The leading proton effect in proton-proton collisions

Nuclear Physics B64 (1973) 493-498 North-Holland Publishing Company

THE LEADING

PROTON

PROTON-PROTON

EFFECT

IN

COLLISIONS

J. G A B A R R O and C P A J A R E S Laboratozre de Physique 77~dortque et Hautes Ener,ews, Orsay. France *

Receded 29 June 1973

Abstract The p spectrum data m the range s = 28 to s = 1995 are described with the triple Regge formula The behavlour of the various couphngs at small Itr is explored. It is found that the non-scahng terms, at s ~ 400 GeV ~- remove the turnover expected ff the triple pomeron vamshes at t = 0 The results are discussed in connection with the expected behavlour of the terms in several models

The triple Regge region is the one where several models can be crucmlly tested, for e x a m p l e , in the multlperipheral absorption m o d e l [3] the triple p o m e r o n coupling does n o t vanish at t = 0. Also in models where the p o m e r o n intercept is lower than one the triple p o m e r o n coupling does not vanish [2, 7] On the c o n t r a r y is the p o m e r o n intercept is one the triple p o m e r o n coupling vanishes [1 ]. O t h e r couplings are also strongly constrained in some models. In particular, in several duality approaches the PPR is required to be zero or small [ 4 - 7 ] . As at is I m p o r t a n t to look at the largest possible energy range to disentangle the various terms and to determine their strength, destroying in this way the correlations b e t w e e n t h e m , we examine in this n o t e the p r o t o n spectrum in p r o t o n - p r o t o n colhsions in the energy range s = 28 to s = 1995 GeV 2 in order to see the present status o f the data in the above mentioned points. We begin with the parametrization o f the residues o f the various couplings This will be done in the most e c o n o m i c a l way. The inclusive cross section in the triple Regge region [8] is given by s d2o

= PPP + PPR + R R P + R R R ,

(1)

dtdM 2 where we neglect the cross terms R P R although there is not any convincing reason to do it at t :¢: 0. At t = 0, this term must vamsh under the same c o n d m o n s as for the PPP term. * Laboratolre assocld au Centre Nanonal de la Recherche Sclentlfique Postal address B~nment 211, Universit~ de Paris-Sud, 91405 ORSAY, France.

J. Gabarro.C Palares.Proton-proton colhstons

494

For the RRP anstead of using the conventional single power of s and M 2 we use an exponential as it has been used in several works previously [9, 10]. This fact is clearly reqmred by the data We take the form R R P . A 1 exp

(A2t + A 3 t 2 ) exp ( A 4 M 2 / s ) .

(2)

In this way we take into account all the daughters of the R trajectory It can be seen as an effectave way to parametraze secondary effects. The PPR and R R R are taken in the conventional way P P R . (~R(0) + 1

C1 RRR

s-

B1

2C~p(t)) ~ - exp

(B2t)

I s ]2c~p(t)

~M2_]

(M2) c~R(0),

(3)

[ s ~ 2c~R(t, exp(C2t) ~-]

(M2)aR(0)"

For PPP we begin with

Dlt PPP

s

('S ]2ap(t) (M 2,}{~p(0} exp(D2t) \M22]

(4)

we have performed two fits to the data of refs. [ 1 2 - 1 4 ] in the triple Regge region an the range M 2 > 4 GeV 2 , s/M 2 > 4 , It[ < 1.05 GeV 2 . In the first fit we take PPR = 0 and the other one we let at vary For the A parameters we take those of ref. [10]. The two fits described correctly all the data included The numerical values of the parameters are in table 1. Therefore the data are compatible with PPR small, even zero. We have allowed the PPP term be non-zero at t = 0 and a good fit is also obtained. However with the values obtained in all these fits we cannot descrabe qualitatively the prelimanary data o f ref. [16] At this energy s = 377 GeV 2, with the values obtained, even if the PPP term vanashes at t = 0 the turnover does not appear at M 2 fixed (5 ~
t-B ( S ~2C~p(t)(M2)C~R(0) S 1 (O~R(0) + 1 -- 2C~p(t)) exp (B2t) \ ~ _ ]

We made a fit to the data of ref. [12 15]. The values found are given In table 1. The fit describes correctly all the data as can be seen in figs 1 - 4 . In fig. 5 we plot the spectrum expected at s = 377 GeV 2.

1 2 3

24.6 24.6 14 96

A1

Table 1

I

dtdM 2

I

6

I

5

7

I

8

I

3)ltl)

28

.171>1tl > . 1 3 o.

• 106 >ltl > .059

}

. .

0 -43.7 1095.0

B]

I

GeV 2

56 5.6 8.58

A4

5 dzO (m b/C~vz) s = 3 7 8 3

2 11 2 11 4.46

A3

9 s/M210

I

0 36.6 32.2

B2

Fig. 1. Comparison of our fit 3 with the data of ref. (12].

0

10

20

30

40

50

60

70

80

90

100

110

5 37 5 37 8.1

A2 264.2 192.1 180 8

C1

0

6.13 5 39 3.06

D2

45 ~ t = - 0 45

, t=-0

0.43 0.496 0 5

a'p

096

33 GeV 2

084 088 092 X=l_N2/s

s = 360

e

08

s:100

•

s=360

o

~ t=-033

s = 100(C~VZ), t = - 0

•

s d2°- ( r n b / G e V 2)

- 2 5 06 -17 4 -10.29

D1 1 04 1 06 1 1

~'R

Fig. 2 Comparison of our fit 3 with the data o f ref [ 15].

2

4

6

8

10

12

14

16

18

10.48 7 56 3 21

C2 0 51 0 52 0 5

aR(0)

-&

r~

496

J. Gabano. C. Palares, proton-proton colhstons

100

~ d~

(mb/GeV2)

lO

s=9295GeV 2

• PT = 07GeV/c 10

% t =-025

S =1995(GeV) 2

E

f

10

o PT=08 t PT=09

CO

¢,~

t =43.35 t =-0.55

•

v

z

~

@

@

GI.

LLI

1

t =-1.05

0.1

0

,

,

,

J

I

,

10

20

30

40

50

60

N2(GeV) 2

Fig 3 Comparison of our fit 3 with the data of ref [ 13]

ld ~ 07

I

08

09

X

Fig 4 Comparison of our fit 3 with the data of ref. [14]

The triple pomeron couplings calculated an our fits are very similar in the range 0.15 < It[ < 0 25, to the triple pomeron coupling extracted from the first finite mass sum rule by saturating the left hand side with resonances [7]. At larger t our couphngs become larger, (particularly the couplings coming from our fit 3). As a matter of fact, we remark that all our fits wdl give a very different behaviour to the Glauber corrections to nd scattering The total nd cross section defect is mainly given by the PPR term [ 11 ], the value of which is very hard to obtain with the present data. Also if the PPP term does not vanish at t = 0, ~t can contribute. Let us finally summarize our main results. The existing data can be well described by the triple Regge formula with a minimum of parameters. At energies around s ~- 400 GeV ~ the non-scaling terms R R R and PPR are not yet negligible. At small t and M 2, they remove the turnover produced by the vamshing of the triple pomeron. Therefore at this energy the turnover could not exist even if the triple pomeron vanishes at t = 0. The existence of a deep turnover, as shown b y the preliminary1 data, indicates the vamshmg of a secondary term A good candidate could be the cross term RPR which, if ap(0) = 1, must vamsh. The strength of the PPP couphng, although with large errors, is compatible with the sum of resonances as with was pointed out in several analyses and in the duality approach [4, 5, 7]. The couplings with the present status of the data must be regarded as having large errors because the correlatmns between the parameters are not completely destroyed with the existing data. The most uncertain coupling is PPR although it must be small and

£ Gabarro, C Palares, Proton-proton colhstons

497

400 s d20- ( m b / G e V 2 ) dtdN2

s =377 GeV 2

300

300 mb/GeV 2 s = 377 GeV 2

200 S

200

Itl= oi

d2lF dtdM 2

lO0

100

I

I

I

I

I

I

10 20 30 40 N 2 50 005 01 Fig 5. Proton spectrum at s = 377 GeV 2. (a) Itl kept fixed, (b) M 2 kept fixed

Itl 015

q m t e neghglble for It1 > 0 2.

We t h a n k Prof. B. Petersson for useful dtscussxons and a crmcal reading o f the manuscript and Prof. J.M. Wang for havmg brought to our notme the existence o f the data o f ref. [16]. One o f us (C P.) thanks the LPTHE for Its kind h o s p l t a h t y and the G I F T for financml support.

N o t e added in p r o o f The data o f ref [161 have been reanalysed and now the turnover is not very sharp. On the o t h e r hand n e w data f r o m Coley et al., at the same energy do n o t show any turnover. This last data can be fitted very well with a PPR intermediate b e t w e e n the one o f our two fits in which the PPP vanish at t = 0. In order to reproduce the turnover o f the new data o f Franzini et al. the vanishing at t = 0 o f another t e r m In addition to the PPP t e r m is still necessary.

References [1] VN. GrlbovandAA. Mlgdal, Sov J. Nucl Phys 8(1969) 583, J.B Bronzan, Phys. Rev D7 (1973) 480, C E DeTar, D.Z Freedman and G Venezlano, Phys Rev D4 (1971)1906, A R. White, 8th Rencontre de Morlond (1973) [2] H P.I. Arbarbanel, G F. Chew, M L Goldberger and L M. Saunders, Phys Rev Letters 26 (1971) 937

498

J Gabarro, C Palares. Proton-proton colhstons

[3] L. Caneshl and A. Schwlmmer, CERN TH 1541 (1972) [4] M.B Elnhorn, M B Green and M.A Virasoro, Phys Letters 37B (1971) 292, M.B. Emhorn, M B Green and M A Virasoro. Phys. Rev D6 (1972)1675: LBL preprmt 768 (1972). [5] H M. Chan, H.I. Mlettmen and R G. Roberts, Nucl Phys. 54B (1973) 411 [6] S H H Tye and G Veneziano, Nuovo Clmento 14A (1973) 711 [7] A. Capella, SLAC PUB 1176 (1973), A. Capella and M,S. Chen, SLAC preprlnt (1973), A Capella, M.S. Chen, M. Kugler and R D Peccl, SLAC PUB 1241 (1973). [8] C E DeTar, C.E Jones, F E Low, J H. Wels, J E Young and C I Tan, Phys..Rev. getters 26 (1971) 675 [9] Ph Sahn and G H. Thomas, Nucl Phys 38B (1972) 375, E D Berger, Ph. Salln and G.H Thomas, Phys. getters 39B (1972) 265, Ph Sahn, 7th Rencontre de Morlond (1972), A. Capella, H Hogaasen and V Rlttenberg, SLAC PUB 1776 (1973) [10] A Capella, H. Hogaase and B Petersson, LPTHE 72/33 (1972) [11] S.A Gurvlts and M S Maranov, Phys Letters 32B (1970) 55, O V. Kanchelll and S G. Matmyan, JETP getters (Soy Phys ) 12 (1970) 50: V V. Amsovlch, P E Volkovltsky and L.D. Dokhno, Phys getters 42B (19721 227, C Qulgg and k g. Wang, Phys getters 43B (1973) 314. k Bertocchl, Proc of the GIFT seminar, Barcelona, 1973 [ 12] J.V. Allaby et al, CERN-ROME Collaboration, Oxford Conf, 1972, J,V Allaby et al, CERN report 70-12 (1970), U Amaldi et al., Phys. getters 34B ~1971) 485 [13] M.G. Abrow et al, Nucl. Phys 54B (1973) 6 [14] M.G Albrow et al, Nucl. Phys. 51B (1973) 388. [15] F. Sannes et al, Phys Rev. Letters 30 (1973) 766 [16] P. Franzmi et al, prehminary results, NAL 1973