Gluon bremsstrahlung effects in hadron-hadron collisions

Volume 119B, number 4,5,6

PHYSICS LETTERS

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GLUON BREMSSTRAHLUNG EFFECTS IN HADRON-HADRON COLLISIONS R.D. F I E L D 1 Particle Theory Group, University of Florida, Gainesville, FL 32611, USA G.C. FOX 2 California Institute of Technology, Pasadena, CA 91125, USA and R.L. KELLY 3 Aret~ Associates, Encino, CA 91316, USA 4 and Lawrence Berkeley Laboratory, Berkeley, CA 94720, USA Received 3 September 1982

We slaow that the inclusion of noncoUinear gluon bremsstrahlung is essential in a quantum-chromodynamic (QCD) description of large transverse energy events in hadron-hadron collisions. Recent data from CERN and Fermilab for both large and small aperture energy triggers give indirect experimental support for QCD and for gluon bremsstrahlung effects.

In leading-order QCD, mesons are produced at large transverse momentum (p±) in h a d r o n - h a d r o n collisions as the result of a hard p a r t o n - p a r t o n collision: one parton from the incoming beam hadron and one from the target hadron, where parton refers to either a quark, antiquark or gluon. The resulting elastic p a r t o n - p a r t o n scattering produces two outgoing partons which subsequently "fragment" into jets o f hadrons producing a four-jet event structure (two large p± jets, a beam jet and a target jet). The invariant cross section for the reaction A + B -+ C + X is written as E d3o/dp3(A + B ~ C + X;s,p.L, Ocm )

= f dxa | ~ dx b

GA--,a(Xa, Q2)GB-,b(X b , Q2)

× D c ~ c ( Z c , Q2) d f / d f ( a b ~ cd; g, P±)-

(1)

1 Work supported in part by the US Department of Energy under Contract No. DE-AS-05-81-ER40008. Work supported in part by the US Department of Energy under Contract No. DE-AC03-81-ER40050. 3 Work supported in part by the US Department of Energy under Contract No. W-7405-ENG-48. 4 Present address. 0 031-9163/82]0000--0000/$02.75 © 1982 North-Holland

where d 6 / d t is the hard scattering p a r t o n - p a r t o n differential cross section, ab ~ cd, with all two-to-two q u a r k - q u a r k , g l u o n - q u a r k , g l u o n - g l u o n , etc. subprocesses being included. The variables g and ib± are the center o f mass energy squared and transverse momentum, respectively, for the hard constituent subprocess. The effects o f soft and collinear gluon emissions off the incoming partons are treated by assigning a Q2 dependence to the parton structure functions, GA~a(X ' Q2) (i.e. the probability that the parton carries a fractional longitudinal momentum z of the hadron from which it came) ,1. Similarly, soft and collinear gluon bremsstrahlung off the outgoing partons results in a Q2 dependence of the "fragmentation functions" Dc_~f(z, Q2) (the number of hadrons of type C carrying fractional longitudinal momentum z within a jet initiated by a parton of type c). The Q2

~1 To leading order, there is an ambiguity in the choice of the energy scale, Q. All choices that increase linearly with the parton-parton transverse momentum,/~±, are equivalent at leading order. In ref. [2]we took Q2 = 2~/(s'2 + i2 + fi2). 439

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dependence of the structure and fragmentation functions is given by perturbation theory (e.g. the AltarelliParisi equations [1]). Since, to leading order, one only need consider the case where gluon radiation is soft or collinear, one is still left with an effective two-to-two subprocess. Unfortunately, eq. (1) is not complete. It has been known for some time that a successful description of single-particle production at high p± requires that one include the effects of the "intrinsic" transverse momentum k I of the partons within the initial hadrons [2]. The incoming partons' momentum cannot be taken to be parallel with the initial hadrons and, in fact, phenomenologically (k±) is quite large (~0.85 GeV for the current Q2 range). This, together with the rapid fall with/~3_ of the basic p a r t o n - p a r t o n cross section, produces a "trigger bias" in single-particle experiments. One preferentially selects events in which the incoming two partons are moving toward the trigger. Previously the effects of this large intrinsic k3_ have been estimated by "smearing" the basic eq. (I). The intrinsic k± is assumed to be distributed as a gaussian (or an exponential) independent of both Q and the process, and one then integrates eq. (1) over these k± values. On the other hand, in QCD, a large effective intrinsic transverse momentum can be understood in terms of noncollinear gluon bremsstrahlung. As illustrated in fig. la, single-particle triggers tend to come from the fragmentation of a large p± parton that is balanced on the opposite (or away) side by several lower momentum partons. The same bias effect occurs for "small aperture" jet (calorimeter) triggers. By this we mean observations that sum the total transverse energy E± in a small region ( ~ 1 sr in the CM frame) of phase space. Such a calorimeter roughly contains all the hadrons from a single-parton jet and good agreement is found between the observed E3_ rate and the invariant cross section for producing a single parton arrived at from eq. (1) plus smearing [3]. However, such small aperture calorimeter experiments are obviously biased toward jetlike events and one is reluctant to claim that these experiments "prove" the existence of QCD jets in hadron-hadron collisions. This particular bias can be avoided by triggering on the total transverse energy into calorimeters that are much larger than parton "jets". Initially, it 440

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PHYSICS LETTERS

g

q

trigger

tr

(a) Single Particle or Small Aperture Calorimeter

r

(b) Large Aperture Calorimeter

Fig. 1. (a) Trigger bias effect for a single-particle or small aperture calorimeter experiment. The large Pi trigger is obtained by combining a two-to-two hard scattering of smaller/)3_ with additional transverse momentum gained by the incoming quarks through the emission (or bremsstrahlung) of gluons. The trigger parton is quite often balanced on the opposite (or "away") side by several lower momentum partons. (b) Trigger bias effect for a large aperture calorimeter experiment. Large transverse energy E3_ is produced by the bremsstrahlung of many low E± gluons in addition to the hard scattering d&/d/(~,/)l). was hoped that such E± triggers would see well-collimated high Pi jets similar to those observed in e+e annihilations. However, recent data from these experiments [4,5] show little evidence for the two high p± jets expected from eq. (1) and, in addition, the large aperture E± cross section is considerably larger than predicted. Naturally, these new results cast doubts on the seemingly successful QCD description of the earlier small aperture data. A theoretical breakthrough has come in the development of the Monte-Carlo parton shower approach first introduced by Fox and Wolfram [6] and by Odorico and collaborators [7] for e+e - annihilation (see also ref. [8]). Here the initial quark and antiquark, produced by the "decay" of a virtual photon of invariant mass Q, are allowed to bremsstrahl gluons until their invariant masses have been degraded to some cut-off mass/a c. The invariant masses of radiated partons are kinematically constrained to be less than those of their parents with the difference being converted into

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the transverse momentum o f the emitted gluons. The radiated gluons may themselves radiate more gluons, producing a shower of partons. The emission of many gluons is treated independently, using a simple "leading-pole" approximation, but exact kinematics are maintained. The extension of this method to h a d r o n - h a d r o n collisions is described by Fox and Kelly [9]. The hard scattering two-to-two subprocess cross section dt~/di(g,/~±), is calculated to leading order exactly (the black boxes in fig. 1) with all remaining parton emissions estimated using the Monte-Carlo parton shower "leading-pole" approach. Final state partons have timelike invariant masses and are allowed to radiate until their masses are below/1A. Initial partons have spacelike invariant masses with the maximum (negative) value taken to be Q2 = _ 4 i 6 2 , 2 . They are evolved (backwards) until they reach a cut-off value of --(,u B c )2 . Multiparton cross sections are approximate but all gluon emissions are retained including the (infinite sum of) divergent soft and collinear configurations. However, here one is both not restricted to these collinear (or soft) configurations only and exact kinematics are maintained at each emission. Therefore, we believe that the approach is superior to eq. (1) for investigating any questions involving the overall event structure in h a d r o n - h a d r o n collisions * a Even with the QCD Monte-Carlo approach, one must smear over an intrinsic k± of the incoming low mass off-shell partons inside the nucleons. A value o f (kr) = 0.75 GeV at an invariant mass squared scale of - 4 GeV 2 (/a~ = 2 GeV) was arrived at in ref. [9] by a comparison with the transverse momentum spectrum of muon pairs produced in the process pp ~/a+/a + X. This value is smaller than the value of (k±) = 0.85 GeV found using eq. (1); however, it is still sizable. Note that with the QCD Monte-Carlo method, the "effective" incoming parton transverse momentum now depends on the scale Q2, whereas previously with eq. (1) it was universal and independent of Q2. In this paper we examine how large aperture calorimeter experiments are biased in favor of par*on sub-

,2 This choice for Q saves a considerable amount of computer time as is discussed in ref. [9]. ,3 The new formalism handles correctly the off-shell kinematics of parton-parton scattering which is usually ignored if one simply smears eq. (1). See, e.g., ref. [ 10].

23•30 December 1982

processes involving an anomalously large amount of gluon bremsstrahlung as illustrated in fig. lb. In the small aperture case (fig. la), the bremsstrahlung is opposite to the trigger, whereas a large aperture calorimeter catches most of the gluon bremsstrahlung. If one asks for a large amount of transverse energy in a h a d r o n - h a d r o n collision, nature gives this E± in the way that is most efficient. Because of the rapid decrease in the hard p a r t o n - p a r t o n scattering cross section with increasing i61, one has, in effect, a source of outgoing partons whose intensity falls rapidly with increasing CM energy g. In contrast to this, in e+e annihilations, one has a monoenergetic source of partons with CM energy g = Q2 and for large Q2 the twojet structure is evident. In both e+e - annihilations and h a d r o n - h a d r o n collisions, wide angle gluon emission is an effect of only a few percent. However, the steep spectrum in the hadron case means that small corrections to larger cross section scatterings (smaller i6±) can dominate a t a n y given large p± ,4. This is illustrated in fig. 2. Fig. 2a shows a typical "untriggered" event at x/s = 24 GeV, in which one clearly sees a two-jet structure in the transverse momentum plane with total transverse energy E± approximately equal to 2i6±. On the other hand, fig. 2b shows a "triggered" event in which anE± > 10 Ge.V was demanded. Here 2/3± is only 6 GeV with bremsstrahlung making up the remaining E±. Fig. 2c shows the profusion of partons generated at x/s = 540 GeV in an E± triggered event. Of course, experiments do not measure quarks and gluons; they observe hadrons. A complete treatment requires that one combine the QCD perturbative parton level calculations with a model of the nonperturbative hadronization phase and, unfortunately, there is little theoretical guidance for this latter stage. Fragmenting the many quarks and gluons independently in the h a d r o n - h a d r o n CM frame according to the standard " F e y n m a n - F i e l d " (FF) technique [ 11 ] as in eq. (1) is clearly not correct. Firstly, there are many soft quanta for which the FF technique is inadequate and inappropriate. Secondly, when there are many ,4 It is not possible to eliminate this effect by increasing Q, or by increasing the hadron-hadron CM energy x/~, because in QCD the amount of gluon bremsstrahlung (the effective intrinsic kl) is an essentially constant (up to logarithms) fraction of the transverse momentum,/~l, of the basic two-to-two hard scattering. 441

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(o) Untriggered

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-5-

Fig. 2. Transverse momentum projections for typical events: (a) untriggered event at x/~ = 24 GeV, (b) and (c) triggered events at ~ = 24 and 540 GeV, respectively. Partons are denoted by dashed lines (gluons), solid lines (quarks) and heavy solid lines (beam fragments). quark and gluon jets involved, one cannot consider them as independent. Here presumably the separation of color is the relevant quantity and we use the "color string" approach described by Field and Wolfram for e+e - annihilation in ref. [12] and by Fox and Field in ref. [8]. All gluons are forceably split into a q~ pair and color singlet strings (or "clusters") are formed which have a distribution of invariant mass. Clusters with mass less than 3 GeV are allowed to "decay" isotropically in their rest frame according to the simple phase method of Field and Wolfram [12]. In addition, there are large mass clusters ( > 3 GeV), which we parametrize by back-to-back FF jets in the string CM frame. Our approach will be discussed in more detail elsewhere. Here we compare the results with the recent NA5 data from CERN [4,13]. 442

Fig. 3 shows a comparison of the predictions of the hadronized parton shower approach with the data for small (A~ = 90°), medium (A~o = 90 ° back-to-back) and large (A~o = 360 °) aperture calorimeter triggers. In each case the calorimeter subtends the range 54 ° ~< 0 ~< 135 ° in polar angle. The agreement between the data and the theoretical predictions is quite good. Note that for the small aperture triggers there is less difference between the parton level and the hadron level. In addition, in going from the small Atp = 90 ° trigger to the large A~ = 360 ° trigger one changes the bias from the type illustrated in fig. la to that illustrated in fig. lb. The model successfully combines these two aspects of gluon bremsstrahlung. Furthermore, it is not possible to explain the large difference in rates for the three triggers in fig. 3 by hadronization alone without noncollinear gluon bremsstrahlung. Eq. (1) alone predicts a parton level (A¢ = 360 °) cross section that is a factor of 10 less than the parton shower Monte-Carlo (parton level) curve shown in fig. 3 (see the parton level analysis presented in ref.

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[9]). Even after hadronizing, eq. (1) gives a (A~0 = 360 °) cross section that is at least a factor of 10 too small. On the other hand, if one is only interested in rate and not in overall event structure, then eq. (1) plus smearing correctly reproduces the small aperture (A~0 = 90 °) and single-particle trigger invariant cross sections. In fig. 4a, we break up the calculations for 10 ~
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E± trigger (10 ~ El ~ 11 GeV) from various hard scattering/~± values. The solid curve is the result of the QCD patton-shower Monte-Carlo model, Which includes noncollinear gluon bremsstrahlung, whereas the dashed curve is the prediction of eq. (1), which includes only collinear and soft gluon effects. These results are at the parton level and do not include hadronization effects. (b) Comparison of the predictions of the hadronized QCD parton-shower Monte-Carlo model with data on the planarity distribution from NA5 [4,13].

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other hand, the parton shower approach (with bremsstrahlung) yields roughly equal contributions for 2.5 ~
(2)

where ~max and ~min maximize and minimize, respectively, the sum o f p 2 in the P.tx and p±y plane (P is the two-dimensional analogue of sphericity). In fig. 4b we compare the experimental NA5 planarity distribution with the predictions of the hadronized parton shower Monte-Carlo model for 10 < E ± < 12 GeV. The model gives taP>~ 0.5 independent orE±, in agreement with the NA5 results. As pointed out by the NA5 group [13], the naive two-jet predictions of eq. (1) (without added gluon bremsstrahlung) do not agree with the shape of the planarity distributions and have an E l dependence that is not obsei-ved. We believe that we have significantly improved the QCD formalism for the production of large p± partons and hadrons in hadron-hadron collisions beyond the leading-order result in eq. (1). Incoming and outgoing partons are allowed to radiate (or bremsstrahl) additional gluons. Our method reduces to eq. (1) in the collinear (or soft) configuration but approximates noncollinear (2 -->N ) subprocesses as well. We calculate the E± distributions and find that QCD does give a good description of both the magnitude of the cross section and the event shape (nonjetlike) of large aperture calorimeter experiments. Furthermore, we have learned an important lesson. There is no such thing as an unbiased large p± experiment. Each type of trigger preferentially selects out a certain class of events. Nature gives you what you ask for in the way that is most efficient. Large aperture E± triggers bias one in favor of events in which a large number of gluons have been emitted. Higher and higher E± is produced by a larger and larger multiplicity of hadrons with each hadron having only a slightly increasing mean p±. Single-particle triggers at high p±, on the other hand, bias one against large amounts of gluon radiation (one cannot afford to waste any energy). Singleparticle triggers, of course, are often balanced on the away-side by several lower Px partons. As the p± of a single-particle trigger is increased, the overall event 443

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multiplicity decreases slightly in contrast to the E± case. Our new formalism will significantly alter the away-side predictions from that in the standard QCD analysis [2]. The away-side is biased towards multiparton configurations and will tend to have a softer transverse m o m e n t u m spectrum. This in turn will affect the preferred form for the gluon fragmentation functions. The results presented here, of course, do not prove the existence of QCD gluons. The data do, however, provide indirect support for QCD and for gluon bremsstrahlung effects. By combining information from a variety of triggers, one is beginning to reveal the details of the large p± production mechanism in h a d r o n hadron collisions. So far everything is consistent with QCD.

References [1] G. Altarelli and G. Parisi, Nucl. Phys. B126 (1977) 298. [2] R.D. Field, Phys. Rev. Lett. 40 (1978) 997; R.P. Feynman, R.D. Field and G.C. Fox, Phys. Rev. D18 (1978) 3320.

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[3] C. Bromberg et al., Nucl. Phys. B171 (1980) 1. [4] C. DeMarzo, Phys. Lett. l12B (1982) 173. [5] B. Brown et al., Properties of high transverse energy hadronic events, Fermilab-Conf.-82134-EXP. [6l G.C. Fox and S. Wolfram, Nucl. Phys. B168 (1980) 285. [7] R. Odorico, Nucl. Phys. B172 (1980) 157; P. Mazzanti and R. Odorico, Phys. Lett. 95B (1980) 133; Z. Phys. C7 (1980) 61. [8] G.C. Fox, lectures presented at 1981 SLAC Summer School, CALT-68-863 (1981); R.D. Field, lecture given at Conf. on Perturbative QCD (Florida State University, March 1981), AlP Conf. Proc. No. 74 (Particles and Fields subseries No. 24). [9] G.C. Fox and R.L. Kelly, preprint LBL-13985 (CALT68-890 ( 1982); and in: Proton-antiproton collider physics 1981, AlP Conf. Proc. No. 85. [10] W.E. Caswell, R.R. Horgan and S.J. Brodsky, Phys. Rev. D18 (1978) 2415. [11] R.D. Field and R.P. Feynman, Nucl. Phys. B138 (1978) 1. [12] R.D. Field and S. Wolfram, A QCD model for e+eannihilations, Univ. of Florida preprint UFTP-82-12 (1982). [13] P.A. Polakos, Large transverse energy hadron-hadron interactions at 150 and 300 GeV/c, talk presented at Xlllth Intern. Symp. on Multiparticle dynamics (Volendam, Netherlands, June 1982).