High ET production in QCD

Nuclear Physics B250 (1985) 450-464 © North-Holland Publishing Company

H I G H E r P R O D U C T I O N IN Q C D M. GRECO INFN, Laboratori Nazionali di Frascati, Frascati, Italy

Received 30 September 1983 (Revised 10 June 1984) The production of large transverse energy is discussed as the effect of multigluon emission produced in the hard scattering of the hadron constituents. Analytical formulae are given, based on resumming techniques to all orders in a~, and successfully compared with recent experiments at SPS, ISR and p~ collider energies.

I. Introduction

Hadron production of high transverse energy-momentum ( E T - - p r ) is normally believed to result from hard scattering among hadron constituents and to provide a direct test of the short-distance behaviour of strong interactions. A characteristic jet structure is then expected to dominate the final states. Motivated by these ideas hadron collisions at very high energies have recently been investigated by various experiments [1-5] with large geometrical acceptance. The abundant production of events with large values of transverse energy, first reported by the NA5 group [1] at the C E R N SPS, has been confirmed at Fermilab [2] and ISR [3] energieg, and even more copiously observed [4, 5] at the C E R N p~ collider. However, the measured cross sections, which change strongly with energy, are much larger than excepted [6] from Q C D four-jet production. In addition, up to reasonably large Ev, the event structure does not indicate a sensible contribution from high-pv jets originated in a hard scattering of the constituents. Only very recently calorimeter-triggered experiments at the C E R N ISR [7] and p~ collider [5, 8] have finally observed an important contribution from jet production at very large transverse energy. The question arises therefore as to whether there exist two physically distinct mechanisms operating in a hadron-hadron collision at large El-, appearing with a different configuration of the final states as well as with quite different cross sections. While there is little doubt that the jetty events, which are seen at higher Ex, reflect a hard scattering of the constituents and can henceforth compared with the predictions of perturbative QCD, the origin of the softer component has not been definitely clarified yet and various interpretations have been given so far. We only mention here models [9, 10] with sizeable effects of fragmentation into hadrons of the constituents participating into the hard scattering and of the spectator partons, soft 450

M. Greco / High E r production in QCD

451

models [I I] without hard scattering which generate events isotropically and gluon bremsstrahlung from the constituents [12]. In particular in a recent letter [12] we have suggested that a mechanism similar to the one responsible for the transverse momentum properties [13] of DrelI-Yan pairs and weak bosons produced in hadron collisions is also operating here. The idea is quite simple. In any hard scattering process among the constituents a fraction of the initial parton subenergy is released in the form of soft QCD radiation, whose spectrum can be calculated to all orders in a~. Furthermore, the corresponding spectrum factorizes and, to leading order, is independent of the particular hard scattering process. Of course the very tail of the spectrum is modified by the detailed dynamics of a particular hard scattering process which takes over at appropriate large E-r, similarly to what happens in lepton pair production when p ~ - - O ( M ) . In spite of the nai'vety of the model used to illustrate these i d e a s - t o simplify the calculation only quark-quark interactions were considered, with energy scaling cross sections - the results reproduced the qualitative behaviour of the data. In the present paper we investigate further this scheme, providing a quantitative study of the idea of a unique d y n a m i c s - the hard scattering of the hadron constituents accompanied by emission of QCD r a d i a t i o n - o p e r a t i n g in high-energy hadron collisions at large E-r [14, 15] (a gist of some of the results has been presented in [14]). We address in particular various questions of both theoretical and experimental interest: the role played by gluons as a source of radiation and the corresponding observable implications in comparison with quark-initiated processes, the dependence on the beam type (~, p, ~), the effect of scaling violations, the relative role played by the hard and the soft component, the dependence on experimental kinematical acceptance (Ay-, zl~h-cuts), and so on. A remarkable feature of our results lies in the fact that they are all analytic. Based on certain improved leading logarithmic approximations, which have been carefully studied and phenomenologically tested [16] in electroweak pairs production and e" e- annihilation, they can be taken with comfortable confidence not only for direct comparison with data, but also for testing various Monte carlo models, inspired by QCD but usually including ad hoc assumptions which are of common use for data analysis. The paper is organized as follows. In sect. 2 we report the basic formulae for hard jet production, in sect. 3 we discuss the soft gluon contributions and finally in sect. 4 we discuss our results and give our final conclusions. 2. The hard jet yield We start with the well-known formula [17] for the invariant jet cross section for hadron-hadron collisions at c.m. energy squared S: do"

II

d°"Jkt

M. Greco / High Er production in QCD

452

in terms of the parton subprocesses p; + p) --' pk + p,, where s=x,x2S, t and u are the usual M a n d e l s t a m variableg, and the indices i, j, k, ! refer to q, (I and g. The variable q2 a p p e a r i n g in the structure functions F,(x, q2) represents some characteristic scale of order p~-, when scaling violations are incorporated in the calculation. The expressions for d~r/dt have been reported m a n y times earlier [17] and are summarized below for the reader's convenience:

do" rra~(q2) ]A(s, t, u)[ 2 d-~-=

"

s2

,

(2)

with [A[2 indicated below for the various Q C D subprocesses: q;qj -* q,cb, q,qj ~ q,~b

(i#j),

[Al2=~(s2+u2)/,

4[s'+u

(3a)

2,

s'+t"~

8 s2 27 ut"

(3b)

qiqi~q~qi,

[A["=~+--~}

qiq'~q'q"

4[$2+u 2 /2+ u2"~ 8 u 2 [m[2. - 9 ~.7 + - - .- ~ ) . 27 st'

(3c)

q~ch~gg'

IAI2=2-7\~--t

(3d)

gg--, q,q,,

IAI~-= g \ - ~ - / j

q,g--'qig,

[A[2=

9\

gg-~gg,

[A[ 2=

3

] -3\--~-

I"

- ~ \---~],

us / + \ "s2

t2

(3e)

u ' + ,s-~

t2 ] '

(3f)

.

(3g)

As is well known, and from direct inspection ofeqs. (3), the d o m i n a n t contributions to the various cross sections come from terms - ! / t 2, 1/u 2, reflecting the exchange of vector gluons. Furthermore, the colour factors present in the different IAI 2 clearly favour gluon-initiated subprocesses, as already emphasized in the literature [17]. These two observations will be of importance also for the soft gluon effects which are discussed in the next section. From eqs. (1) and (2) one obtains

do'h"'o - ,k a2" 2 ~ f f dx, dx2 F,(x,, q2)F,(x~, q2)x/l 2pr rr-~-[Al.,k,, dEv t " -4p~/s s 2

(4)

where E T = 2pr is the transverse energy corresponding to a 2-jet final state with transverse m o m e n t u m Pl.

M. Greco / High Er production in QCD

453

It is useful to introduce a scaled c.m. parton subenergy squared p = - s / S = x~x2, so that the hard contribution to the transverse energy distribution finally becomes do- hard

dE.,

S 2 ,-,~ __

dX,x, F,(x,, q )F~ ~ , q2 41 - E]-/Sp

IA(p, ET)]7,k,. (5)

This expression can be used with some confidence only for sufficiently large ET tO describe the tail of the distributions experimentally observed. In fact soft terms neglected in this lowest-order calculation dominate and completely modify the Er behaviour at medium E-r values. Even at large ET higher-order corrections of O(a~) might be of importance, as indicated by preliminary estimates [18]. For the present purpose eq. (5) is sufficient to give us a resonable estimate of the role played by the hard component relative to the soft one, because of the lack of a precise knowledge of the gluon structure functions leading to a theoretical uncertainty of order of a factor of two.

3. The soft gluon yield The relevant role played by the QCD phenomena of multiple gluon emission in hard processes, and particularly for dilepton production in hadron collisions, is recognized now by many authors [16]. The high degree of sophistication reached by resumming the perturbation theory to all orders in a~ in certain improved double leading approximations has matched the impressive accuracy of the experimental data, leading to a quite detailed undestanding of the Drell-Yan processes and weak boson production [19]. In particular, from the successful analysis of the PT eftects one naturally expects some peculiar features in the Pr, ET, (n)-distributions of the hadron produced in association to the lepton pairs and weak bosons as well [20]. In the absence of a correspondingly detailed observation of such hadronic properties (see [21] for a review of existing data) it is natural to look for similar effects in other hadronic processes. Then a qualitative study of multigluon emission effects in purely hadronic hard collisions was carried out in ref. [12]. Here we give a more quantitative analysis of this phenomenon. We start with the soft transverse momentum KT distribution of the QCD radiation emitted by the initial legs, when there is no detection of the final jets resulting from the hard collision (minimum bias events): dP I dcrh(Q) d 2 K r - ~ d2KT

~ f], ~=o n.j=

=--1 2rr

d2k3j.(k,j)6,2,

~ k.r_K T \i-i

b dbJo(bKr) exp [A(b, O)]

(6)

M. Greco / High Et production in QCD

454

with

C A(b, Q)= ,-v J dq~rj'~(qv)Jo(bq~) -

2(c, + c2) fO.,2 d q l -In

rc

ao

ql

.Q--Q-.a(qT)[Jo(bq,)\ qr/

1].

(7)

In eqs. (6)-(7), o-h is the Born cross section for the hard process p ~ + p 2 ~ h , obtained from eqs. (2)-(3), and c~ and c~ are the appropriate colour factors for quarks and gluons, i.e. cq =- cF-= 4 and c,-= cA -= 3. The upper bound of the transverse momentum phase space of the emitted radiation has been put to ~Q. Equation (6) is based on the factorization property of soft emission in gauge theories [24] (although this paper strictly deals with the 2-3 jet cross section, the remarkable simplicity of the result is very suggestive of a generalization to higher orders) and on the resummation techniques of the perturbation series in the improved double leading logarithmic approximation [16]. Then Q2 is a large scale (,4 2~ k 2 ~ Q2), which depends on the kinematical variables of the process. The choice of the scale Q is generally not unique. To leading order a particular choice will only affect the finite terms of order a~, which have to be added perturbatively to the resummation of the leading logarithmic terms of eq. (6). This is explicitly shown in ref. [25] in the process of electroweak pair inclusive production. It is however clear that in case of integration over the final state h, which is the case discussed below, see eq. (13), a large scale at disposal which is much larger than k-r, can only be of order of the initial parton-parton subenergy*. A similar procedure also holds in QED, for the soft radiative correction to any scattering process, e.g. e ' e - , ~ ' t z - , . . . , where Q - c . m . energy at disposal for radiation. In particular one can easily verify there that a minimal finite m o m e n t u m transfer Itlmm, which defines a given scattering process, does not fix the scale of the logarithmic terms arising from the soft photon radiation. Similarly the soft Er spectrum, where Er is the total transverse enegy of the Q C D radiation emitted by the initial legs, is given [20] by dP d E1

1 d~rh(Q) ~-~

h

0%

- - -

d E-I

Y 25 II

n ~ O /'1 • / = l

d2kTjf~(kTj)6 =

k~-Er

1

=-f--~If~idxe-"~rlexp{f d2ql.f(qT)[e"~,-,]} 1 77"

' f x, }

dxh(x, Q)

(8a)

" We have explicitly checked that a factor of two change of this scale does not affect appreciably our final results.

M. Greco / High E, production in QCD

455

with

h(x,

XET

Q) = cos

--

dqv In

~"

×exp

--

ao

a(qv) sin

(qTx)

qT

(8b)

I

do qT \ qT/ It could be of interest, in some particular processes, to look at the distribution of transverse energy associated with the production of a transverse momentum K~. This is the case, for example, in the study of the hadronic system accompanying Drell-Yan pairs on weak bosons. Then, the cross section weighted by gluonic transverse energy is [20] 1 dZh(Q) o-h d 2 K T

d2k,if~(k,j)

Y~ n.1 .=1 i"'

1

k r~ 6 '2' •

k-r,-K, ,-I

bdbJo(bK,)exp[,,:l(b,O)]xg(b,O )

27r

(9)

where

g(b,Q)

2(c,+c2) f°/2 "n"

dqTIn ( --Q)

Jo

a(qT)J,,(bq,).

(10)

\ qT]

From eqs. (6) and (9) the average transverse energy / ~ T ( K r ) iS then calculated as a function of the transverse momentum K r as

(,

/~T(KT) = gO d2 K v ] / \

o-,, d2K,i "

( 1l )

It is worth of noting that the distributions (8) and (9), the latter expressed in terms of Er, become very similar if the transverse energies are not too small. So far we have considered just the energy-momentum properties of the parronic system. To obtain the final distributions in hadron collisions, one has to take into account the parton densities, as in eqs. (4, 5), namely d°'~°'"

dEr -

~

IJ

v.h

d~h

dx, dx2 ~(x,, q2)Fj(x2, q2) "~(x,x2S)

~, fp' dp ft 'dx' --F~(x., q 2)Fj ( P q-~\dO''''"] Ot:T iL h

mm

~

Xl

and similarly for do'/d2Kr and d~,/d2KT. A few comments are in order here. First, one could be interested is studying the properties of the hadronic system produced in association to a particular hard final state, namely for fixed h. This is the case, for example, in studying the reaction H I "4- H 2 ~ JI 4- J2 4- X, where J~ and J2 a r e two hard jets. Then the energy-momentum properties of the accompanying hadrons will give us informations on the QCD dynamics in the initial patton system. The different colour structure of quarks and

456

M. Greco/ HighEr productionin QCD

gluons will affect the properties of the emitted radiation, as it explicitly appears in eqs. (7), (8), (10), through the CF, CA factors. A measurement* therefore of the KT (or E-r) distribution of such a hadronic system produced in pp collisions at the collider energies, where the gluon contribution is overwhelming, as discussed in the next section, would be of particular interest, as compared for example to the analogous distributions for Drell-Yan pairs, which is dominated by quark-antiquark annihilation. On the other hand, let us consider the case where one does not single out a particular hard final state, as for the so-called minimum bias events. Then one has to sum over h and integrate over the final parton momenta. The radiation from the final legs is automatically taken into account, because the process of dressing the final partons corresponds to a unit probability. This can be explicitly seen from the distributions (6)-(9), which are indeed normalized to one. Of course a measured value of E l differs from the radiative E~ of eq. (8), by an amount (Ertin), which can be directly estimated from the final partonic state, as discussed explicitly below. Then, for fixed i and j, the initial parton states, integration over the final states gives, using eqs. (2), (3), (8), do -'j~h 7ra~ dP

E.

!tm,n--iC';dE,'

(13)

where the factors cii are obtained from eqs. (3) and Itmin]--=-P?rmi, is the minimum value of the transfer momentum in the subprocesses p ~ + p ) ~ h . Eq. (13) is a consequence of the factorization property of the soft spectrum, as indicated explicitly in eq. (8). Therefore the quantity (P-rmi,,)-2 fixes the scale of the soft component to dcr/dEr. From our understanding of deep inelastic phenomena one would expect that a value (PTmin) -2 -- l GeV 2 gives the right order of magnitude, and indeed the analysis of the experimental data for,,,"S - 20-540 GeV, as shown in the next section, confirms this naive expectation. One finally obtains from eqs. (12), (13) the result d°'~°r'dE,- ~ c , i f , dp f ' d X ' F ' ii ..... Jp x,

p q 2']1~,~1~1-~i( ''ra: d P S p), (x,,q2)¢ ( x--~l'

( 141

and similarly for do-/dK~ and d Z / d K ~ . So far the lower bound p,.~. of the parton-parton subenergy has not been indicated explicitly. It is clear that for a fixed and sufficiently large ET in eq. (14), simple kinematical considerations demand pS>~2E~ and therefore p,,,~. = 2E~r/S. On the other hand, being the distribution dP/dET appropriately normalized to unity, the quantity

zmc'-=Ec,,

dp /5., ....

dx, F,(x,)F, Xl

* An analysis of UAI results, in this spirit, is in progress.

I/m.il

(15)

457

M. Greco / High E 7 production in Q C D

is bounded by the total inelastic cross section. Then eq. (15) can be used to get another of magnitude estimate of the absolute lower limit fi,,~,, which could be useful in the extrapolation of (14) to the Iow-Ev region. Then pro,, = max (/~mi,, 2 E ~ / S ) . It has to be stressed that our results, based on eq. (14), and concerning the relevance of soft gluon effects in the semi-hard region of medium-large ET, do not depend at all on the value of ~6m~,, which is used only as a regulator at low Er for phenomelogical reasons. Let us finally comment on the validity of our expression (14). It is clear that this result cannot be trusted at very large E~ (2E-r ~x/S), when both the I)LLA breaks down and genuine had scattering effects, discussed in the previous section, are expected to take over. Indeed, evidence for jet structure at very large ET has been clearly observed at ISR and p~ collider [5, 7, 8]. Eq. (14) is therefore expected to hold in a range of medium-large values of ET and the relative roles of the two components will indicate more precisely the transition region for each process. On the other hand the extrapolation of eq. (14) at too small values of Er presents some degree of uncertainty from the point of view of perturbation theory. Furthermore, the contributions to ET from initial and final states cannot be simply factorized as in eq. (13). This is clear from the following observation. Let us write, for the observed ET distribution, do fl d E-rrob~-

d E r~o

dETf, o( "~8( ET.. - ET.,,t- ET,i~) d-'~r \dE-rrad d E f . . / ~ " '

(16)

where ET~o and ET.. denote the contributions of the initial and final states respectively. In compact notation, and within the usual soft approximation, we have d20. dErr~d dETfi,,

)" f dp F,i(p) d P ( p ) do.h(p) . O,h dET~.d dET,.

(17)

Then for ET~,t ~'(ET,~), one obtains dETob ~}. "

dpFo(P)

dP

[ do" h \

which reduces to eq. (14) with a simple shift of the transverse energy scale. In the actual calculations (ETa.) is of order of a few GeV. Notice that for the integral over Ewf~. in the r.h.s, of (18) automatically includes the bremsstrahlung from the final legs. Furthermore, the radiation emitted from the initial legs, up to a value KT (or ETrd0), does not affect appreciably the average (El~i.), after K~ is summed to the back-to-back final patton transverse momenta. The situation here is different from the analogous case in deep inelastic scattering, where the knocked parton has (E-n~.)~0 in the absence of bremsstrahlung and acquires then an average (ET,.)-(Ewr~d), just because of balancing the K-r of the radiation.

M. Greco / High Er production in QCD

458

On the o t h e r h a n d , for small ET, one can write eqs. (16), (17) as

do"

d ETobs

)2 f dp F,i(P) I d E

u,h

( dcrh'~F dP ] ~"°\d E~.] l_dE ~ . ] ,:,~,~_~ _~,~o ,

(19)

.....

which c o u l d give a better a n s w e r for this region. O f course, a m o r e accurate c a l c u l a t i o n c o u l d be d o n e n u m e r i c a l l y , but it will further c o m p l i c a t e the n u m e r i c a l analysis, a n d is not the natural region o f a p p l i c a t i o n o f the ideas discussed above.

4. Results and discussion In the previous sections we have given the main formulae, and for phenomenological applications we still have to specify the parton densities. We will first use scaling quark and gluon distributions, which are simpler for numerical use and enough to describe the main features of our results. The effect of scaling violations will be d i s c u s s e d later. Then the valence p and rr structure functions are

x u P ( x ) = A,,x°'5( 1 - x) 3 ' xdV (x) = Aax°5( 1 - x) 4 , x V ~ ( x ) = A.,x°~( 1 - x ) ,

(20)

where Au, Aa a n d A,, are d e t e r m i n e d from the n o r m a l i z e d c o n d i t i o n s J uP(x) dx = 2, & ( x ) d x = 1 a n d J V~(x) d x = 1. The g l u o n d i s t r i b u t i o n s are given by

x G P ( x ) =3(1 - x ) s, xG"(x)=2(l

-x) 3 .

(21)

The effect o f scaling violations will be c a l c u l a t e d using the p a r a m e t r i z a t i o n o f ref. [22]:

NC xc(x, Q ~ ) = B ( D + I , A / C ) .

x A 1 xC) D, ( -

(22)

with N = 2, A = 0.421 - 0.0412L C = 2 - 0.6223g °s a n d D = 3.37 + 0.4319g for v = u e : N=I, A = 0 . 3 6 4 - 0 . 0 3 6 8 g , ( 7 = 2 - 0 . 5 4 1 4 g °s a n d D = 5 . 0 9 + 0 . 3 4 6 3 g for v = d v, where, as usual, g = In [In (Q2/A2)/In ( Q o2 / A -"~) ] with Q o = 4 G e V 2 a n d .1 = 0.4 GeV. F u r t h e r m o r e , the gluons are p a r a m e t r i z e d as [22]

xG(x, Q2) = A ( I + B x + Cx2)(l - x ) t ) + E e F ~ , with A = 0.9243 + 2.51 go5, B = 8.558 - 9.227g °3 - 0.655g t 5 , C = 53.57 - 6 8 . 7 8 g ° 3 + 19.3g,

(23)

M. Greco / High E t production in Q C D

459

D = 6 + 1.454g, E = 11.29g 2 , F = 41.24+ 5071g. In the following our results will be based on eqs. (20), (21) unless stated explicitly. Finally, we have parametrized a ( k ~ ) as a ( k ~ ) = ( 1 2 r r / 2 5 ) l n [ ( k 2, + A 2 ) / A 2] with A = 1 GeV and A - 0.3 GeV, agreement with previous p h e n o m e n o l o g y o f Drell-Yan processes [ 16]. We show first in fig. 1 our results for rrp collisions at 300 GeV c o m p a r e d with the NA5 results [1]. The full curve refers to the soft contribution o f eqs. (14)-(18). The normalization is absolute and, as stated above, depends on [tm,,I t which is taken to be 1 GeV 2. An inelastic cross section o-~net--- 22 mb fixed Pm~,, through eq. (15), to the value/~m~,-~ 10-2. Furthermore, the scale o f the observed Er differs from Err~,d by the a m o u n t (ET~,) = 2 GeV, which is estimated from the hard cross section.

L0-26

o.~%~ ,

-rr- p 300 GeV

10 .27

~

Io ~8

uj~ 1 0 2 9 J

b

-'o ! ,~-30 _

\

I 0 -3~ __

.

\-

1 0 - 5 2 __

I 0 " 33

I

0

!

4

i

I

I

8

I

I

,

12

16

,t

E T (GeV ,Fig. I. T r a n s v e r s e e n e r g y d i s t r i b u t i o n in rrp collisions at ,, .s = 24 GeV. T h e d a t a are from ref. 11]. See text for the t h e o r e t i c a l curves.

460

M. Greco / High E r production in QCI)

, ~_ .

~---

.

.

_

~

-r

I

I

.

171<3

j

1

] w-~

I ~

I0 -z

0

1771< I

•

,~,~ i

20

%

.~ .,~',~" 40

,

60

~

,

,. 80

'

i

I00

ET GeV

Fig. 2. Transverse energy distributions in p15 collisions at .'.~ = 540 GeV. The data are from ref. [4]. See text for the theoretical curves.

The latter is also shown in fig. 1 (dashed line). Finally the approximation for small E1 given by eq. (19) is also indicated (dotted line). From inspection of this figure it is clear that the soft mechanism describes quite well the observed spectrum up to reasonally large Ew, until the hard component takes over. Notice that the fallott of the soft term is steeper when scaling violations are taken into account. Furthermore, a renormalization of the hard term by a sort of K-factor, of order of two, as indicated by preliminary estimates, is also suggested by the figure. We would not like to push too much the comparison with data at very small E r, because of possible ettects from experimental cuts and fragmentation, as well as for the theoretical uncertainty of our approach to this very soft region. In fig. 2a our results are compared with the UAI data [4] at the C E R N p~ collider. The inelastic cross section has been fixed at the value o"m~ ----40 mb. The normalization is the same given above, i.e. Itm,,~- ' = 1 GeV 2. The theoretical curve is obtained with no restriction on the phase space of the emitted radiation. In order to study the rapidity (y) and the azimuthal (&)-dependence we have restricted the full ,.l,y or Ad) gluon ranges by a factor of two and three, and compared with data in figs. 2b, c. From the inspection of these figures follows that all dependences on the kinematical variables S, y and ~h are well reproduced. Furthermore, in fig. 2b the region of transition between the soft and the hard components, the latter is shown in the figure, is around E] = 50 GeV, which is also consistent with the data, So far the gluon contribution, which is dominant at the collider energies, has been calculated with a scaling density go(x) given in eq. (21). The effect of scaling

M. Greco / High E r production in QCD

461

\

',\ ,\

\

~>

, \ , \

I.,i,I

% -2 I0

,

\

I

1

1

I

20

40

60

80

1

E T (GeV)

Fig. 3. T r a n s v e r s e energy d i s t r i b u t i o n in pl5 collisions at q s = 540 GeV, for two dif[erent g l u o n distributions as defined in the text.

violations, as well as the use of the gluon density of eq. (23), referred to as g', is indicated in fig. 3, and amounts to a correction factor of order 2-3 to the scaling result. Notice that our results do not depend on any assumption on the fragmentation into hadrons of quarks and gluons. This is not unconceivable since we look at totally inclusive distributions and therefore hadronization effects should be almost completely washed out. Furthermore, because of a strong dominance of the gluons contribution, one should observe differences in the structure of the final states, as compared, for example, with what it is observed in purely quark-initiated processes, like the production of Drell-Yan pairs or weak bosons. In particular the ET behaviour of the hadron multiplicities or the transverse energy-momentum properties should reflect the effect of the different colour factors Cw: and CA associated to the QCD radiation emitted from the initial partons. A typical reaction to study would be, for example, p~--,J~ + J 2 + X , where J. and J2 are two hard jets observed in the final state. Then the properties of the associated hadrons in X should show appropriate similarities with those observed for the minimum bias event and at the same time reveal differences with the case of the production of electroweak pairs.

M. Greco / High Er production in QCD

462

I0 z5

"

:

I

OQOO0 6

O

I0 27 ~s

•

+

: 63

G~V

10.28

10-29

!0-3o

%

10-31

"7

i0-]2

-J

i0-33

10-3t.

°o

10-3s

T~ J

10-36

t 10-37 0

I

I

I

,I

I

I

L

,

5

10

15

20

25

30

35

t.O

=_J

t.5

ET IGeVl Fig. 4. T r a n s v e r s e energy d i s t r i b u t i o n in p p collisions at ,,"s = 63 GeV. The data are from ref. [23]. See text for the theoretical curve.

M. Greco / High E T production in QCD

463

We also show in fig. 4 the comparison with the very recent ISR data of the AFS collaboration [23]. The theoretical curve, from eq. (14), which includes scaling violations, is calculated with no restriction on the phase space of the emitted radiation, with an inelastic cross section o"~"el= 30 mb. Notice here a large contribution from the q u a r k - q u a r k subprocess. From the above discussion it follows that the soft Er distributions obey the following scaling law: d O"s°ft [2E~\ E 1 -= f l x r ~ r----~--'/, dET \ ,JS/

(24)

with the scale of cP °n given by 1/Itmml. The approximate validity of (24) is based on neglecting logarithmic corrections from scaling violations and on the assumption ET = E~r,d+(Ern,) = ETr~a, which is reasonable for ET not very small. Notice that, on the contrary, the hard component obeys a different scaling law, namely hard

J

E 3u6r

r dE-r - f ( x 3 ) .

(25)

In conclusion we have shown that most of the events which are produced at reasonably large E-r in high-energy h a d r o n - h a d r o n collisions are the manifestation of gluon bremsstrahlung associated to the hard scattering. The application to this class of processes of the resumming techniques to all orders in a~, which were found quite successful in describing the Pr properties of electroweak DrelI-Yan pairs, led us to a simple, analytical description of the observed phenomena, independent of any assumption on the hadronization of the partons. The resulting formulae describe, with no free parameters, the experimental findings for a quite large range of energies, and with various beams. More informations could be extracted from the data, in addition to the obvious study of back-to-back jets. They can give complementary informations on Q C D dynamics, and compared with the observed features in Drell-Yan processes, could reveal important differences leading to dyscriminate between quarks and gluons. The author gratefully acknowledges the kind hospitality of the C E R N Theory Division, where part of this work was done. References [I] [2] [3] [4] [5] [6] [7]

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