c

Volume 43B, number 5

PHYSICSLETTERS

5 March 1973

A TRIPLE REGGE ANALYSIS OF THE REACTIONS K - p -* A + X A N D K - p ~ 1~0 + X A T 14.3 G e V / c

K. PALER, T.P. SHAH, R.J. MILLER, J.J. PHELAN Rutherford High Energy Laboratory, Chilton, Didcot, Berks., UK

B. CHAURAND, B. DREVILLON, G. LABROSSE, R. LESTIENNE, D. LINGLIN, R.A. SALMERON Laboratoire de Physique Nucl~aire des Hautes Energies, Ecole Polytechnique, Paris, France

and R. BARLOUTAUD, A. BORG, C~ LOUEDEC, F. PIERRE and M. SPIRO D(partement de Physique des Particules Ele'mentaires, CEN Saclay, France Received 22 January 1973 New data from the reactions K - p ~ A + X and K - p ~ ~o + X at 14 GeV/c are presented.From an analysis of the distributions of M ~ within the framework of ~i triple Regge formalism we obtain the effective Regge trajectories corresponding to p, K or K* and nucleon exchange.

The data presented in this letter come from an exposure of the hydrogen fdled CERN 2 m bubble chamber to an r.f. separated beam of 14.3 GeV/c K - mesons. These data correspond to a microbarn equivalent of 10 events//~b. The reactions: K-p~A+X

(12500 events)

(1)

K - p ~ K° + X

(23000 events),

(2)

I(Cl) Kp--,,.A+X AT 1/,.3GeV/c 19.0

9.0

/

-1.0 (b)

were obtained from events which contained at least one observed neutral decay and a charged particle multiplicity from zero to eight. In reaction (1) no attempt has been made to remove A's originating from ~o decays but those coming from ,-o and - - decays have been excluded. The cross sections for reactions (1) and (2) are 2.3 + 0.1 mb and 7.8 -+ 0.4 mb respectively. These cross sections are corrected for decay losses due to the fiducial region and undetected decay modes. In figs. la and lb we show the scatter plots o f x (i.e. the scaled longitudinal C.M. momentum = p~/p*(max)) against the mass squared M2X of the system denote d by X for reactions (1) and (2) respectively. For both reactions because the transverse momentum is limited the regions of target fragmentation (denoted

K~----R*+X AT 1&.3 GeV/c

GeV 2

19.0

9-°t

/./ /

-1.0 " ' -1.0

0.0

1.0

×

Fig. 1. a) A scatter plot of x A versus M ~ for the reaction K - p ~ A + X. With contours for ~T = 0.0 and 1.0 GeV/c. b) A scatter plot of x ~ o versus M ~ for the reaction K - p ~o + X. With contours for PT = 0.0 and 1.0 GeV/c.

437

Volume 43B, number 5

PHYSICS LETTERS

5 March 1973

A÷B "--q"C.X B [A'-'-'~ C)

K-p~A÷X AT 14.3GeVIc

100-

10:

1_

by: p K ~ A and p K ~ Ko) and corresponding tOp x A go ~ - 1 . 0 and projectile fragmentation ( K - ~ A ant] K - p g o ) and x A g o ~ 1.0 are well separated. This separation appears to hold for values o f M 2 less than 10 GeV 2. For reaction (2) there are very few events in the target fragmentation region. This feature is consistent with the dominance of g o production over K ° production and the absence of mechanisms which exchange exotic quantum numbers, in this case a Z*?. The triple Regge formalism [1] (for an inclusive reaction of the type A + B ~ C + X) suggests that we can describe the production of the inclusive system X for S/M 2 and M 2 large (S = total centre of mass energy squared) i.e. Ixl large, by the diagram shown in fig. 3. From this one obtains the expression: d2° ~ ( t ) M 2(~2(0)-2~1(t)) at f i x e d S ,

(3)

2

where a 2 corresponds to the dominant trajectory involved in the a I B ~ a l B reaction. The square of the centre of mass energy for this reaction is M 2 (as indicated on fig. 3). A qualitative agreement with the above expression can readily be seen from the distribu-

o oS events are Ko~o t If we assume that all the observed KsK and the observed A°K~ events are equally AK° and AK° we obtain an approximate upper limit to the number of K° decays. The value obtained is: o(K-p ~ K° + X)/o(K-p -~ go + X) = 0.10. 438

F",,

do.

Fig. 3. The triple Regge diagram for the reaction A + B ~ C + X and the process A B C.

dt

J1 ,

_P

X(x

>0.0)

( b)K-P.~'b 300

30

Z:'

(x>0.O)

A

(x <0.O),~j r,

1.0

10.0 20.0 Mx2 GeV 2

Fig. 2. a) The distribution of M~( for x A < 0.0 and x A > 0.0 (shown dashed) for the reaction K - p ~ A ÷ X. b) The distribution of M~( for X~o <_0.0 and X~o > 0.0 (shown dashed) for the reaction K - p ~ K° + X. tions o f M 2 f o r x < 0.0 a n d x > 0.0 for reactions (1) and (2) which are shown in figs. 2a and 2b respectively. For reaction (1) the growth of do/dM 2 with M 2 for 2.0 <~M2 ~< 10.0 GeV 2 is much larger for the projectile fragmentation region than the target fragmentation region. For a given value of a2(0 ) this feature is consistent with a lower intercept for the trajectory a 1 in the K - p A process than for the p K ~ A process, i.e. qualitatively consistent with nucleon exchange as compared with K or K* exchange. For reaction (2) there are virtually no events in the region corresponding to the p K ~ ~ o process as mentioned earlier. For the K - p g o process the growth of dcr/dM2 is equalitatively consistent with meson exchange for the a 1 trajectory. To obtain quantitative values for the effective trajectory a 1 we have selected regions o f M 2 for various t-intervals such that the unmodified triple Regge for-

Volume 43B, number 5

(o)

PHYSICS LETTERS

5 March 1973

K--LL^

K"P-Lwo

.4," t (eev z ) //~/ -,0 / ( , o.oo.° '

j / /

~z(O ) = 0.5//__.~+

t (GeV z ) -2.0 -1.0 0 0

T

-t~O

pp..---tV'-X

DATA .

~0,.0~.0 / odt)

° C K ' ~ ~

°CNoc . ~' I[.~' I.

RESULTS FROM f .,,~/~f,/

1.0

(b) p K--~-A t {GeV 2 )

ocp) oo.o _]_-~ ~ ~

(£ It)

1.0

Fig. 4. The effective trajectories for the processes: a) K - P go with a2 (0) = 0.5. The results from Chliapnikov et al. are shown as a broken line. b) p K - A with '~2(0) = 0.5.

mula might be relevant (eq. (3)) and that the effects of resonances and phase space limitations are suppressed for all the t-intervals considered. Since we have to use a range of finite values for M 2 (i.e. non asymptotic) the value of a 2 ( 0 ) could depend on the range of M ~ used. Hence we use the same range o f M 2 for each t-interval so that the mean value ofc~2(0 ) will be the same for each range of t. For each t-interval and range of M2x we have fitted the distribution of do/dM 2 to the formula:

(do/dM2)t = K(M2x)b(t) where K and b(t) are the parameters to be fitted. In general the fits have a good confidence level, only one fit has a confidence level less than 1%. F r o m the values of b(t) and assuming a value for a9(0) one can obtain a value for a 1(t). F o r the reactions K - p g o and p K__A we have assumed 0~2(0) = 0.5. This value appears reasonable for the range of M2x used and since the a 1B channel is non-exotic (i.e. t~2(0) being associated with meson exchange). F o r the reaction K - p A the ct1B S-channel is p p and for the range o f M 2 used the total cross section for ~ p behaves like S - 1 ancl since

0.0

0.0

1.0

/ ~(t ) '2.0

Fig. 5. The effective trajectory for the process K - P A with ~x2(0) = 0.0. The effective trajectories from the analyses of p P ~r+ data are shown as broken lines. Otot ~ $2~: (0) a value cx2(0) = 0.0 appears to be appropriate. The values of t~l(t ) obtained using the above values o f t~2(0 ) are shown in figs. 4a, 4b and 5. The values of the trajectory parameters obtained from a straight line fit to these values of t~l(t ) are presented in table 1. Our results can be compared with those from previous analyses and those obtained from the analysis of two-body scattering and a linear fit to the masses of the resonance poles. The comparison with the latter results is facilitated by the straight lines shown on figs. 4 and 5 which correspond to the trajectories: ap = 0.5 + t, OtK, = 0.2 + t, otK = --0.25 + t and aNa = --0.4 + t. The effective trajectory found from our K - p ~ o data is expected to correspond to the p-trajectory. It has a slope consistent with that for ap but the intercept is too low. A similar determination of the p-trajectory was made by Chliapnikov et al. [2] using K + p K ° data. Their result is shown by a broken line on fig. 4a. To obtain their result a value of ot2 = 1.0 was used. When allowance is made for this value ofct 2 our results are consistent with those of Chliapnikov et al. and our intercept is then within 3 S.D. of that for ap. Our analysis of the p K - A data yields an effective trajectory which corresponds to the K or K* trajectory. The intercept is between that for the otK and a K , but the slope is too small. However, in general the values oft~ 1(t) are more consistent with CtK,. A similar result has been obtained by Ganguli and Sadoulet from a modified triple Regge analysis o f ~ p ~ A + X data at 5.7 GeV/c [5]. The effective nucleon trajectory we have obtained 439

Volume 43B, number 5

PHYSICS LETTERS

Table 1 Values of trajectory parameters. Process

K - P ~o

p K- A

K- p A

Assumed value 0.5 of a2 (0)

0.5

0.0

Range of M2v (GeV2 )

4.0 ~ 13.0

3.0 ~ 7.0

2.0 ~ 8.0

al(0)

0.12 -+0.07

-0.17 ±0.16

-0.29 -+0.22

~l'

1.20 ± 0.15

0.38 ± 0.25

0.61 ± 0.25

has an intercept consistent with that for OtNa but the 1 slope is too small by about 1~- S.D. The nucleon trajectory has been previously determined, using a triple Regge analysis, by Ranft et al. [3] and Chen et al. [4]. These analyses used p p 7r+ data and their results are shown as broken lines on fig. 5. Again we note that these analyses used a 2 = 1.0 or 0.8 and even with these large values ofct 2 the intercepts are too small. Our results suggest that the nucleon exchange mechanism is more dominant in our data than in the data used in previous determinations. This increased dominance may be due to the different kinematics and the fact that only 1 = ~1 exchanges are allowed in the K - p A process. Thus in conclusion we have obtained values for the effective/9, strange meson and nucleon trajectories using a triple Regge analysis. Allowing for the

440

5 March 1973

inherent uncertainties in the application o f this type of analysis to this relatively low energy data and the unknown contamination of Z ° events we feel that these trajectory values give encouragement to extend this type of analysis to higher energy data and particularly at several values of energy so that the uncertainties associated with the value of ct2 (0) can be removed. We emphasise the improvement in the triple Regge determination of the effective nucleon trajectory. All these results suggest the significance of a triple Regge approach to the understanding of inclusive reactions in specific kinematic regions. It is a pleasure to acknowledge the many informative discussions with Drs. H. Miettinen, R.G. Roberts and I)~P. Roy.

References [1] C.E. D~Tar et al., Phys. Rev. Lett. 26 (1971) 675; R.D. Peccei and A. Pignotti, Phys. Rev. Lett. 26 (1971) 1076; M.S. Chen, L.L. Wang and T.F. Wong, BNL - 15834 preprint 1971 ; C. Risk, UCRG - 20841 preprint 1971; G. Pancheri-Sdvastrava and Y. Srivastrava et al., Nuovo Cim. 2 (1971) 381; J. Finkelstein and R. Rajaraman, Phys. Lett. 36B (1971) 459. [2] Chliapnikov et al., Phys. Lett. 35B (1971) 581. [3] J. Ranft and G. Ranft, Nucl. Phys. B45 (1972) 237. [4] Chen et al., Phys. Rev. D7 (1972) 1667. [5] S.N. Ganguli and B. Sadoulet, CERN preprint D. Ph. II/PHYS 72-35.