IL NUOV0 CIMENTO VOL. 21 A, N. 2 21 Maggie 1974

Correlations between a Forward Proton and Central Pion

in pp Collisions at ISI~.

]~. g. SQUll~ES and D. M. WE]3]3E]~

University of Durham, Mathematics Department - Durham

(ricevuto il 26 Novembre 1973)

Summary. - - We show that the apparent long-range correlation between a forward diffractively produced proton and a central pion observed in pp collisions at high energies is kinematical in origin and that a very simple model fits the data.

l~ecent da ta f rom the CHLM group (1) on pp sca t te r ing shows evidence for long-range correlation. I n par t icular the forward ( t r iple-pomeron?) dif- f ract ive p ro ton peak in the inclusive cross-section is missing when a charged

part ic le is observed in the centra l region (see Fig. 1). In this no te we show ~hat the appa ren t long-range correlat ion is k inemat ica l in origin and tha~ the lower curves of Fig. 1 can be obta ined f rom the upper one using a ve ry simple model with no free parameters .

The model can be unders tood b y reference to Fig. 2. Since we are observ- ing the p ro ton in i ts f ragmen¢at ion region we can couple it to a sum of leading l~egge poles (including the pomeron) and t he r eby write for the cross-section for producing a p ro t on of r ap id i ty y, and a pion of r ap id i ty y, (see Fig. 2 a))

(1)

(1) M.G. ALBROW, A. BAGCHUS, D. :P. BARKER, A. BOGAERTS, B. BO~NJAKOVI(~, J. R. BROOKS, A. B. CLEGG, F. C. ERN~, C. N. P. GEE, D. It. LOCKE, F. K. LOEBINGER, 13. G. MURPHY, A. RUDGE and J. C. SENS (CERN-HOLLAND-LANCASTElC-MANCRESTER COLLARORATION): Phys. Lett., 44 B, 207 (1973).

413

414

10

10 o

10-

]~. J . S Q U I R E S a n d D . M . W E B B E R

150 100 50 0 I I I - - • I~

• • wO • • 4 O 0 e

+

{ ! 1.00 0:85 0:9o o95 x

Fig. 1. - Inclusive cross-sections (1) for proton-proton interactions at s = 929.5 (GeV)% The top set of points are the data for the inclusive spectrum pp--> p + X . The crosses represent the spectrum when a charged particle is observed near 117.5 ° (upper graph) or near 90 ° (lower graph) in the centre of mass. The open symbols represent our pre. dictions based on data (2) for the following processes: o p~>7:-, n ~+ ~>~- , ~ p ~ > ~ - , v p ~ > = - . The curves represent the extrapolation from the p ! > ~ - point at MS= 55 (GeV) 2 as described in the text.

where ~ a refers to t he s c a t t e r i n g of a p r o t o n a n d a reggeon, M 2 is t he square

of t he muss of the p R sys t em (which is u f u n c t i o n of yp) a n d y: is the r a p i d i t y

of the charged pa r t i c l e i n t he p R cen t re -o f -mass s y s t e m :

(2) y o = y'o + y ,

(3) W. D. SHEPHARD, Z. T. POWERS, N. N. BISWAS, N. M. CASON, V. P. KENNEY and D. W. THOMAS: Phys. Rev. Lett., 28, 703 (1972); S. STONE, T. FERBEL, P. SLAT- TER~ and B. WEaNeR: Phys. Bey. D, 5, 1621 (1972); W. H. SIMS, J. HANLON, E. 0. SALANT, R. S. PANVlNI, R. R. KI~S~Y, T. W. MOl~I~IS and L. VoN LINDERN : .3['~el. Phys., 41B, 317 (1972).

CORRELATIONS BETWEEN A FORWARD PROTON AND CENTRAL PION ETC. ~ 1 ~

where y is the rap id i ty of the pl~ system. The quan t i ty G is a p roduc t of reg- geon coupling cons tan t and propaga tor .

For x of the p ro t on ~ 0.9 the main cont r ibu t ion to (1) will come f rom the pomeron , whereas for x ~< 0.9 we expect o ther Regge poles to dominate . Thus,

in the region of in teres t , the re are several t e rms con t r ibu t ing to the sum in (1). However we assume tha t , provided there is no leading-particle e//eet, the charged-

a)

R p,~" fp ',p

Fig. 2. - Diagramatie representation of the model used.

part icle r ap id i ty d is t r ibut ion (1/a~)(d~R/dYo) is independent of It . I n par t ic- u lar it is the same when R is a reggeon or a pomeron . This is con t r a ry to wha t was assumed in early versions of the nova model , etc., bu t appears to be suppor ted b y recen t evidence on mul t ip l ic i ty dis t r ibut ions (3). Wi th this assumpt ion we can replace the last fac tor of (1) b y the inclusive charged-par t ic le p robab i l i ty for any exper imenta l ly measured process a t the same energy and y. (see Fig. 2 b)). Then given d%D/dy ~ (the uppe r curve of Fig. 1) we can predic t da~,/dydy¢. To obta in the lower curves of Fig. 1 we need to t r ans la t e the

charged-par t ic le angle in to yo. We do this using

(3) P± ' ( -- log tg (0/2)) ~ sinh ( - - log tg (0/2)) sinh y~ ----- imp_i_ p~_)~ slnh

Here we assume t h a t the charged par t ic les produced are pions so t h a t we can ignore m e. The error th is makes is negligible. Thus the angular range (90 ~= 14) ° corresponds to y¢ between - - 0.25 and + 0.25 and the angular range (117.5 =[= 12.5) ° to yo between -- 0.75 and - - 0.25. We obtain the values of (1/(~)(d(~/dyo) f rom the processes l isted in the capt ion to Fig. 1. We only include processes where the charge of the observed part icle is different to t h a t of the incident par t ic le so t h a t leading-part ic le effects are removed.

Unfo r tuna t e ly we do not have suitable inclusive da ta for the lower region

(a) J. WK~TMORE: Di/]raction dissoe/iatio~ in pp interaction at NAL, NAL preprin~ NAL-Conf-73/68-EXP.

416 r,. j. SQUIRES and 1). ~. WEBBER

of x. However if we assume, in the central region of phase space, t h a t / ( m , y'o, p.°)

depends only on y'o and p±o then we can extrapolate our prediction. The results

of this are shown in Fig. 1. We see from Fig. 1 tha t the agreement is satisfactory. I n part icular there is

no indication tha t pomeron exchange is in any way different f rom reggeon

exchange, and the peak for x ~ 1 is completely removed by our model, in

agreement with the data. I n fact our model predicts a somewhat faster fall-

off near x ---- 1 t han is observed experimentally. This might be due to the energy

resolution of the experiments. Final ly we note tha t L~ BELLAC, MIETTIiNEYN and ROBERTS (4) have carried

out a somewhat similar calculation, in tegrated over the region x > 0.9, and

also obtained agreement with data. KASMAN (5) has also considered this type

of correlation in terms of various models of diffractive scattering.

(4) M. LE BELLAC, It. I. ~IETTINEN and R. G. ROBERTS: Strttcture o/two-body correla- tions in high-energy hadron production, Rutherford Laboratory preprint (1973). (5) J. KASMAN: Correlation between the leading proton and pious in high-energy proton- proton collisions, Westfield College preprint (1973).

• RIASSUNTO (*)

Si mostra l'origine einematiea della eorrelazione a lungo raggio the si evidenzia fra un protone prodotto per diffusione in avanti e un pione centrale, osservata in urti pp ed alte energie. Si mostra anche che un modello molto sempliee approssima i dati.

(*) Traduzione a cura della Redazione.

P e 3 i o M e H e HO.rlytteHO.

b y Socie ta I t a l i a n a di F i s ica

P r o p r i e t h l e t t e r a r i a r i s e r v a t a

D i r e t t o r e r e sponsab i l e : C A R L O C A S T A G N O L I

S t a m p a t o in B o l o g n a da l l a T ipogra l i a Compos i to r i coi t i p i del la T ipogra f i a M o n o g r a f

Ques to fascieolo ~ s t a t o l icenzia to da i t o r e h i 1' 8-V-1974