonance with spin-parity JP = 3 - .

R Baldz et al / K= productton 40.

385

20.

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KT[- mass (GeV) Fig 13 The higher moments M 01 < Itl< 04(GeV/c) 2

= 3, 4 a n d J = 5 , 6 f o r K O n - as a

function of mass, in the t interval

5 3 The moments as a funcnon o f t In figs 1 4 - 1 7 we gave the t dependence of the moments in the mass regmns of the K*(890) (0.84 < M < 0 94 GeV) and the K*(1420) (1.34 < M < 1 50 GeV). The terms (Y~) up to Jmax = 4, Mma x = 2 have been included in the fits. Figs. 18 and 19 show the higher moments m the K*(1420) regmn, obtained from fits with Jmax = 4, Mma x = 4 and wxth Jmax = 6, Mmax = 2 Again, these moments are consistent with zero The data are normahzed such that N< Y~o>= da/dt, the &fferentlal cross secUon Wlttun the mass interval

R BaMt et a l / K;r production

386

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-t (GeV/c)2 Fig

14 T h e m o m e n t s N ( y M ) as a f u n c t z o n o f t, m t h e K * + ( 8 9 0 ) r e g i o n (0 84 < MKz r < 0 9 4 G e V )

n

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R Baldz et a l / KTr productton

388

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Fzg 16 The m o m e n t s N ( Y~4) as a functzon o f t, m the K * + ( 1 4 2 0 ) region (1 34 < MK~ < 1 50 GeV)

S

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R Baldt et a l / K~rproductzon 3.

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5.4 Conclusions

We have measured Kit production b y K ÷ and K - beams in the non-charge-exchange reactions (1). The statlst]cs obtained are an order of magnitude larger than m previous experiments at the same energy. The dependence on mass MKn and m o m e n t u m transfer t o f the moments N ( y M ) o f the Kit decay angular distribution has been determined Investigation o f the significant moments shows that the mass region up to 1 6 GeV can be described b y S-, P-, and D-waves with hehcity zero and one A detailed amplitude analysis and study of production mechamsm Is the subject of refs. [3,4] and of the following paper [1 ]. We gratefully acknowledge the hospitality and technical assistance of CERN, as well as the loan of equipment b y the EP Division. We thank the Fonds National Smsse

R Baldt et al / Krr productton 6*

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0

.8

tO.

J = 6 M=~'

S.

2 5

O.

0

-S.

-2

-10

O.

-4.

J = 6 M=O

-15.

I

-~'0 • •0

2

, 4

I

, 6

I

-6

, 8

-8 1,0

J

-10 0

.2

-t

4

6

8

0

•0

I

i 2

I

, .4

I,I, •6

.8

(GeVIc) 2

Fig 19 The hzgher moments M = 3, 4 and J = 5, 6 as a functzon of t, m the K*-(1420) region

for support of the project. We thank the techmcxans of the Umverslty of Geneva for expert asszstance, and A Delavy for help with computing. We thank A.D. Martin, B. Morel and B. Schrempp for many useful discussions on the analysis of the data

References [1] A D Martin et al, Nucl Phys B134 (1978) 392 [2] R Baldi et al, Phys Lett 63B (1976) 344 [3] R Bald1 et al, Amphtudes and exchange mechamsms for K* resonances produced by the reaetzons K~p ~ K*±p at 10 GeV/c, Phys L e t t , submitted [4] A Mermoud, Mesure et analyse en ondes partmlles de la production du syst~me KOTrdarts la r~actzon K~p ~ (K~lr±)p ~ 10 GeV/c, Ph D thesis, Umverszty of Geneva, 1977