- Email: [email protected]
c
Nuclear Physics B54 (1973) 333-354. North-ltolland Publishing Company
ONE
PION PRODUCTION
IN pp COLLISIONS
AT
16.2 GeV/c
Y. G N A T , G. A L E X A N D E R , O. B E N A R Y , S. D A G A N , J. G R U N H A U S , A. L E V Y , Y. O R E N and J. S C H L E S I N G E R * Department o f Physics and Astronomy, Tel-A viv University, Tel-A viv, ISrael Received 20 December 1972 Abstract: A study of pp interactions at an incident momentum of 16.2 GeV/c leading to twoprong non-strange final states was carried out in an exposure of the 2m CERN hydrogen bubble chamber. The c.m. angle and momentum distributions for the outgoing particles in the final states pnrr ÷ and ppn ° are presented and discussed. These final states were analysed in terms of quasi two-body final states - N(NTr), with the pion-nucleon system in an I = t2 or I = 53 state. A determination of these two isospin amplitudes and their interference term is then carried out. The reaction pp ~ pnn + is tound to be well described by a Reggeized exchange model, as well as by a double Regge-exchange model.
1. Introduction in this p a p e r we p r e s e n t results o n a s t u d y o f elastic scattering and o n e - p i o n p r o d u c t i o n in p p i n t e r a c t i o n s at 16.2 G e V / c . T h e events c o m e from ~ 15 0 0 0 pictures t a k e n in the C E R N 2 m b u b b l e c h a m b e r . E x p e r i m e n t a l details of the e x p o s u r e are given elsewhere [ 1 ].
2. E x p e r i m e n t a l p r o c e d u r e a n d cross sections A t o t a l o f 10 0 0 0 n o n - s t r a n g e t w o - p r o n g events were f o u n d in a scan o f the film. T h e events were p r o c e s s e d t h r o u g h the p r o g r a m c h a i n T V G P and S Q U A W . T h e hypotheses pp -+ p p ,
(1)
p p -+ ppTr 0,
(2)
pp ~ pnTr +,
(3)
p p -+ p p M M prr+MM 7r+rr+MM,
(4)
2 prongs * Present address: Faculte des Sciences, UniversitO de l'Etat a Mons, Belgique.
(5)
Y. (;nat et al., pp collisions at 16.2 G e V / c
334
Table 1 S u m m a r y of cross s e c t i o n s Channel
No. o f events
p p ~-- pp pprr
Cross s e c t i o n (rob)
3209
9.36 +~ 0.49
412
1.06 t 0.09
789 ( 4 0 0 ) a)
2.09 t 0.14
0
pnTr ÷ ppMM pn*MM _, 7r+~+MM
3307
2prongs
7717
7.54 +- 1.00
20.1
+ 1.1
a) In the analysis of this c h a n n e l w e use o n l y the 4 0 0 events w i t h cos On+ < 0 w h i c h c o n s t i t u t e s an u n b i a s e d sample. 100
I
i
i
I
i
~ ~l
I
I
50 20 lO
t5 1
o5 - pp ~
]~ ~[ - pp~pnn* -
.2 .1
2 prongs
pIo---,
I
2
,
.~
pprr*
t
I
5
, t*,l
\
10
20
i I i l,l 50
100
p,~b (G.,v/~) Fig. 1, The d e p e n d e n c e of the cross s e c t i o n o n i n c i d e n t lab m o m e n t u m for the p r o c e s s e s : p p ~ 2 prongs, p p ~ ppn °, p p ~ p n n ÷, and p p ~ A++n. D a t a was t a k e n from t h e p r e s e n t w o r k and f r o m the w o r k s listed in refs. [3, 4]. F i t s to the e x p r e s s i o n o ~ Plal~ are s h o w n .
Y. (;nat et al., pp collisions at 16.2 GeV/c
335
Table 2 Values of the exponent n evaluated by fitting the cross sections to the expression a - PI~I~z. Ch'annel
n
pp -- 2 prongs pprr0 -" pnn + A++n
0.38 +-0.04 0.64 + 0.08 1.00 +-0.03 1.87 +-0.05
were attempted for each event. For events giving a satisfactory fit (confidence level of better than 2% for the 4C fits and 4% for the IC fits) to more than one hypothesis, the ionization of the tracks was checked for consistency with that predicted from the kinematic fit. After imposing cuts on the fiducial volume, the m o m e n t u m and angle of the incident beam, and the missing mass, the ambiguities between the 4C and IC fits amounted to ~ 4% and for these events the 4C fit was accepted. The ambiguities between the two 1C hypotheses amounted to ~ 20%. The c.m. angular distributions of the outgoing baryons for events giving a unique fit to a 1C hypothesis show that the baryons are always emitted into opposite hemispheres. Following the procedure previously utilized [2] we have resolved the IC ambiguities by requiring that the c.m. baryon angles (Obl and 0b2 ) satisfy the condition [COS0bl - C O S 0 b 2 1 > 1.8. Values of the cross sections for the reactions examined in the present experiment are given in table 1. The value of the cross section for the elastic channel has been corrected (~ 15%) for small angle losses which are evident from the t-distribution. In fig. 1 we have plotted as a function of incident m o m e n t u m the values of the cross sections determined in the present work together with the values found at nearby energies [3,4]. The dependence of the cross sections on the incident lab m o m e n t u m was adequately fitted to the power law form o ~Plal~~. The values determined for the exponent n, which are listed in table 2 are essentially the same as those found by Hansen et al. [4].
3. Angle and momentum distributions In the analysis of the data we have used for reaction (3), in order to ensure an unbiased sample, only that sample of events (400 events) for which the n + c.m. angle satisfies the condition cos 0% < O. This procedure, which does not distort the data (the symmetry of the initial pp state dictates that all final-state distributions be symmetric about cos 0* = 0), was also followed by Dehne et al. [5] at 10 GeV/c and Ginestet et al. [6] at 8.1 GeV/c. The t-distributions of the outgoing baryons for the various channels are shown in fig. 2. The distribution for the elastic channel (fig. 2a) shows a clear depletion
Y. Gnat et al., pp collisions at 16.2 GeV/e
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Fig. 2. The distributions of momentum transfer between the outgoing baryons and the initial protons (the smaller of the two possible momentum transfers is plotted) for (a) elastic scattering, (b) the final state pwr ° (two entries per event) and for the final state pn~r+, (c) the proton, (d) the neutron. o f events for - t ~< 0.03 ( G e V / e ) 2 w h i c h is due to the loss o f events w i t h small s c a t t e r i n g angle. A fit o f this d i s t r i b u t i o n over the i n t e r v a l 0.5 ~> t ~> 0 . 0 3 5 ( G e V / c ) 2 to the e x p r e s s i o n A e bt yielded for the slope, b -- 8.54 -+ 0.17 ( G e V / c ) 2 and for the optical p o i n t , A = 77 + 5 m b / ( G e V / c ) 2. Using the results o f the fit we c o m p u t e d a 15.4% c o r r e c t i o n to the elastic c h a n n e l . By m e a n s o f the optical t h e o r e m and using the t o t a l cross section value for p p i n t e r a c t i o n s at o u r energy [4], Oto t = 3 9 . 0 + 0.6 rob, we calculate the optical p o i n t , otot/16~h2 -- 78 + 2 m b / ( G e V / c ) 2 w h i c h assuming t h a t c~ = Re f ( 0 ) / I m f ( 0 ) ~ 0 agrees well w i t h the value d e t e r m i n e d from the t-distribution.
337
Y. Gnat et al., pp collisions at 16.2 G e V / c
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338
Y. Gnat et al., pp collisions at 16.2 G e V / c
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339
Y. (;nat et al., pp collisions at 16.2 GeV/c
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340
Y. Gnat et al., pp collisions at 16.2 GeV/c
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4. lsospin analysis A study of the c.m. distributions of the kinematic variables in the final states pp~T0 and pnrr +, in particular the c.m. opening-angle distributions of the pion with each outgoing baryon (see fig. 8), shows that the pion is closely associated with one o f the outgoing baryons. This suggests the possibility of dividing the events into the following quasi-two-body channels: pp -+ p(nrr+),
(6)
pp -+ n(prr + ),
(7)
pp -+ p(wrO).
(8)
1.5
Y. Gnat et al., pp collisions at 16.2 GeV/c 40
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343
Y. Gnat et al., pp collisions at 16.2 G e V / c
U P
N11i=1/2,3/2 Iri'
P
N2
Fig. 9. Feynman t-channel diagram for one pion production. the values of 1.5 -+ 0.2 mb and 0.6 + 0.1 mb for the cross sections of the processes (6) and (7) respectively. This same selection criterion was also applied by B0ggild et al. [7] in their analysis at 19 GeV/c. Using the values of the cross sections for the three reactions (6), (7) and (8) and charge independence, one can determine the I = ~- and I = 23-amplitudes and the interference term. Explicitly, at fixed incident momentum, we have the relations [7] ]A 3 ]2 =4_30 [n(Pn+)],
(A)
I A 1 12 = o [p(p~r0)] + o[p(n~+)] - .~o[n(pTr+)],
(B)
1
Re (A 1A 3) = ~ 2 { 2o [p(pTT0)] -- o [p(nzr+)] -- l o [n(pWv)] }.
(C)
The ]A21] are defined as the mnplitudes integrated over phase space for the final state Nrr system having isospin/. In table 3 we summarize the values obtained for I A 1 12, IA 3 ]2, and Re (A ~A 3) in the present experiment together with the values determined at 7 GeV/c [8] and 19 GeV/c [7]. 11 should be noted that in the analysis of the data at 7 GeV/c the outgoing pion was grouped with that baryon for which the M(N70 is a minimum, a criterion which is approximately equivalent to using the minimum c.m. opening angle. We notice the marked difference m the energy behaviour of the two amplitudes. While ] A 112 exhibits a gradual decrease with incident momentum, the IA 3 12 amplitude drops sharply. The dominance of the 1 = ~ amplitude at the higher energies and its weak energy dependence are characteristic of a diffractive process (pomeron exchange). The IA 312 amplitude which is not compatible with pomeron exchange does exhibit a strong energy dependence. The interference term, Re (A ~A 3 ), which is relatively small does not show any clear dependence on the incident momentum. Table 3 Values of the magnitude of the isospin amplitudes and the interference term determined in this work and those found at 7 GeV/c [8] and 19 GeV/c 171. Incident momentum (GeV/c)
IA 1 12 (rob)
IA 3 12 (mb)
Re ~ ~A 3) (mb)
7.0 16.2 19.0
3.8±0.7 2.4e0.2 2.3±0.3
3.2±0.7 0.8±0.1 0.7±0.1
0.2±0.6 0.3±0.2 0.5±0.4
344
Y. Gnat et al., pp collisions at 16.2 Ge V/c
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345
Y. Gnat et al., pp collisions at 16.2 G e V / c
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346
Y. Gnat et aL, pp collisions at 16.2 GeV/c
The behaviour of the isospin amplitudes as a function of the invariant mass of the baryon-pion system, M(Nn), or tile momentum transfer between tile Nn system and the incident proton can also be obtained froln relations (A)~(C) using the cormsponding differential cross sections instead of tile total cross sections. In fig. 10 tile behaviour of the mnplitudes is displayed, as a function of M(Nrr). The amplitude [A 3 12 is seen to be completely dominated by dx++(1236) production, while the amplitude ]A 112 shows a broad enhancement from threshold up to ~ 1.7 GeV. The interference term is positive near threshold and then fluctuates up to 1.7 GeV between negative and positive values averaging to a small positive value. The behaviour of the mnplitudes as a function of the momentum transfer displayed in fig. 11, shows the ]A 1 [2 amplitude to have a stronger t-dependence than that of the ]A 3 ]2 aanplitude. F o r t values of 0 to ~ 0.3 (GeV/c) 2 the interference term is positive and thereafter becomes essentially zero. Our findings are consistent with the results obtained in a similar isospin analysis carried out at 7 (;eV/c [8]. T6rnqvist [91 has suggested a graphical method for studying, as a function of M(Nrr), the relative importance of two isospin amplitudes which describe three final states related by charge independence. To this end we define three cross section ratios, YI(P, nn+)' Y2 (n, P rr+), and Y3(p, pn0), where Yi = ° i / ( ° l + 02 + 03)" Plotting the Y's for given M(NTr) intervals along axes perpendicular to the sides of an isosceles triangle (sides in the ratio 3:3:2), will result in all the points falling within tile inscribed circle. It can be shown [9] that representing the Y's in this fashion is equivalent to plotting the complex quantity Z z
(A 1 +iA3)(,A 1 --
//13)*
LAI]2 + [A312
'
where tile origin of tire complex plane is at the center of file circle, the real axis is directed to the point where A 3 = 0 (,i.e., Y1 = .~, Y2 -- 0), and the imaginary axis is d i r e c t e d t ° t h e p ° i n t w h e r e A l = A 2 ( i - e . , Y l -3-g ~x/~-,Y2 =3-)8• Distance along the real axis is then the difference between the squares of the amplitudes ( I A I [2 -- [A 312)/(IA 112 + IA312) and the distance along the imaginary axis is proportional to the interference term 2 Re ( A ~ A 3 ) / ( I A 1 b2 + [A 312). On the circumference of the circle the interference between tire mnplitudes is m a x i m u m , i.e., [ cos ~b[ = 1, where q5 is the phase between tile two amplitudes. In fig. 12 we have plotted our data and for comparison the data at 7 GeV/c on the T/3rnqvist plot. We notice the overall similar behaviour of the curves; namely, as one proceeds from low to high M(Nrr) values the curves move in a clockwise direction. For low M(,Nn) values and again for high M(Nrr) values the IA l I mnplitude is dominant. The [A31 mnplitude attains its maximum value at about the mass of the A++(1236). The 7 GeV/c data shows considerable interference at the A ++ mass region (perpendicular distance from the real axis) while the 16 GeV/c data shows no interference at this mass.
Y. Gnat et aL, pp collisions at 16.2 GeV/c
347
G 1/2
)" n
~x% 1.2s
v[.(..°)] Fig. 12. T6rnqvist plot of the present data (solid curve) and the data at 7 GeV/c (dashed curve). See text for explanation of the plot. 5. The pnTr+ final state The general kinematical features of the reaction pp -+ pnn + at our energy suggest that this process proceeds through a peripheral mechanism. As discussed in sect. 3, the outgoing baryons are seen to be strongly collimated along the incident beam direction. We will therefore attempt to describe the features of this final state by means of two different t-channel models. First we discuss a Reggeized pion exchange (RPE) model of Bali et al. [10] in the form used by Kobe et al. [1 1] in the analysis of the pnn + final state at 12 GeV/c, and then we will evaluate a double Regge (DR) model in a form suggested by Berger [ 12] and also applied in the analysis of the 12 GeV/c data [11]. Assuming that the reaction pp -+ pnn + proceeds by a one pion exchange in the lower leg and 7rN -+ ~rN scattering at the upper v e r t e x , then we can describe the
348
Y. Gnat et aL, pp collisions at 16.2 GeV/c
p
tl
P
tl
Sl
n*
I Sl W*
s2 p
t2
(a)
s2
rt
P
t2
(b)
P
js, p
t2
n
(o)
Fig. ]3. One-pion exchange diagrams (a) n ÷ meson exchange, (b) n o meson exchange, (c) double
Regge diagram with n +meson and pomeron exchange. process by the two diagrams shown in figs. 13a and 13b, with rr+ and rr0 exchange, respectively. In the proposed model we use the on-mass-shell nN -+ nN scattering data to describe the upper vertex and a Reggeized form for the exchanged pion. Since the n+p elastic scattering cross section dominates over the charge-exchange reaction and the pn+n coupling constant is a factor of 2 larger than the prr°p coupling constant, we subsequently consider only the rr+ exchange diagram (fig. 13a). The explicit form for the RPE model at fixed incident momentum and with reference to the notation in fig. 13a is
(rr%) •
d4 o
'
2
d l t 2 l d s l d ~ 1 cog2(_ t 2 ) l F ( t 2 ) i 2 211 - cos (rran(t2))] X
( s ~ ]2C%r(t 2) ~ l k ~ ff dZoTr+p(Sl' t l ) kS20 / d~21 '
where [F(t2)l 2 = s2 . s2.
~ ,
.tl . M P2
~~( m r2 - t 1
t2),
Y. Gnat et aL, pp collisions at 16.2 GeV/c
40
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l
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349
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(GeV/c)
n,ln I 0.8 1.0
¢1
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o
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0.2
0.4
0.6
-t,, (G-V/c) 2
0.8
1.0
o o
02
~o
-tp (Gev/c) 2
Fig. 14, The four-momentum transfer distributions of the outgoing baryons in reaction (3) calculated with respect to that initial proton with the smaller momentum transfer. (a) The neutron and (b) the proton for the sample of events satisfying the requirement It21 < 1 (GeV/c) 2. For the sample of events satisfying the requirements It] I, I t2E < 1 (GeV/c) 2 and s I > 4 (GeV) 2, (c) the neutron and (d) the proton. The solid curves are the predictions of the RPE model and the dashed curves are those of the DR model. w h e r e g2 is the pmr + c o u p l i n g c o n s t a n t and the pion trajectory, aTr(t2) = a'~r(t 2 - m 2 ) , w a s taken w i t h slope a'~ = 1 (GeV/c) - 2 . T h e off-mass-shell m o m e n t u m o f the pion,
k~ ff is c a l c u l a t e d in the 7r+p rest frame w i t h the virtual-pion m a s s given b y , m 2 f f = - t 2.
350
Y. G n a t et al., p p collisions at 1 6 . 2 G e V / c
30
,-
I
'
I
12
d
20
~
O
IJ ~
O
i 2
I
-
3
4
3
4
i 2
M ( p . ' ) G..,, Fig. 15. T h e M(prr +) d i s t r i b u t i o n for (a) the s a m p l e of events for w h i c h It21 < I ( G c V / c ) 2, (b) for the s,-unple of e v e n t s w i t h the r e q u i r e m e n t s [ ! l h It21 < 1 ( G e V / c ) 2 and s 1 > 4 (GeV) 2. The curves as e x p l a i n e d in c a p t i o n of fig. 14.
For the on-mass differential cross sections of the rr+p scattering process, we have used the phase shift values of the energy-dependent theoretical CERN fit [131 for s 1 ~< 4 GeV. For higher values o f s 1 we approximate the t I distribution by the expression e 7-7t ~ as suggested by Wolf [ 14]. Besides an overall normalization constant the only free parameter in this model, s20, was set equal Io 0.68 (GeVI 2 as evaluated in the fit of the 12 GeV/c data [ 11 ]. We have calculated the predictions of the RPE model for the various distributions using a Monte-Carlo program. Since in the RPE model we restrict t 2 < 1 (GeV/e) 2 so as not to approach the pole at %~ ~ 2, we also apply the same cul to the data. The t n and tp distributions shown in figs. 14a and 14b respectively, are seen to be well described by tile model. In figs. 15a and 16a are shown respectively, the M{prr +) and M(nrr +) distributions which are also well described by the indicated curves. The A++(1236) peak is reproduced by the model as one might expect since we have used as input the experimental data for the rr+p -+ rr+p vertex. However, the good description obtained for the broad low-mass enhancement in the M(nrc+) distribution is a relevant test of the model. We have determined the Gottfried-Jackson angle distribution in the nrr+ rest frmne (cos 0(;j(nrr+)), the Treiman-Yang angle distribu-
351
Y. Gnat et aL, pp collisions at 16.2 G e V / c 'r
T
r
]
"r
r
'
1----
/ /
30
--
20
-
2 0 [--
>, o O~
(")
t
(")
10
0 2
3
4
5
M (n 'n'*) GeV Fig. 16. The M ( n n +) distribution with the predictions of the RPE model and DR m o d e l shown by the solid and dashed curves respectively. The selection criteria explained in caption of fig. 15 have been applied.
tion * in the p n + rest frame (~bTy(prc+)) and in the n n + rest frame (q~Ty(nTr+)) and these are shown in figs. 17a, 18a and 18b respectively. While a good description of the cos 0 G j ( n n +) and Cyy(pTr+) distributions is given by the model, a poor fit is obtained for the ~bTy(nn+) distribution. However, as shown below, a good description of the q~yy(nn+) distribution is obtained for that sample of events for which M(wr +) > 2 GeV. We next consider the DR model shown in fig. 13c where a p o m e r o n exchange is introduced at the upper vertex b e t w e e n the p and n + meson. Using previously defined n o t a t i o n and that shown in fig. 13c we have for the DR model the expression
dtt2ldsld~l
x/~12[l-cos(tract(t2))]
s~0
\s~0!
eAtl'
• The 0Gj(NI.) and ¢~Fy(N]Tr) angles for the reaction PiP2 ~ N1N2~r are defined with respect to a right-handed coordinate frame in the N 1. rest system. The z-axis is directed along the line of flight of that initial proton (p ] ) which has the smaller four-momentum transfer to the N l~r system. They-axis is the direction given by N 2 X P2"
352
Y. Gnat et al., pp collisions at 16.2 GeV/c 120
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40
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.+)
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i
® 30
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20
d
Z
10
o
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o cos
0c. 1.(n r v+ )
Fig, 17. The Gottfried-Jackson angle calculated in the nn + rest frame; (a) events selected so that I t 2 I < 1 (GeV/c) 2, (b) events selected so that I t lh I t2l < 1 (GeV/c) 2 and s I > 4 (GeV) 2. The solid and dashed curves are explained in caption of fig. 14.
,
where s 1 = s 1
2
l
2
t 2 - Mp - f(m,r
t1
t2). F o r the p o m e r o n t r a j e c t o r y w e u s e
a p = 1 a n d the t w o free p a r a m e t e r s Sl0 a n d s20 are set e q u a l to I ( G e V ) 2 a n d 2 . 2 6 (GeV) 2 respectively. The facto r e At1 with A = 8 (GeV/c) -2 is introduced in order
to describe the t 1 distribution. In the description of the upper leg of the diagram
353
Y. Gnat et al., pp collisions at 16.2 GeV/¢ i
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180
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d~T.y ( n . + ) , ( d e g r e e s )
Fig. 18. T h e T r e i m a n - Y a n g a n g l e c a l c u l a t e d in (a) t h e p n ÷ rest f r a m e a n d (b) t h e n~r ÷ rest f l a m e w i t h t h e s e l e c t i o n I t21 < 1 ( G e V / c ) 2. F o r t h e s a m p l e o f events w i t h t h e r e q u i r e m e n t s [ t I I, I t21 < 1 ( G e V / c ) 2 a n d s I > 4 ( G e V ) 2 , t h e T r e i m a n - Y a n g a n g l e is c a l c u l a t e d in t h e (c) p n ÷ rest f r a m e a n d (d) in t h e n n ÷ rest f r a m e .
by pomeron exchange we restrict the M(n+p) > 2 GeV (to exclude the 7rN resonance region) and also It 11< 1 (GeV/c) 2. At the lower vertex we retain the restriction It21< 1 (GeV/c) 2. We have calculated the predictions of the DR model and have compared them with the sample of data which was subjected to the three cuts outlined above. In order to facilitate a comparison of the RPE and DR models we have also calculated the prediction of the RPE model with the new cuts. We notice that the t n and tp distributions (figs. 14c and 14d) and the M(p~ +) and M(n~ +) distributions (figs. 15b and 16b) are well described by the DR model as well as by the RPE model. Likewise
354
Y. Gnat et al., pp collisions at 16.2 GeV/c
the G o t t f r i e d - J a c k s o n a n d T r e i m a n - Y a n g d i s t r i b u t i o n s in the p~+ and n n + rest frames (figs. 17b, 18c and 18d) are well described b y the m o d e l . Here we n o t e t h a t the qSTy (nzr+) is also well described b y the R P E m o d e l . We w o u l d like to t h a n k N. B a r f o r d , S. G o l d s a c k and M. L o s t y o f I m p e r i a l College, L o n d o n , for m a k i n g t h e film available to us. We a c k n o w l e d g e the help o f P. K a t z and 1. S t u m e r at various stages o f the e x p e r i m e n t . T h e valuable help o f o u r t e c h n i c a l and s c a n n i n g s t a f f is greatly a p p r e c i a t e d .
References [1 ] Y. Gnat, M. Sc. thesis, Tel-Aviv University (1972). [2] G. Alexander et al., Phys. Rev. 173 (1968) 1322. [3] O. Benary et al., NN and ND interactiom,UCRL 20000NN (1970); J. Ginestet et al., Nucl. Phys. B13 (1969) 283. [4 ] J.D. Hansen et al., Compilation of cross sections Proton induced reactions, CERN-HERA 7O-2 (1970). [5 t tt.C. Dehne et al., Nuovo Cimento 53A (1968) 232. [6 ] J. Ginestet et al., Nucl. Phys. B13 (1969) 283. [7] H. Boggild et al., Phys. Letters 30B (1969) 369. [8] G. Yekutieli et al., Nucl. Phys. B38 (1972) 605. [9 ] N.A. T6rnqvist, Phys. Rev. 161 (1967) 1581 ; Commentationes Physico -- Mathematical 41 (1971) 351. [10] N.F. Bali et al,, Phys. Rev. Letters 19 (1967) 614. [ 11 ] P. Kobe et al., Exchange model analysis of the reaction:~ pp ~ pnrr + and pp ~ pprr+rr- at 12 GeV/c, Bonn-Hamburg Mt~nchen Collaboration preprint (1972). [12] E.L. Berger, Phys. Rev. 179 (1969) 1567. [13] A. Donnachie et al., Phys. Letters 26B (1968) 161. [14] G. Wolf, Phys. Rev. 182 (1969) 1538.
ONE
PION PRODUCTION
IN pp COLLISIONS
AT
16.2 GeV/c
Y. G N A T , G. A L E X A N D E R , O. B E N A R Y , S. D A G A N , J. G R U N H A U S , A. L E V Y , Y. O R E N and J. S C H L E S I N G E R * Department o f Physics and Astronomy, Tel-A viv University, Tel-A viv, ISrael Received 20 December 1972 Abstract: A study of pp interactions at an incident momentum of 16.2 GeV/c leading to twoprong non-strange final states was carried out in an exposure of the 2m CERN hydrogen bubble chamber. The c.m. angle and momentum distributions for the outgoing particles in the final states pnrr ÷ and ppn ° are presented and discussed. These final states were analysed in terms of quasi two-body final states - N(NTr), with the pion-nucleon system in an I = t2 or I = 53 state. A determination of these two isospin amplitudes and their interference term is then carried out. The reaction pp ~ pnn + is tound to be well described by a Reggeized exchange model, as well as by a double Regge-exchange model.
1. Introduction in this p a p e r we p r e s e n t results o n a s t u d y o f elastic scattering and o n e - p i o n p r o d u c t i o n in p p i n t e r a c t i o n s at 16.2 G e V / c . T h e events c o m e from ~ 15 0 0 0 pictures t a k e n in the C E R N 2 m b u b b l e c h a m b e r . E x p e r i m e n t a l details of the e x p o s u r e are given elsewhere [ 1 ].
2. E x p e r i m e n t a l p r o c e d u r e a n d cross sections A t o t a l o f 10 0 0 0 n o n - s t r a n g e t w o - p r o n g events were f o u n d in a scan o f the film. T h e events were p r o c e s s e d t h r o u g h the p r o g r a m c h a i n T V G P and S Q U A W . T h e hypotheses pp -+ p p ,
(1)
p p -+ ppTr 0,
(2)
pp ~ pnTr +,
(3)
p p -+ p p M M prr+MM 7r+rr+MM,
(4)
2 prongs * Present address: Faculte des Sciences, UniversitO de l'Etat a Mons, Belgique.
(5)
Y. (;nat et al., pp collisions at 16.2 G e V / c
334
Table 1 S u m m a r y of cross s e c t i o n s Channel
No. o f events
p p ~-- pp pprr
Cross s e c t i o n (rob)
3209
9.36 +~ 0.49
412
1.06 t 0.09
789 ( 4 0 0 ) a)
2.09 t 0.14
0
pnTr ÷ ppMM pn*MM _, 7r+~+MM
3307
2prongs
7717
7.54 +- 1.00
20.1
+ 1.1
a) In the analysis of this c h a n n e l w e use o n l y the 4 0 0 events w i t h cos On+ < 0 w h i c h c o n s t i t u t e s an u n b i a s e d sample. 100
I
i
i
I
i
~ ~l
I
I
50 20 lO
t5 1
o5 - pp ~
]~ ~[ - pp~pnn* -
.2 .1
2 prongs
pIo---,
I
2
,
.~
pprr*
t
I
5
, t*,l
\
10
20
i I i l,l 50
100
p,~b (G.,v/~) Fig. 1, The d e p e n d e n c e of the cross s e c t i o n o n i n c i d e n t lab m o m e n t u m for the p r o c e s s e s : p p ~ 2 prongs, p p ~ ppn °, p p ~ p n n ÷, and p p ~ A++n. D a t a was t a k e n from t h e p r e s e n t w o r k and f r o m the w o r k s listed in refs. [3, 4]. F i t s to the e x p r e s s i o n o ~ Plal~ are s h o w n .
Y. (;nat et al., pp collisions at 16.2 GeV/c
335
Table 2 Values of the exponent n evaluated by fitting the cross sections to the expression a - PI~I~z. Ch'annel
n
pp -- 2 prongs pprr0 -" pnn + A++n
0.38 +-0.04 0.64 + 0.08 1.00 +-0.03 1.87 +-0.05
were attempted for each event. For events giving a satisfactory fit (confidence level of better than 2% for the 4C fits and 4% for the IC fits) to more than one hypothesis, the ionization of the tracks was checked for consistency with that predicted from the kinematic fit. After imposing cuts on the fiducial volume, the m o m e n t u m and angle of the incident beam, and the missing mass, the ambiguities between the 4C and IC fits amounted to ~ 4% and for these events the 4C fit was accepted. The ambiguities between the two 1C hypotheses amounted to ~ 20%. The c.m. angular distributions of the outgoing baryons for events giving a unique fit to a 1C hypothesis show that the baryons are always emitted into opposite hemispheres. Following the procedure previously utilized [2] we have resolved the IC ambiguities by requiring that the c.m. baryon angles (Obl and 0b2 ) satisfy the condition [COS0bl - C O S 0 b 2 1 > 1.8. Values of the cross sections for the reactions examined in the present experiment are given in table 1. The value of the cross section for the elastic channel has been corrected (~ 15%) for small angle losses which are evident from the t-distribution. In fig. 1 we have plotted as a function of incident m o m e n t u m the values of the cross sections determined in the present work together with the values found at nearby energies [3,4]. The dependence of the cross sections on the incident lab m o m e n t u m was adequately fitted to the power law form o ~Plal~~. The values determined for the exponent n, which are listed in table 2 are essentially the same as those found by Hansen et al. [4].
3. Angle and momentum distributions In the analysis of the data we have used for reaction (3), in order to ensure an unbiased sample, only that sample of events (400 events) for which the n + c.m. angle satisfies the condition cos 0% < O. This procedure, which does not distort the data (the symmetry of the initial pp state dictates that all final-state distributions be symmetric about cos 0* = 0), was also followed by Dehne et al. [5] at 10 GeV/c and Ginestet et al. [6] at 8.1 GeV/c. The t-distributions of the outgoing baryons for the various channels are shown in fig. 2. The distribution for the elastic channel (fig. 2a) shows a clear depletion
Y. Gnat et al., pp collisions at 16.2 GeV/e
336 i
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~ .4
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Fig. 2. The distributions of momentum transfer between the outgoing baryons and the initial protons (the smaller of the two possible momentum transfers is plotted) for (a) elastic scattering, (b) the final state pwr ° (two entries per event) and for the final state pn~r+, (c) the proton, (d) the neutron. o f events for - t ~< 0.03 ( G e V / e ) 2 w h i c h is due to the loss o f events w i t h small s c a t t e r i n g angle. A fit o f this d i s t r i b u t i o n over the i n t e r v a l 0.5 ~> t ~> 0 . 0 3 5 ( G e V / c ) 2 to the e x p r e s s i o n A e bt yielded for the slope, b -- 8.54 -+ 0.17 ( G e V / c ) 2 and for the optical p o i n t , A = 77 + 5 m b / ( G e V / c ) 2. Using the results o f the fit we c o m p u t e d a 15.4% c o r r e c t i o n to the elastic c h a n n e l . By m e a n s o f the optical t h e o r e m and using the t o t a l cross section value for p p i n t e r a c t i o n s at o u r energy [4], Oto t = 3 9 . 0 + 0.6 rob, we calculate the optical p o i n t , otot/16~h2 -- 78 + 2 m b / ( G e V / c ) 2 w h i c h assuming t h a t c~ = Re f ( 0 ) / I m f ( 0 ) ~ 0 agrees well w i t h the value d e t e r m i n e d from the t-distribution.
337
Y. Gnat et al., pp collisions at 16.2 G e V / c
400 350 300
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250
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90
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-.1
-.5
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(0no)
.5
Fig. 3. c.m. angular distributions of (a) the protons, (b) the n o meson in the final state ppn °. The t-distribution for the p r o t o n s in the ppn 0 final state was fitted over the interval 0.5 ~> - t ~> 0.05 to the expression A e bt and yielded a slope of b = 4.5 + 0.2 ( G e V / c ) 2. Similar fits to the p r o t o n and neutron distributions for reaction (3) yielded the slope values 5.7 + 0.4 (GeV/c) - 2 and 4.0 -+ 0.4 ( G e V / c ) - 2 respectively. The results of the various fits are indicated in the corresponding figures.
338
Y. Gnat et al., pp collisions at 16.2 G e V / c
4O0 35O
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350
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120
~> 9 o "6 O
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,
I
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Fig. 4. The folded c.m. angular distributions o1"(a) the proton, (b) the neutron, (c) the n* meson in the final state pnn +. The c.m. angular distributions for reaction (2) are shown in fig. 3 and for reaction (3) we show the folded distributions in fig. 4. Peyr,m plots of the outgoing particles in reactions (2) and (3) with the associated projections on the longitudinal and transverse momentum axes are given in figs. 5 and 6, respectively. The baryons are seen to be peripherally produced, while the pion distributions show a concentration of events around PL = 0. The baryon-pion invariant mass distributions for reactions (2) and (3),M(prr°), M(pTr +) and M(nrr +) are respectively shown in figs. 7a, 7b and 7c. A distinct peak is seen in the M(prr ÷) distribution at the mass of the A++(1236). A fit of this distribution to peripheral phase space (the outgoing baryons were weighted
339
Y. (;nat et al., pp collisions at 16.2 GeV/c
3
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Fig. 5. The Peyrou plots for the outgoing particles in the reaction pp ~ ppn °, (a) the protons, (b) the n o meson, and the projections onto the longitudinal and transverse momentum axes. by the f a c t o r e S 7 t p + 4tn) and a Breit-Wigner f u n c t i o n w i t h the v a l u e s M = 1236 MeV and F = 120 MeV yielded a cross section o f 0.32 -+ 0.05 m b for the process pp --* A + + n . T h e M ( p n 0) and M ( n n +) d i s t r i b u t i o n s s h o w b r o a d low-mass e n h a n c e ments.
1.5
340
Y. Gnat et al., pp collisions at 16.2 GeV/c
3
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4. lsospin analysis A study of the c.m. distributions of the kinematic variables in the final states pp~T0 and pnrr +, in particular the c.m. opening-angle distributions of the pion with each outgoing baryon (see fig. 8), shows that the pion is closely associated with one o f the outgoing baryons. This suggests the possibility of dividing the events into the following quasi-two-body channels: pp -+ p(nrr+),
(6)
pp -+ n(prr + ),
(7)
pp -+ p(wrO).
(8)
1.5
Y. Gnat et al., pp collisions at 16.2 GeV/c 40
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343
Y. Gnat et al., pp collisions at 16.2 G e V / c
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Fig. 9. Feynman t-channel diagram for one pion production. the values of 1.5 -+ 0.2 mb and 0.6 + 0.1 mb for the cross sections of the processes (6) and (7) respectively. This same selection criterion was also applied by B0ggild et al. [7] in their analysis at 19 GeV/c. Using the values of the cross sections for the three reactions (6), (7) and (8) and charge independence, one can determine the I = ~- and I = 23-amplitudes and the interference term. Explicitly, at fixed incident momentum, we have the relations [7] ]A 3 ]2 =4_30 [n(Pn+)],
(A)
I A 1 12 = o [p(p~r0)] + o[p(n~+)] - .~o[n(pTr+)],
(B)
1
Re (A 1A 3) = ~ 2 { 2o [p(pTT0)] -- o [p(nzr+)] -- l o [n(pWv)] }.
(C)
The ]A21] are defined as the mnplitudes integrated over phase space for the final state Nrr system having isospin/. In table 3 we summarize the values obtained for I A 1 12, IA 3 ]2, and Re (A ~A 3) in the present experiment together with the values determined at 7 GeV/c [8] and 19 GeV/c [7]. 11 should be noted that in the analysis of the data at 7 GeV/c the outgoing pion was grouped with that baryon for which the M(N70 is a minimum, a criterion which is approximately equivalent to using the minimum c.m. opening angle. We notice the marked difference m the energy behaviour of the two amplitudes. While ] A 112 exhibits a gradual decrease with incident momentum, the IA 3 12 amplitude drops sharply. The dominance of the 1 = ~ amplitude at the higher energies and its weak energy dependence are characteristic of a diffractive process (pomeron exchange). The IA 312 amplitude which is not compatible with pomeron exchange does exhibit a strong energy dependence. The interference term, Re (A ~A 3 ), which is relatively small does not show any clear dependence on the incident momentum. Table 3 Values of the magnitude of the isospin amplitudes and the interference term determined in this work and those found at 7 GeV/c [8] and 19 GeV/c 171. Incident momentum (GeV/c)
IA 1 12 (rob)
IA 3 12 (mb)
Re ~ ~A 3) (mb)
7.0 16.2 19.0
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3.2±0.7 0.8±0.1 0.7±0.1
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344
Y. Gnat et al., pp collisions at 16.2 Ge V/c
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345
Y. Gnat et al., pp collisions at 16.2 G e V / c
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346
Y. Gnat et aL, pp collisions at 16.2 GeV/c
The behaviour of the isospin amplitudes as a function of the invariant mass of the baryon-pion system, M(Nn), or tile momentum transfer between tile Nn system and the incident proton can also be obtained froln relations (A)~(C) using the cormsponding differential cross sections instead of tile total cross sections. In fig. 10 tile behaviour of the mnplitudes is displayed, as a function of M(Nrr). The amplitude [A 3 12 is seen to be completely dominated by dx++(1236) production, while the amplitude ]A 112 shows a broad enhancement from threshold up to ~ 1.7 GeV. The interference term is positive near threshold and then fluctuates up to 1.7 GeV between negative and positive values averaging to a small positive value. The behaviour of the mnplitudes as a function of the momentum transfer displayed in fig. 11, shows the ]A 1 [2 amplitude to have a stronger t-dependence than that of the ]A 3 ]2 aanplitude. F o r t values of 0 to ~ 0.3 (GeV/c) 2 the interference term is positive and thereafter becomes essentially zero. Our findings are consistent with the results obtained in a similar isospin analysis carried out at 7 (;eV/c [8]. T6rnqvist [91 has suggested a graphical method for studying, as a function of M(Nrr), the relative importance of two isospin amplitudes which describe three final states related by charge independence. To this end we define three cross section ratios, YI(P, nn+)' Y2 (n, P rr+), and Y3(p, pn0), where Yi = ° i / ( ° l + 02 + 03)" Plotting the Y's for given M(NTr) intervals along axes perpendicular to the sides of an isosceles triangle (sides in the ratio 3:3:2), will result in all the points falling within tile inscribed circle. It can be shown [9] that representing the Y's in this fashion is equivalent to plotting the complex quantity Z z
(A 1 +iA3)(,A 1 --
//13)*
LAI]2 + [A312
'
where tile origin of tire complex plane is at the center of file circle, the real axis is directed to the point where A 3 = 0 (,i.e., Y1 = .~, Y2 -- 0), and the imaginary axis is d i r e c t e d t ° t h e p ° i n t w h e r e A l = A 2 ( i - e . , Y l -3-g ~x/~-,Y2 =3-)8• Distance along the real axis is then the difference between the squares of the amplitudes ( I A I [2 -- [A 312)/(IA 112 + IA312) and the distance along the imaginary axis is proportional to the interference term 2 Re ( A ~ A 3 ) / ( I A 1 b2 + [A 312). On the circumference of the circle the interference between tire mnplitudes is m a x i m u m , i.e., [ cos ~b[ = 1, where q5 is the phase between tile two amplitudes. In fig. 12 we have plotted our data and for comparison the data at 7 GeV/c on the T/3rnqvist plot. We notice the overall similar behaviour of the curves; namely, as one proceeds from low to high M(Nrr) values the curves move in a clockwise direction. For low M(,Nn) values and again for high M(Nrr) values the IA l I mnplitude is dominant. The [A31 mnplitude attains its maximum value at about the mass of the A++(1236). The 7 GeV/c data shows considerable interference at the A ++ mass region (perpendicular distance from the real axis) while the 16 GeV/c data shows no interference at this mass.
Y. Gnat et aL, pp collisions at 16.2 GeV/c
347
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~x% 1.2s
v[.(..°)] Fig. 12. T6rnqvist plot of the present data (solid curve) and the data at 7 GeV/c (dashed curve). See text for explanation of the plot. 5. The pnTr+ final state The general kinematical features of the reaction pp -+ pnn + at our energy suggest that this process proceeds through a peripheral mechanism. As discussed in sect. 3, the outgoing baryons are seen to be strongly collimated along the incident beam direction. We will therefore attempt to describe the features of this final state by means of two different t-channel models. First we discuss a Reggeized pion exchange (RPE) model of Bali et al. [10] in the form used by Kobe et al. [1 1] in the analysis of the pnn + final state at 12 GeV/c, and then we will evaluate a double Regge (DR) model in a form suggested by Berger [ 12] and also applied in the analysis of the 12 GeV/c data [11]. Assuming that the reaction pp -+ pnn + proceeds by a one pion exchange in the lower leg and 7rN -+ ~rN scattering at the upper v e r t e x , then we can describe the
348
Y. Gnat et aL, pp collisions at 16.2 GeV/c
p
tl
P
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s2 p
t2
(a)
s2
rt
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t2
(b)
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js, p
t2
n
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Regge diagram with n +meson and pomeron exchange. process by the two diagrams shown in figs. 13a and 13b, with rr+ and rr0 exchange, respectively. In the proposed model we use the on-mass-shell nN -+ nN scattering data to describe the upper vertex and a Reggeized form for the exchanged pion. Since the n+p elastic scattering cross section dominates over the charge-exchange reaction and the pn+n coupling constant is a factor of 2 larger than the prr°p coupling constant, we subsequently consider only the rr+ exchange diagram (fig. 13a). The explicit form for the RPE model at fixed incident momentum and with reference to the notation in fig. 13a is
(rr%) •
d4 o
'
2
d l t 2 l d s l d ~ 1 cog2(_ t 2 ) l F ( t 2 ) i 2 211 - cos (rran(t2))] X
( s ~ ]2C%r(t 2) ~ l k ~ ff dZoTr+p(Sl' t l ) kS20 / d~21 '
where [F(t2)l 2 = s2 . s2.
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~~( m r2 - t 1
t2),
Y. Gnat et aL, pp collisions at 16.2 GeV/c
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Fig. 14, The four-momentum transfer distributions of the outgoing baryons in reaction (3) calculated with respect to that initial proton with the smaller momentum transfer. (a) The neutron and (b) the proton for the sample of events satisfying the requirement It21 < 1 (GeV/c) 2. For the sample of events satisfying the requirements It] I, I t2E < 1 (GeV/c) 2 and s I > 4 (GeV) 2, (c) the neutron and (d) the proton. The solid curves are the predictions of the RPE model and the dashed curves are those of the DR model. w h e r e g2 is the pmr + c o u p l i n g c o n s t a n t and the pion trajectory, aTr(t2) = a'~r(t 2 - m 2 ) , w a s taken w i t h slope a'~ = 1 (GeV/c) - 2 . T h e off-mass-shell m o m e n t u m o f the pion,
k~ ff is c a l c u l a t e d in the 7r+p rest frame w i t h the virtual-pion m a s s given b y , m 2 f f = - t 2.
350
Y. G n a t et al., p p collisions at 1 6 . 2 G e V / c
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M ( p . ' ) G..,, Fig. 15. T h e M(prr +) d i s t r i b u t i o n for (a) the s a m p l e of events for w h i c h It21 < I ( G c V / c ) 2, (b) for the s,-unple of e v e n t s w i t h the r e q u i r e m e n t s [ ! l h It21 < 1 ( G e V / c ) 2 and s 1 > 4 (GeV) 2. The curves as e x p l a i n e d in c a p t i o n of fig. 14.
For the on-mass differential cross sections of the rr+p scattering process, we have used the phase shift values of the energy-dependent theoretical CERN fit [131 for s 1 ~< 4 GeV. For higher values o f s 1 we approximate the t I distribution by the expression e 7-7t ~ as suggested by Wolf [ 14]. Besides an overall normalization constant the only free parameter in this model, s20, was set equal Io 0.68 (GeVI 2 as evaluated in the fit of the 12 GeV/c data [ 11 ]. We have calculated the predictions of the RPE model for the various distributions using a Monte-Carlo program. Since in the RPE model we restrict t 2 < 1 (GeV/e) 2 so as not to approach the pole at %~ ~ 2, we also apply the same cul to the data. The t n and tp distributions shown in figs. 14a and 14b respectively, are seen to be well described by tile model. In figs. 15a and 16a are shown respectively, the M{prr +) and M(nrr +) distributions which are also well described by the indicated curves. The A++(1236) peak is reproduced by the model as one might expect since we have used as input the experimental data for the rr+p -+ rr+p vertex. However, the good description obtained for the broad low-mass enhancement in the M(nrc+) distribution is a relevant test of the model. We have determined the Gottfried-Jackson angle distribution in the nrr+ rest frmne (cos 0(;j(nrr+)), the Treiman-Yang angle distribu-
351
Y. Gnat et aL, pp collisions at 16.2 G e V / c 'r
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tion * in the p n + rest frame (~bTy(prc+)) and in the n n + rest frame (q~Ty(nTr+)) and these are shown in figs. 17a, 18a and 18b respectively. While a good description of the cos 0 G j ( n n +) and Cyy(pTr+) distributions is given by the model, a poor fit is obtained for the ~bTy(nn+) distribution. However, as shown below, a good description of the q~yy(nn+) distribution is obtained for that sample of events for which M(wr +) > 2 GeV. We next consider the DR model shown in fig. 13c where a p o m e r o n exchange is introduced at the upper vertex b e t w e e n the p and n + meson. Using previously defined n o t a t i o n and that shown in fig. 13c we have for the DR model the expression
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x/~12[l-cos(tract(t2))]
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eAtl'
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352
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,
where s 1 = s 1
2
l
2
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t1
t2). F o r the p o m e r o n t r a j e c t o r y w e u s e
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to describe the t 1 distribution. In the description of the upper leg of the diagram
353
Y. Gnat et al., pp collisions at 16.2 GeV/¢ i
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Fig. 18. T h e T r e i m a n - Y a n g a n g l e c a l c u l a t e d in (a) t h e p n ÷ rest f r a m e a n d (b) t h e n~r ÷ rest f l a m e w i t h t h e s e l e c t i o n I t21 < 1 ( G e V / c ) 2. F o r t h e s a m p l e o f events w i t h t h e r e q u i r e m e n t s [ t I I, I t21 < 1 ( G e V / c ) 2 a n d s I > 4 ( G e V ) 2 , t h e T r e i m a n - Y a n g a n g l e is c a l c u l a t e d in t h e (c) p n ÷ rest f r a m e a n d (d) in t h e n n ÷ rest f r a m e .
by pomeron exchange we restrict the M(n+p) > 2 GeV (to exclude the 7rN resonance region) and also It 11< 1 (GeV/c) 2. At the lower vertex we retain the restriction It21< 1 (GeV/c) 2. We have calculated the predictions of the DR model and have compared them with the sample of data which was subjected to the three cuts outlined above. In order to facilitate a comparison of the RPE and DR models we have also calculated the prediction of the RPE model with the new cuts. We notice that the t n and tp distributions (figs. 14c and 14d) and the M(p~ +) and M(n~ +) distributions (figs. 15b and 16b) are well described by the DR model as well as by the RPE model. Likewise
354
Y. Gnat et al., pp collisions at 16.2 GeV/c
the G o t t f r i e d - J a c k s o n a n d T r e i m a n - Y a n g d i s t r i b u t i o n s in the p~+ and n n + rest frames (figs. 17b, 18c and 18d) are well described b y the m o d e l . Here we n o t e t h a t the qSTy (nzr+) is also well described b y the R P E m o d e l . We w o u l d like to t h a n k N. B a r f o r d , S. G o l d s a c k and M. L o s t y o f I m p e r i a l College, L o n d o n , for m a k i n g t h e film available to us. We a c k n o w l e d g e the help o f P. K a t z and 1. S t u m e r at various stages o f the e x p e r i m e n t . T h e valuable help o f o u r t e c h n i c a l and s c a n n i n g s t a f f is greatly a p p r e c i a t e d .
References [1 ] Y. Gnat, M. Sc. thesis, Tel-Aviv University (1972). [2] G. Alexander et al., Phys. Rev. 173 (1968) 1322. [3] O. Benary et al., NN and ND interactiom,UCRL 20000NN (1970); J. Ginestet et al., Nucl. Phys. B13 (1969) 283. [4 ] J.D. Hansen et al., Compilation of cross sections Proton induced reactions, CERN-HERA 7O-2 (1970). [5 t tt.C. Dehne et al., Nuovo Cimento 53A (1968) 232. [6 ] J. Ginestet et al., Nucl. Phys. B13 (1969) 283. [7] H. Boggild et al., Phys. Letters 30B (1969) 369. [8] G. Yekutieli et al., Nucl. Phys. B38 (1972) 605. [9 ] N.A. T6rnqvist, Phys. Rev. 161 (1967) 1581 ; Commentationes Physico -- Mathematical 41 (1971) 351. [10] N.F. Bali et al,, Phys. Rev. Letters 19 (1967) 614. [ 11 ] P. Kobe et al., Exchange model analysis of the reaction:~ pp ~ pnrr + and pp ~ pprr+rr- at 12 GeV/c, Bonn-Hamburg Mt~nchen Collaboration preprint (1972). [12] E.L. Berger, Phys. Rev. 179 (1969) 1567. [13] A. Donnachie et al., Phys. Letters 26B (1968) 161. [14] G. Wolf, Phys. Rev. 182 (1969) 1538.