Z. Phys. C - Particles and Fields 38, 449-452 (1988) F 'tkzles and F ts

�9 Springer-Verlag 1988

On the anomalous large transverse energy events observed in proton-lead scattering

K. Sridhar Department of Physics, University of Bombay, Kalina, Santa Cruz, Bombay 400 098, India

Received 16 September 1987

Abstract. It has been shown that a study of correlation between the average rapidity, ( y ) , and transverse energy, Er, can be used to distinguish between different origins of large transverse energy events observed in p - P b scattering in the HELIOS experiment. If the large E r events are to be attributed to a nuclear dependence of structure functions then the hard scattering picture implies a positive correlation among the above two quantities, contrary to that seen in experiment.

1 Introduction

In this note, we discuss the anomalous large transverse energy events (large E T events) observed in p - Pb scattering in the HELIOS experiment [1]. In principle, such an extension of the E r range, beyond the kinematic limit allowed by the kinematics of p - p scattering can be understood either (a) in terms of multi-scattering effects, [2], or (b) in terms of an extension of the nuclear structure functions beyond the nucleon kinematic limit of the Bjorken scaling variable (x=--Q2/2MNV) of unity [3]. (In this definition, Q2 and v are the usual deep-inelastic scattering variables and MN is the mass of the nucleon). In this note, we show that a study of the correlation between the mean value of the rapidity, ( y ) , and Er can, in principle, distinguish between these two sources of large E r events.

Non-trivial nuclear effects have been exhibited by now, in different, high energy experiments. The nuclear dependence of structure functions, the EMC effect, first discovered by the EMC group [4], has been studied ever since, by a large number of dedicated experiments [5]. Another effect is the anomalous nuclear enhance- ment (ANE) of the large-pr jet and large-pr particle production in rcA and pA collisions [6]. Both these effects have generated a lot of theoretical activity and a large number of models have been suggested, [7-9], to explain the EMC effect. ANE has been traditionally

explained in terms of multiscattering effects [10]. However, a nuclear dependence of structure functions has implications for the A-dependence of large-pr jets. Among the models suggested to explain the EMC effect, there exists a class which involve collective effects inside the nucleus [11]. These imply an extension of the structure function in the cumulative region beyond x = 1, which is the kinematic limit for the parton inside a nucleon. Models for EMC effect without such a cumulative region are shown not to be compatible with ANE, whereas in the models which have such a region, at least the experimentally observed trend of ANE can be reproduced by the nuclear dependence of structure functions alone [12]. In principle, a study of the differential distributions of large-pr jet production cross-sections can be used to distinguish between these two sources of ANE in these processes [3].

Such an extension of the nuclear structure functions in the cumulative region also implies an increase in the centre-of-mass energy available for the reaction when nuclear targets are used instead of nucleon targets. The calorimetric studies of the E r distribution in p - Pb collision, with 200 GeV/c proton beam shows precisely such an extension of the E r range [1]. The 200 GeV/c lab energy of the proton beam results in the following centre-of-mass energy of the p-nucleon system

x/~/N = 2x/~NE . ,,~ 20GeV

where MN is the nucleon mass and EB the beam energy. Hence the kinematic limit on the transverse energy is 20 GeV for p - N collisions. However, experimental data extends upto ET ~ 50 GeV.

In the EMC models, where the EMC effect is explained [13] due to the formation of structures Hr with mass rMN, the nucleus contains some very fast partons. If the parton comes from a structure Hr, then it carries a fraction x : O < x < r , of the average momentum of a nucleon. Hence the maximum total

450

transverse energy from a scattering from Hr will be

(ET)~,~ = v / r ' x /~ /N ~ v/-r.20 GeV.

Thus an extension of the Er-range is expected in these models.

The anomalously large ET-tail can also be repro- duced in terms of multi-scattering effects [2]. In these explanations, the final state is constructed out of many hadrons, each possessing a transverse energy typical of soft processes ( ~ 0.4 GeV) and the large ET tail is built up from summing over these many hadrons. Calculations are based on the 'wounded-nucleon' model [14], where one assumes that in hadron-nucleus collisions each of the 'wounded' nucleons in the nucleus gives rise to a string and the strings in turn give rise to hadrons. One essentially builds up the final-state hadron distributions in terms of a compound Poisson distribution which is obtained by convoluting the Poisson distribution in the number of strings created with the Poisson distribution in the number of hadron pairs from the string. With a proper choice of para- meters, such as typical values of inelastic proton- nucleus cross-section etc., the large ET tail can be explained. This choice of input parameters are, however, claimed to be an overestimate [15].

However, there is yet another aspect of the HELIOS data: the correlation between ( y ), the average rapidity and ET, the transverse energy. It is found that ( y ) decreases with increasing ET. If the observation of the extended ET-range is a signature for cumulative effects, then the basic process responsible for the large Er- events is a single hard scattering. We have studied the correlation between ( y ) and ET and we give the details of our calculation and then discuss the results.

2 Calculations in the hard scattering picture

In the hard scattering picture, we have the protons 'a' and 'b' coming from the target and the beam, carrying momentum fractions xl and x2 respectively. The scattered partons fragment into jets. The kinematics reveal that only three variables can be chosen independently and we choose these to be x~, y and XT = 2pT/~SS. The other variables may all be written in terms of these variables and, in particular, we have (in the p - p c.m. frame)

xle-ZV (1)

x 2 - 2xx e- r _ 1

XT

We assume the partons to be massless and, therefore, we need no longer distinguish between pseudorapidity and rapidity. We also use PT and E r interchangeably. The y-range in the lab 0.4 < y < 2.6 when transformed to the p - p c.m. (fl ~ 0.993) gives - 2.4 < y < - 0.2. It is this asymmetric cut about the zero in rapidity that gives a non-zero value for ( y ) .

For a negative rapidity cut, from the kinematics one

would expect a positive correlation between ( y ) and E r contrary to that seen in experiment. For fixed s, an increase in transverse energy would imply a decrease in the longitudinal energy and, therefore, rapidity moves towards zero in the limit that the longitudinal energy approaches zero. For a negative rapidity cut, this would mean that rapidity increases with transverse energy. It is, therefore, clear that the correlation between transverse energy and rapidity seen in experiment, is not simply a kinematic effect.

The basic triple differential cross-section in xl, x2 and f is given by

dat~ a b d~ - ~FA(XOFB(XE)-d{ (ab -~ cd) (2)

dxl dxzd~ a,b

where d~/d~ (ab ~ cd) is the subprocess cross-section and the sum is over all the parton species. It has been shown [16], that d~/df is to a good approximation independent of the subprocess: a factorization is there- fore possible so that one may replace the sum over parton species by a single effective subprocess i.e.

daa dxl d x z d ~ - P A(XOPs(x2)F(;O'no~2 /g 2. (3)

The variables g, f, fi are Mandelstam variables for the subprocess and we have

g= xlx2s; t= -- Xt ~SSpre-r; ~ = -- X2x/FSSpTe '. (4)

The function PA,B(X) is given by

P(x) = q(x) + 9/4g(x) (5)

where q(x) and g(x) are quark and gluon densities respectively, and we have

F(Z) = Z2 + Z + 1 +Z -1 +Z-2 ; Z=~t/~=Xze2Y/x1 (6)

One may rewrite this triple-differential cross-section in terms of x 1, x r and y and integrate over xl

d2a x~s ~ dxl - - e y J .~g-PA(x1)PB(x2)F()(.). (7)

dxrdy s X~o xl

The lower limit of xl integration, Xzo, comes from the upper bound of unity on the Xa-value and we have

Xzo = - e.- 2r . (8) [_XT

The upper limit of x~ integration is r, with r > 1 signalling the cumulative region.

We define ( y ) over the distribution dZa/dydxr as

y2 dZa

!i dyy d ~ X T (9) ( Y ) = y2 d2a

d y - - rl dydxr

where ( y ) is a function of XT.

This gives us using (7) Y2

I dyyer i dx'S(xl,xT, y) (y) =, . . . . (lO)

S2dyeY i dx, S(Xl,XT, y) Yl X l o

where

S(x1, XT, y) = P a(xOP.(xz)F(z)/x~. (11)

Writ ing dS/dx T as S', we have

d(y) - (y) 'R(xr) (12)

dxr where

'i sdyer i dxlS' R(XT ) = yl mo [ (Y)T ' - (Y)T]

75 dyye r i dxx S Yl 2Clo

r where (Y)r' denotes average of y over e y j dxaS'

Xlo

and (Y)r denotes average of y over e y i dxaS we Xlo

choose

PB(x2) = (1 - x2) ~ + 9(1 - x2) p (14)

and fl being the exponents of the quark and gluon distr ibutions respectively. F r o m sum rules we expect that e = 3 and fl = 5. With this choice of P~(x2), we have

S' : - S. {2x1 e - ' ) f(xl , xr, y) (15) t

where

_ u ( x 2 ) ~ f(Xt'XT'Y) (1- -x2~(xle-ZYz2)

1 dF(z) .g2 (16) -g(z) dz

and

u ( x 2 ) = 1 + 9 ( 1 - x 2 ) p - ~ "

A Monte Car lo compu ta t ion of the absolute value of S'/S over the allowed values of x 1, xr and y showed that this quant i ty is positive and, in fact, greater than one. Since S can be seen to be positive f rom its definition, S' is negative. It then means that the sign of R(xr ) is control led by the difference term, ( Y ) r ' - ( Y ) r . We see in (15) that (2xle-Y/x~r) is a decreasing function of y. Also

df (x l ' xr 'y ) - 92c~ x e-2y~A'u(xz) dy (1 - x2) 1 L

451

�9 E 9 (fl - ~)2(1 - x2) p - ~ - 1{ 1 + 9 ( 1 - x y - ~}

L 8~ [1 + 9(1 - x2) p - ' - 1]. u(x2)

+ ~ 1 - - - e -y Z + I - 2Xle-rz Xr \ xr / d

_ _ e - Y

xr F(z)

[ 22 (dF~ 2 ] (17) �9 6zz+2z+2Z-Z-F(z~\dT. j _]"

A computa t ion of this quant i ty showed that for all al lowed values of x 1, x r and y it was always negative indicating that f(xl , y, Xr) is a decreasing function of y. This implies that T ' samples smaller values of y than does T. Thus

( Y ) r , < ( Y ) r (18)

and, therefore, the function R(XT) is negative for all values of xr.

Rewriting (12) as

( y ) = ( y ) o exp R(z)dz (19) XTo

we find that R ( x r ) < 0 implies ( y ) is an increasing function of x r since (Y)o is also negative.

In our computa t ions , we have included the cumulat ive region and neglected the low-x r region. T h e cuts in x r and y were made to reproduce those in the H E L I O S experiment. Our results are not very sensitive to the choice of c~ and ft.

3 C o n c l u s i o n s

The da ta on correlat ion between ( y ) and Er , as seen in the H E L I O S experiment, cannot be explained if the large E r events come from a single hard scattering. Our analysis is model - independent and we do not invoke any part icular model of nuclear structure functions. I t remains to be seen, therefore, whether mult i-scat tering effects can reproduce the observed correlation�9

Acknowledgements. The author wishes to acknowledge the invaluable help received from Sourendu Gupta and R.M. Godbole. The author also wishes to acknowledge a Research Fellowship from the University Grants Commission, India.

R e f e r e n c e s

1. T. Akesson: Proc. of Int, Europhysics Conf. on High Energy Physics, Bari, Italy (1985) p. 633, L. Nitti, G. Preparata (eds.)

2. N. Pisutova et al.: Phys. Lett. 172B (1986) 451 3. S. Gupta, R.M. Godbole: Phys. Rev. D33 (1986) 3453 4. J.J. Aubert et al.: Phys. Lett. 123B (1983) 275 5. E.L. Berger: Proc. of XXIII Int. Conf. on High Energy Physics,

Berkeley (1986), Vol. 2, p, 1433 6. C. Bromberg et al.: Phys. Rev. Lett. 42 (1979) 1202; D.

Antreasyan et al.: Phys. Rev. D19 (1979) 764

452

7. C.E. Carlson, T.J. Havens: Phys. Rev. Lett. 51 (1983) 261

8. J.D. de Deus et al.: Z. Phys. C--Particles and Fields 26 (1984) 109

9. S. Gupta, K.V.L. Sarma: Z, Phys. C--Particles and Fields 29 (1985) 329

10. J. Hufner et al.: Phys. Lett. 166B (1986) 31 1 I. See, for example, models in [7, 9]

12. S. Gupta, R.M. Godbole: Z. Phys. C--Particles and Fields 31 (1986) 475; R.M. Godbole: Proc. of the Int. Conference on High Energy Physics, Bari, Italy, 1985, p. 628, L. Nitti, G. Preparata (eds.)

13. See [9] 14. A. Bialas et al.: Phys. Rev. D25 (1982) 2328 15. J.V. Noble: CERN Preprint TH 4513/86 16. B. Combridge, C. Maxwell: Nucl. Phys. B239 (1984) 429