A2− production in the reaction π−p → K−KS0p at 9.8 and 18.8 GeV

Nuclear Physics B145 (1978) 349-366 © North-Holland Publishing Company

A~ PRODUCTION IN THE REACTION n-p --> K-K~p AT 9.8 AND 18.8 GeV

CERN-Munich (MPIO Collaboration V. CHABAUD, B. HYAMS, C. JONES and P. WEILHAMMER CERN, Geneva, Switzerland W. BLUM, H. DIETL, G. GRAYER I), W. KERN 2), W. KOCH 3), E. LORENZ, G. LUTJENS, G. LUTZ, J. MEISSBUGER 4) and U. STIERLIN Max-Planck Institut far Physik und Astrophysik, Munich, Germany Received 21 July 1978

Results of two spark chamber experiments on A2 production in the reaction *r-p K-K~ (~ 7r+*r-)pat 9.8 and 18.8 GeV are presented. Decay angular distributions and differential cross sections are given, and the energy dependence of the cross section o[Ir-p ~ A~(~ K-K°)p] is compared with results from lr-p ~ A~(~ 3*r)p.

1. Introduction In this paper we report on measurements of A~ production in the reaction 7r-p -~ K-K~(-+ rr+rr-)p.

(1)

•This experiment was performed at the CERN Proton Synchrotron (PS) at 9.8 and 18.8 GeV incident momentum. The detector was the CERN-Munich spectrometer [1]. The aim o f this experiment was to study the s- and t-dependence on the A2 production cross section, and the decay angular distribution of the K-K~ system in the mass region from threshold to 1.6 GeV. The production of charged A2 mesons has been studied in many electronic and bubble chamber experiments both near threshold [ 2 - 5 ] and at high energies [ 6 - 1 4 ] . 1) Now at Rutherford Laboratory, Chilton, Didcot, Oxfordshire, UK. 2) Now at Southeastern Massachusetts University, N. Dartmouth, Mass., USA. 3) Now at DESY, Hamburg, Germany. 4) Now at Institut fiir Kernphysik, Jiilich, Germany. 349

350

K

Chabaud et al. / A~ production

At high energies it exhibits some interesting properties: (i) the A~ is produced by natural parity exchange in an almost pure state (I ], m >= 12, - 1 ) in the t-channel helicity frame); (ii) the cross section decreases rather slowly with increasing energy. In most previous experiments of A~ production in pion-proton or pion-nucleon interaction, the A~ was observed by its decay into a three-pion f'mal state. In order to extract the A~ meson amplitude JP = 2* from the dominant 1+ and 2- states, a complex partial-wave analysis had to be performed. An alternative possibility for • ÷ studying A[ production is to measure a two-body decay of the A~ such as K-+K° (or 7r~ ). In this channel the A~ is observed with little background from other states, since only states with natural spin-parity can occur. In addition, the twobody decay involves fewer kinematic parameters. The low background and the small number of kinematic variables permit a straightforward spin and helicity determination of the A2. Using the same apparatus at two different energies reduces systematic errors in the study of the energy dependence of the cross section. A difficulty of the study of the channel A~ ~ K-+K~ is the small branching ratio of less than 10%.

2. Apparatus The experimental set-up is shown in fig. 1 and is described in detail in ref. [1]. The experiment used an unseparated pion beam from the PS. The incident beam was defined by four scintillation counters $1 ..... $4. Pions were tagged with two threshold ~erenkov counters ~1 and ~2. Incident pions interacted in a 50 cm liquidhydrogen target H2. The directions of the beam particle and the charged forward. going secondaries were measured in three sets of wire spark chambers, Wl, W2, and W3, with magnetostrictive read-out. A wide-gap magnet of 2 T • m bending power

,;11; I I I I ft

(~1

(~ 2

W~

Sl

I t I , I

'1

If 1

S2 $3 $4 Ss S6 Sv S8

0

1

2

I

I

!

3m I

W3 S~S,o

Fig. 1. Schematiclayout of the spectrometer: C1, C2, beam Cerenkovcounters; S1 ... SIO scintillation counters; W 1 ... W 3 sets of wire spark chambers;H2 liquid-hydrogentarget; M spectrometer magnet.

V. Chabaud et al. / A~ production

351

served, together with the chamber sets W2 and Ws, as a momentum analyser for the forward-going secondary particles. Except for a beam entrance hole and an exit window, the target was completely surrounded by lead scintillation sandwich counters Ss in order to reject events with emission of Ir°'s or more than one charged recoil particle. The anticoincidence counters $7, forming a window in front of the analysing magnet, and Ss, lining all magnet-gap faces, further suppressed unwanted triggers. The scintillation counter $6, with a small hole on the beam trajectory, sensed interactions with forward-going charged particles. The 32-element hodoscope $9 served for the selection of three charged secondary tracks. A small counter $1o vetoed beam particles that interacted at the end of the apparatus. The complete trigger condition was: [ S 1 " S 2 • S 3 • S--4] • S 6 • S l o

• S5('~

2 hits)" $7 • Ss " $9( = 3 hits).

3. Data processing and event selection A total of 0.8 X 10 6 triggers at 9.8 GeV and 1.3 X 10 6 triggers at 18.8 GeV were recorded in this experiment. Only a small fraction of these had the two-vertex topology of reaction (1). In order to separate them from the much more numerous triggers from the reaction zr-p -~ zr-lr+Tr-p,various cuts were applied during an early stage of the event reconstruction: (i) three tracks were required in the spark chamber set W2, thus limiting the V ° decay volume between the primary vertex and the beginning of W:; (ii) from the beam trajectory and the three secondary trajectories, the point of the closest approach was calculated. In the case of a genuine single-

i

i

18.8 GeV

6000

o

400C

Z ~J

,.>, 200(

0.4

0.6

0.8

r,-~.~(OeV)

Fig. 2. Invariant ~÷~- mass distribution for V°'s, Plab = 18.8 GeV.

352

11. Chabaucl et al. / A ~ production

vertex solution, the event was rejected. Furthermore, two secondary tracks had to form a vertex separated from the intercept of the remaining track with the beam trajectory. Only those events where the V ° vertex was downstream from the production vertex were fully reconstructed. Fig. 2 shows the invariant 7r+~r- mass of the V °'s at 18.8 GeV with a clear K ° signal. Furthermore, we selected only events with a V ° mass between 486 and 509 MeV. Figs. 3(a) and (b) show the square of the mass of the invisible recoil particle after K-'K° assignment to the forward-going system. A peak around the proton mass is observed at both data sets. The width of the distributions is compatible with the expected resolution for a missing proton. For the final event selection, we required the square of the missing mass (MM ~) to be between 0.5 and 1.25 GeV 2 at

200

9.8 GeV X

150

~z tOO

50

__,_r (18

1.6 (MISSING

2.4

• 3.2

6.0

3.2

4.0

MASS) 2 (GeV2)

150[ ~oe

uJ

0.S

1.6 2.4 (MISSING MASS)2(GcV 2)

Fig. 3. Missing-mass squared distributions for K-K° events at 9.8 and 18.8 GeV. The cuts for a missing proton are indicated by arrows.

K Chabaud et

aL/A~production

353

9.8 GcV

6(] x o

1.0

1.2

I.&

1.6

1.6

~.0

1.6

1.8

2.0

mzR (GcV)

125

"~ lOG o z

75

5C

25

1.0

1.2

1.4 mK~ (GcV)

Fig. 4. Observed K"K0 mass spectra at Plab = 9.8 and 18.8 GeV. 9.8 GeV, and between 0.15 and 1.4 GeV2 at 18.8 GeV. The f'mal samples (figs. 4a and b) contain 995 events at 9.8 GeV and 2150 events at 18.8 GeV. Small background contributions to these samples come from the following reactions: lr-p ~ K-K°(pn °) K-K°(nT:) -->

~r--Ko y+.

From the MM2 distribution, we estimate a background in our samples of (3.8 + 0.5)% at 9.8 GeV and (5.2 + 1.0)% at 18.8 GeV. 4. Acceptance correction and absolute cross-section determination In order to obtain the differential cross sections do/dM, do/dt, and da/d~2, and the absolute cross section, the observed data have to be corrected for losses caused by our detector.

354

II. Chabaud et al. / A ~ production

For fixed s and an unpolarized target, reaction (1) can be described by four kinematic variables: mKK = the invariant K-K ° mass; t = the square of the four-momentum transfer from the initial to the rmal proton; 0, q~ = the decay angles of the K- in the t-channel helicity frame of the K-K ° system. The losses caused by our detector can be subdivided into a class which depends on the event configuration, i.e. on the kinematic variables, and a class which is independent of the event configuration. The configuration-dependent losses from secondary interactions and decay in flight of the K- and the lr* were corrected by weighting individual events. The mean value and the range of these weight factors was ( W(9.9 GeV)) = 1.35,

varying between 1.20 and 1.70 ;

( W(18.8 GeV)) = 1.25,

varying between 1.09 and 1.40.

i

l

I

I

I

i

9.8 GeV

16

~e

0tU

6

°;

Itl = 006 GeV2 Itl =0.4 Oev2 i 1.1

I 1.2

1!3

1'.4

115

1!6

i

i

mK~ (GeV)

I

[

I

i

18.8 GeV

.~3o ~2s ~

Q. W ¢,..)1 5

~

_

Itl = 0 . 0 6 It[=0.4

C~V2 GeV 2

5 |

1.1

I

1.2

I

1.3

I

1.4

I

1.5

I

1.6

m K R (GeV)

Fig. 5. Acceptance of the spectrometer for Monte Carlo generated events of reaction (1) with isotropic decay of the K-K 0 system.

355

V. Chabaud et al. / A ~ production

The most important configuration-dependent loss was caused by the geometry of our spectrometer, covering only about 0.15 sr. Fig. 5 shows examples of the acceptance A (mKK) for an isotropically decaying K-K ° system at two t-values. For the acceptance correction the same procedure as in ref. [1] was applied. The data were binned in mKK and t. For fLxed mK~ and t, the produced decay angular distribution Iprod(~2) Can be written in terms of spherical harmonics YM(~2): Lmax Iprod(~'-~) = Nprod ~ L=O

L ~ eM< yM> Yff(~2), M=O

with Nprod = produced number of events in mK~., t-bin, eM = 1 f o r M = 0 and eM= 2 forM>~ 1, ((Yff), y M ( ~ ) is shorthand for (Re yM), Re Yff(~)). The (yM) are the normalized spherical harmonic moments. The observed angular distribution Iobs(I2) is connected to the moments by Lmax

Iobs(~2)=A(f2)Nproa ~

L=O

L

~

M=O

eM(YM) yLM(~),

with A (~2) being the acceptance for events with the decay angles 0 and ¢; A (~2) was calculated by the Monte Carlo method. The moments were determined by maximum likelihood fits. Owing to the small number of events, Lmax was limited to 4 (S-, P-, and D-waves) below 1.4 GeV. Between 1.4 and 1.6 GeV mass, also (Y~5), (Y~), (Y~6), and (Y~) were added to allow for an F-wave (g meson). Most of the moments were found to be compatible with zero and were successively eliminated from the fits. This reduced the number of free parameters and permitted a fine mass binning in subsequent fits. Finally, only the four moments (Y~2), (Y~2), (Y~4), and (I~4) were found to be significant below 1.6 GeV mass. The ffmal fits yielded these four moments and the true number of produced events Nprod, together with their statistical errors. For the absolute cross-section determination, the configuration-independent losses were taken into account by a global multiplication factor F. This factor accounted for a series of small corrections listed in table 1. table 1. The following total cross sections from 1.0 to 1.6 GeV in mass and from train to - 0 . 4 GeVa in t were determined: o[lt-p ~ K-K°( -> 7r÷~r-)pl = 2.93 + 0.27 gb

at 9.8 GeV,

o[rt-p -+ K-'K~(-,'- rr÷lr-)p] = 1.61 - 0.14/ab

at 1.8.8 GeV.

The 'one-event' cross sections are o(1 event) = 0.171 + 0.015 nb

at 9.8 GeV,

o(1 event) = 0.205 + 0.016 nb

at 18.8 GeV.

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V. Chabaud et al. / A ~ production

Table 1 Geometry-independent correction factors F i for the cross-section determination Origin of correction

Plab = 9.8 GeV

Plab = 18.8 GeV

F i ± AF i

Fi ± A F i

Beam contamination e, # Beam contamination K-, pBeam attenuation in H2 Interaction in mylar around H2 Interactions in $2, $3 Interactions secondaries in the set-up Anticounter jamming Effects in $9 (array): dead space 5-ray in fourth counter interaction behind array 6-ray in Ss Electronics + counter inefficiencies Electronics dead-time Reconstruction losses: program inefficiency random 4 th track K ° mass cut Background after K ° mass cut b) Missing-mass cut Background after MM cut

1.035 1.020 1.025 0.990 1.005 1.085 1.040

-+ 0.010 ± 0.010 -+ 0.000 a) +- 0.000 a) ± 0.000 a) ± 0.010 ± 0.005

1.030 1.005 1.025 0.990 1.005 1.085 1.020

± 0.010 -+ 0.000 ± 0.000 ± 0.000 ± 0.000 ± 0.010 ± 0.010

1.025 1.030 1.005 1.005 1.010 1.020

± 0.000 a) -+ 0.005 ± 0.000 a) ± 0.005 ± 0.010 ± 0.010

1.025 1.030 1.005 1.005 1.010 1.000

-+ 0.000 -+ 0.005 ± 0.000 ± 0.005 -+ 0.010 -+ 0.000

1.050 1.020 1.010 0.995 1.025 0.975

± 0.030 ± 0.005 ± 0.000 a) ± 0.000 a) -+ 0.005 ± 0.005

1.050 1.000 1.015 0.995 1.045 0.960

-+ 0.030 ± 0.005 ± 0.000 a) ± 0.000 a) ± 0.010 ± 0.010

Total correction factor F = rl F i

1.440 ± 0.110 c)

a) a) a) a)

a) a) a)

a)

1.350 ± 0.100 c)

a) Error smaller than 0.25%. b) After application of all other cuts, i.e. not identical with background of fig. 2. e) The overall error includes the estimate of systematic errors.

5. T h e d i f f e r e n t i a l cross s e c t i o n s d o / d M , d o / d t a n d t h e m o m e n t s ( y [ n ) as a f u n c t i o n

of mass Fig. 6 s h o w s t h e c o r r e c t e d mass s p e c t r a for Itl < 0 . 4 GeV a . I n b o t h d i s t r i b u t i o n s o n l y t h e signal o f t h e A2 a r o u n d 1300 M e V is observed. C o n t r a r y t o t h e observat i o n s in t h e r e a c t i o n 7r-p -+ K + K - n at t h e same energies [15] n o t h r e s h o l d e n h a n c e m e n t is seen. Fig. 7 ( t a b l e 2) show~ t h e d i f f e r e n t i a l cross sections d a / d t i n t e g r a t e d over t h e mass range 1 . 2 0 - 1 . 4 2 G e V . Also d i s p l a y e d is t h e d i f f e r e n t i a l cross s e c t i o n o f d o [ d t f r o m t h e r e a c t i o n rt-p + K + K - n at 18.4 G e V [ 1 5 ] , w h e r e isospin I = 0 partial waves are also p r e s e n t . A r e m a r k a b l e d i f f e r e n c e is observed.

V. Chabaud et al. / A ~ production

357

9.8 GeV

200 180 160 140

10.0

6.0 4.0 ZO

:~

120 100 L9

80 60

aD "D

4.0 2.0 1.0 1.1 1.2 1.3 I./, 1.5 1.6

raKE (GeV)

Fig. 6. Corrected mass spectra at 9.8 and 18.8 GeV for It[ < 0.4 GeV 2. Fig. 8 (tables 3a and b) shows the four m o m e n t s (I~2), (Y~2), (Y°44), and (IA4) as a function o f m KK, after integration in t, from train to --0.4 GeV 2 . As already mentioned, the other m o m e n t s were consistent with zero.

Table 2 do/dt for 1.20 < mK~` < 1.42 GeV Aid (GeV 2 )

do/dt at 9.8 GeV (jab/GeV2 )

do/dt at 18.8 GeV 0zb/GeV 2)

train-0.045 0.045-0.08 0.08-0.12 0.12-0.17 0.17-0.22 0.22-0.30 0.30-0.50 0.50-0.80

4.64 6.81 7.16 7.08 5.69 4.95 2.74

2.24 3.08 3.99 3.55 3.13 3.03 1.26 0.34

+ 0.68 -+ 0.97 + 1.00 ± 0.95 ± 0.85 ± 0.71' + 0.39

+ 0.29 + 0.38 + 0.44 ± 0.38 ± 0.35 + 0.31 + 0.13 ± 0.05

V. Chabaud et al. / A~ production

358

• et 9.8 G¢¥ • o118.8 GeV -'-0.2=

I I

for 1.20-< mKk <1,42 OeV

doIdt(lt-p---~,K*K'n) at 18.4 GeV 2

10. 05.0

~++~_

~ 2.G

"o

1.0 05

0.2

o.1

.1 o.2 o.3 o.~ ols Itl

d6

o'.7 o.8

(GeV2)

Fig. 7. Differentia] cross section do/dt at P]ab = 9.8 and 18.8 GeV; 1.20 < rnK~ < 1.42 GeV.

t, sO

01S~

,

< Y 2 > o.Io~_

"2

-oos~

~_~_

,

'

~ 8G~v

, ---+-

-Ol oh < v 0 > - o o.. 1 4 -o.Ic -0.15

...

,,2 ooI-+- +


1.0

1!1

1.12

1 I3

t 1.4

mKK(GeV)

lt5

1.6

1.0

11

1.2

1.3

14

1.5

1.6

mKg(GeV)

Fig. 8. t-channel moments (Yo), (Y~), ( Y~4), and (Y~) as a function of mass for Plab = 9.8 and 18.8 GeV; Itl < 0.4 G W 2.

V. Chabaudet al. / A ~ production

359

Table 3a

(Yr,)versus mK~ for Itl < mK~ (GeV)


1.06 1.16 1.26 1.34 1.45 1.55

0.078 0.662 0.112 0.122 0.060 0.106

(1.00-1.10) (1.10-1.20) (1.20-1.30) (1.30-1.40) (1.40-1.50) (1.50-1.60)

0.4 GeV 2 at 9.8 GeV (y22) + 0.046 ± 0.030 ± 0.015 ± 0.015 ± 0.036 ± 0.038

0.006 -0.042 -0.073 -0.082 -0.072 -0.035

(Y~4) ± 0.026 ± 0.020 ± 0.010 ± 0.007 ± 0.018 ± 0.032

0.012 -0.045 -0.122 =-0.098 -0.064 -0.107

(Y~) ± 0.043 ± 0.030 ± 0.016 ± 0.017 ± 0.034 ± 0.046

-0.014 -0.031 -0.080 -0.095 -0.040 -0.009

± 0.030 ± 0.023 ± 0.013 ± 0.009 ± 0.026 ± 0.038

Table 3b

(yr~) versusm KK for [t I < mK~.. (GeV)

(yO)

1.05 1.16 1.23 1.28 1.32 1.37 1.42 1.47 1.55

0.049 0.062 0.110 0.076 0.107 0.093 0.076 0.051 0.068

(1.00-1.10) (1.10-1.20) (1.20-1.25) (1.25-1.30) (1.30-1.35) (1.35-1.40) (1.40-1.45) (1.45-1.50) (1.50-1.60)

0.4 GeV 2 at 18.8 GeV (y~) + 0.048 ± 0.038 ± 0.029 ± 0.014 ± 0.016 ± 0.016 ± 0.024 ± 0.029 ± 0.025

0.011 -0.047 -0.095 -0.097 -0.093 -0.092 -0.101 -0.098 -0.073

(yO) + 0.038 ± 0.020 ± 0.016 ± 0.009 ± 0.009 ± 0.011 ± 0.018 ± 0.014 ± 0.015

-0.062 -0.034 -0.066 -0.155 -0.125 -0.144 -0.159 -0.131 -0.110

(y,~) + 0.057 + 0.041 ± 0.031 ± 0.014 + 0.018 ± 0.015 ± 0.028 ± 0.030 + 0.024

0.064 -0.041 -0.125 -0.117 -0.105 -0.100 -0.102 -0.095 -0.104

+ 0.068 ± 0.023 ± 0.018 ± 0.011 ± 0.011 ± 0.016 ± 0.025 ± 0.024 ± 0.019

6. Determination of the A 2 resonance parameters To d e t e r m i n e the r e s o n a n c e p a r a m e t e r s o f the A2, we p a r a m e t r i z e d the mass s p e c t r u m b y a spin-2 Breit-Wigner d i s t r i b u t i o n and a b a c k g r o u n d d i s t r i b u t i o n :

d°

=

c[(

mm°F

m2 _ m2)2 + m2F2+ B

G1

(5)

,

with

R4q4 + 3R2q 2 + q

F

= Fo

m

= mass o f the K - K ~ s y s t e m ,

,

too, Fo = mass, w i d t h o f the A2 r e s o n a n c e , q

= c.m. m o m e n t u m o f the K - in the K - K ° s y s t e m ,

qo

= q at A2 r e s o n a n c e ,

Table 4 Results of fits of A 2 parameters for 1.20 < m K ~ < 1.42 GeV Fit

A B C D

Plab (GeV)

9.8 9.8 18.8 18.8

m(A2) (GeV)

1.312 1.312 1.318 1.316

F(A2) GeV)

± 0.004 ± 0.004 ± 0.002 ± 0.002

126 126 113 101

± ± ± ±

11 14 8 8

Norm. const. C (~b)

Background terms

18.3 18.1 9.6 8.7

0.77 0.69 0.62 0.40

C1 (GeV -1 )

± ± ± ±

0.11 0.66 0.10 0.50

C2 (GeV -2)

0.08 ± 0.66 0.98 ± 0.48

Prob. (×2) (%)

a(A2) a) (t~b)

a(BG) a) 0~b)

a(BG ) a) atot (%)

36 33 29 41

1.88 1.87 1.03 0.97

± ± ± ±

0.11 0.56 0.04 0.19

0.31 0.32 0.13 0.17

± ± ± ±

0.04 0.55 0.02 0.19

14 15 11 15

a) Since the parameters in the fit with linear background (B and D) are highly correlated, the error on the background is rather big. This obviously increases the error on the A2 cross section a(A2).

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V. Chabaud et al. / A ~ production

R

= range parameter = 1 f m ,

C

= normalization constant.

361

The background (BG) was either constant or varying linearly with mass BG = C1 ,

or

BG = Ca + C2m •

The fit used a X2 minimization in the mass range from 1.0 to 1.6 GeV and [ t l < 0.4 GeV 2. The mass resolution of the spectrometer of o = 5.7 MeV at 1300 MeV was folded in. The results of the fits are given in table 4. The fitted shape of the spectrum and the background contribution are indicated in fig. 6. As is evident from the figure, the A2 is sufficiently parametrized by a single pole resonance.

7. The spin density matrix elements in the A2 region From the four fitted moments (Y~n), we calculated the density matrix elements Oi~ in the A2 region (1.20 < mK-K o < 1.42 GeV) for several t-intervals:

Ooo

=

1.585 ( y O ) + 2.127 ( y O ) + 0 . 2 ,

Pl~

=

0.793 (Y°) - 1.418 (Y°) + 0 . 2 ,

Ol-X

= - 1 . 9 4 2 (Y~) - 2.242 (Y~),

(6) Re P2o = - 1 . 5 8 5 (Y~) + 1.372 (Y,~). The results are listed in tables 5a and 5b and shown in fig. 9 as a function of t. Except for very small values of t, Pl I and P1-1 are found to be near their maximum possible values, whereas Poo and Re P2o are decreasing to small values with increasing [t I. We attribute this behaviour to an increase of A2 production by natural parity exchange relative to the background and to the production by unnatural parity exchange. The available statistics, and the method of acceptance correction and determination of the moments, excludes a more detailed analysis. Figs. 9(a) and (b) also display the t-dependence of the combination p÷ = Px 1 + Pl--1 and p - = P~x -- 01-1- The combination 0~1 + 01-1 represents the natural parity-exchange part of the A2 production cross section. It is fairly constant for I tl > 0.1 GeV 2 at both energies. At 18.8 GeV it approaches 1.0, signifying complete dominance of natural parity exchange and no change in the production mechanism of the A2 up to a [tl of 0.8 GeV 2. At 9.8 GeV the value of 011 + Ol-x is around 0.85. In order to extract the A2 production cross section due to natural parity exchange (NPE), we fitted the following expression to the differential cross section: do NPE -

dt'

CB2t ' e-Bt' ,

(7)

t,o 0'. t,J

Table 5a 22 Spin density matrix elements in t-channel helicity frame Pik versus IT[(GeV2)

Poo

0.029 0.064 0.099 0.146 0.193 0.258 0.381

0.323 0.179 0.144 0.249 0.143 0.119 0.030

(tmin-0.045) (0.045-0.08) (0.08-0.12) (0.!2-0.17) (0.17-0.22) (0.22-0.30) (0.30-0.50)

Pll ± 0.113 ± 0.071 ± 0.072 ± 0.078 ± 0.072 ± 0.074 ± 0.075

0.357 0.451 0.459 0.442 0.433 0.446 0.493

It l (GeV 2) for PI-I

± ± ± ± ± ± ±

0.070 0.045 0.045 0.049 0.045 0.046 0.047

0.104 0.366 0.352 0.364 0.312 0.363 0.435

1.20 < m K ~ < 1.42 GeV at 9.8 GeV Rep2o

± ± ± ± ± ± ±

0.097 0.050 0.052 0.050 0.059 0.051 0.053

0.084 0.021 -0.035 -0.009 0.041 0.019 -0.029

± ± ± ± ± ± ±

0.067 0.033 0.036 0.034 0.039 0.035 0.036

P+= P l l +Pl--1

P-= P l l --Pl--1

0.461 0.817 0.811 0.806 0.745 0.809 0.928

0.253 0.085 0.085 0.078 0.121 0.083 0.058

± ± ± ± ± ± ±

0.120 0.067 0.069 0.070 0.074 0.069 0.071

± ± ± ± ± ± ±

0.120 0.067 0.069 0.070 0.074 0.069 0.071 ta

Table 5b Spin density matrix elements in t-channel helicity frame Pi~ versus

It l (GeV 2) for

It-I(GeV2)

Pl--I

0.029 0.063 0.101 0.145 0.195 0.261 0.373 0.603

(tmin-O.045) (0.045-0.08) (0.08-0.12) (0.12-0.17) (0.17-0.22) (0.22-0.30) (0.30-0.50) (0.50-0.80)

Poo 0.206 0.105 0.013 -0.008 0.010 0.083 0.051 0.068

Pll + ± ± ± ± ± ± ±

0.113 0.080 0.062 0.040 0.049 0.042 0.048 0.067

0.412 0.405 0.468 0.466 0.473 0.472 0.478 0.460

+ ± ± ± ± ± ± ±

0.070 0.049 0.039 0.025 0.030 0.026 0.030 0.041

0.203 0.377 0.449 0.480 0.472 0.439 0.527 0.502

Rep2o + ± ± ± + ± + ±

0.063 0.062 0.035 0.033 0.029 0.031 0.036 0.055

IOl

1.20 < m K ~ < 1.42 GeV at 18.8 GeV

0.021 0.002 -0.013 -0.047 0.008 -0.024 -0.011 0.007

+ ± ± ± ± + ± ±

P+= P l l + P l - 1 0.044 0.043 0.024 0.022 0.020 0.021 0.025 0.038

0.615 0.782 0.917 0.941 0.945 0.911 1.005 0.962

± ± ± ± ± ± ± ±

0.094 0.079 0.052 0.041 0.042 0.040 0.047 0.069

P-=Pll 0.209 0.028 0.019 -0.014 0.001 0.033 -0.049 -0.042

± + + ± ± ± ± +

-PI-1 0.094 0.079 0.052 0.041 0.042 0.040 0.047 0.069

V. Chabaud et al. / A ~ production P00 r PO

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w i t h t' = It - tminl, oo

f C=o NeE= J

d o NPE --~dt

,

d o NPE + , do dt' - p(t)

,

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Table 6 Results of fits to the differential cross section doNPE/dt t for natural parity exchange in the A 2 region 9.8 GeV

18.8 GeV

aNPE[A~ ~ K-K~-+ (n+~r")] for 1.20 ~ m K ~" ~ 1.42 GeV and all t

1.96 ± 0.16 ~tb

1.14 ± 0.05 vb

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364

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0.2

0.3

0.4

0.5

0.6

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The pronounced forward dip accounted for by the factor t' is to be expected for a net helicity-flip-one amplitude. Fits using t '2 instead of t' were also tried, but they yeilded unacceptably low ×2 probabilities.

8. s-dependence of the cross section

Expressing the energy dependence of the production cross section as a power law of the laboratory momentum, o ~ pfZ,,

( 8)

we obtain the following values for n from our restricted cross sections at the two energies: n = 1.02 + 0.17 (from the Breit-Wigner fits A and C, table 4) ; n = 0.89 +- 0.18 (from natural parity exchange, table 6 ) . Fig. 11 shows a compilation of the cross section for A~ production by natural parity exchange in the ~r+rr-rr- and K - K ° decay modes. Fitting the cross sections of the two channels separately (dashed lines) yielded the two values of the exponent n(A~ -~ KK.) = 0.84 -+ 0.10 and n(A~ -+ per) = 0.52 -+ 0.06. Despite the different

V. Chabaud et al. /A~ production

365

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Fig. 11. A compilation of the A~ cross section (o NPE) as a function of Plab for the KK. and p r decay modes: upper points: A~. ~ po~r- from refs. [12,6] ; lower points: A~ ~ K-K ° corrected for all K° decay modes; 3.9 GeV data point from ref. [12] ; 9.8 and 18.8 GeV data points from this experiment (corrected for 1.2 < mK~ < 1.4 GeV and Itl < 0.8 GeV2); 22.4 and 23.9 GeV data points from ref. [ 14]. m o m e n t u m range and the different experimental procedures, a combined fit (solid lines) gives an exponent n = 0.64 + 0.06 with a X2 probability o f 36%. The fit also determines the branching ratio R(A2 --> KI~/A2 -->plr) = (7.75 + 1.7) %. This value is in good agreement with the Particle Data Table world average of (6.7 -+ 0.8) %.

9. Conclusion We have measured the production of the A~ meson in the reaction rr-p K - K ° ( -+ 7r÷lr-) p at 9.8 GeV and 18.8 GeV incident momentum. The A~ is observed, at b o t h energies, above a small background of other states (~10%) and can be well parametrized with a D-wave Breit-Wigner form. The A~ is dominantly produced by natural parity exchange (/91 1 + Pl--1 ~'~ 1). The differential cross section doNPE[dt ' has a dip in the forward direction and is well parametrized b y the form Ct' e Bt-. The factor t' is to be expected for a helicity-flip-one amplitude. The energy dependence of the natural parity-exchange part of the cross section is parametrized by o NPE ~ P~a~. This experiment yields n = 0.89 + 0.18 compared to the value n = 0.51 + 0.05 found by Antipov et al. [6] from a study o f A2 production in the pzr decay mode. However, a common fit to all data, (pTr)- and K-K~ decay modes, gives n = 0.64 + 0.06 with an acceptable P(X 2) --- 36%, and at the same

366

1I. Chabaud et al. / A ~ production

time a branching ratio R(A2 ~ KK,/A2 ~ pTr) = (7.75 + 1.7) %, in good agreement with the Particle Data Table value. Whereas our experiment alone is compatible with an energy dependence of o NPE expected from the exchange of a t9 or f Regge trajectory (n = 1), a fit of all available data yields a cross section dependence on energy (n = 0.64 -+ 0.06) about half way b e t w e e n the weak energy dependence for diffractive-like p r o d u c t i o n and the stronger energy dependence for p or f exchange.

References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15]

G. Grayer et al., Nucl. Phys. B75 (1974) 189. G. Ascoli et al., Phys. Rev. Lett. 25 (1970) 962. T.F. Johnson et al., Nucl. Phys. B24 (1970) 253. G. Grayer et al., Phys. Lett. 34B (1971) 333. K. Foley et al., Phys. Rev. D6 (1972) 747. Y.M. Antipov et al., Nucl. Phys. B63 (1973) 175. U. Kruse et al., Phys. Rev. Lett. 32 (1974) 23. G. Otter et al., Nucl. Phys. B80 (1974) 1. C.M. Ankenbrandt et al., Phys. Rev. D8 (1973) 2785. D.J. CreneU et al., Phys. Lett. 35B (1971) 185. H.A. Gordon et al., Phys. Rev. Lett. 33 (1974) 603. V. Chaloupka et al., Phys. Lett. 44B (1973) 211. M.J. Losty et al., Phys. Lett. 56B (1975) 96. M. Margolies et al., Phys. Rev. D14 (1976) 667. G. Hentschel, thesis, University of Munich, 1976; W. Blum et al., Phys. Lett. 57B (1975) 403; G. Grayer et al., AIP Conf. Proc. 13, p. 117.