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GLAS-PPE/1999-08hep-ex/9907011

Progress and Problems in QCD —

Report from the Hadronic Final States Working Group at DIS99

Matteo Cacciaria, Frank Chlebanab, Laurel Sinclairc and Marc Weberd

aCERN, Theory Division, CH-1211 Geneva 23, Switzerland.

bFermi National Accelerator Laboratory, P.O. Box 500, Batavia, IL 60150, U.S.A.

cDepartment of Physics and Astronomy, Glasgow University, Glasgow G12 8QQ, UK.

d Institut für Hochenergiephysik, Universtät Heidelberg, Schröderstraße 90, D–69120 Heidelberg,Germany.

We present a summary of the Hadronic Final States parallel sessions of the DIS99 workshop. Topics were pre-sented over two days and included both theoretical and experimental talks. Recent progress in the understandingof QCD in deep inelastic scattering, e+e− collisions, and in γ and p collisions was discussed.

1. THEORY SUMMARY

During the parallel sessions of the Hadronic Fi-nal States Working Group about forty talks werepresented. Out of these, about ten might be clas-sified as theoretical ones. The issues they dis-cussed ranged from instantons to heavy flavourproduction to higher order QCD calculations. Itis therefore understandable how difficult it mightbe to try to provide an organic summary of sucha widespread collection of interesting topics.We shall therefore try to highlight here what

we consider to be the main points of the variouscontributions, leaving the task of properly intro-ducing and explaining the subject to the individ-ual summaries. Such summaries will not be citedexplicitly in this section, since they can easily befound in these proceedings under the name of theperson who gave the presentation.A common feature can be identified in almost

all the talks given. They clearly focus on the needto go beyond standard fixed next-to-leading order(NLO) QCD perturbation theory as the qualityof the experimental data demands more accuratetheoretical calculations.G. Salam and H. Jung both described phe-

nomenological studies related to the CCFM equa-

tion. This is an evolution equation that goesbeyond the so-called “multi-Regge” limit of theBFKL equation, and also tries to implement ef-fects due to colour coherence (via angular or-dering) and soft particles. As CCFM is harderto solve than BFKL, the question is how sim-ilar the predictions of the two approaches are.Salam argued that, with the inclusion of soft ef-fects, BFKL and CCFM can be shown to leadto identical predictions at the leading log level.Differences at sub-leading level, as well as ambi-guities in the implementation of the equations atthis level, do however remain. Jung described apractical implementation of the CCFM equationin the program SMALLX and showed that a goodphenomenological description of both F2 and for-ward jets data can be achieved.Small-x logarithms are not the only ones ap-

pearing in a QCD perturbative expansion. N. Ki-donakis described how to take care of the largelogs resulting from soft gluon emissions when finalstates are produced near threshold. Resummedexpressions for these terms have been writtensome time ago, but until recently it was still un-clear how to treat these expressions so that thefinal result would indeed only contain the resum-

http://arxiv.org/abs/hep-ex/9907011v1http://arxiv.org/abs/hep-ex/9907011

2

mation of the perturbative series and not furtherspurious effects. In the approach that Kidonakisdescribed, the resummed expression is truncatedat next-to-next-to-leading order, i.e. one orderbeyond what is available as a full fixed ordercalculation. Due to the fairly good convergenceproperties of the series, such a treatment sufficesto bring an improvement over the standard NLOcalculation, and at the same time ensures consis-tency with the perturbative expansion.

One further resummation issue was addressedby S. Kretzer who described how charm effects inparton distribution functions, appearing at fixedorder as log(Q/m), can be resummed using theACOT scheme. He studied both neutral andcharged current deep inelastic scattering (DIS).The difference between fixed order and resummedpredictions does not seem to be within the reachof present experimental accuracy. It is howeverlikely that such resummed approaches will bemore and more important in the future, as ex-perimental precision improves and larger scalesare probed.

S. Frixione reviewed the status of theoreti-cal calculations of heavy quark production. Atsmall and moderate transverse momenta, NLOQCD calculations are available and reliable. Inthe large transverse momentum region, on theother hand, large logs of the form log(pT /m) de-velop. Resummation techniques for such termshave been developed in recent years. By mak-ing use of the Altarelli-Parisi evolution of a per-turbatively calculable heavy quark fragmentationfunction these logs are resummed to all orders.Inclusion of a non-perturbative parametrizationfor heavy quark hadronization effects, such as thePeterson fragmentation function, also provides adescription ofD∗ photoproduction data. Frixionedid however warn that this resummed calculationshould not be used at too small transverse mo-mentum values; a proper combination with thefull fixed-order NLO massive calculation is neces-sary to make it reliable in this region.

A more exotic feature of QCD, namely instan-tons, which also go beyond perturbation theory,was discussed by F. Schrempp. Such objects,originating from the rich structure of the QCDvacuum, can in principle play an important role in

various long distance aspects of QCD. There arealso short-distance implications. It was argued inthis talk that in DIS at HERA there exists a po-tential for observing instanton-induced processesotherwise forbidden by usual QCD perturbationtheory.Back on more standard ground, D. Soper and

M. Grazzini described efforts to produce calcula-tions in fixed order perturbation theory. Soperdescribed a numerical approach to one-loop com-putations: rather than evaluating each diagramanalytically, all diagrams are properly added andthe integrals involved are performed numerically,in such a way that the individual singularitiescancel before integrating. The final result istherefore finite. This method has so far been suc-cessfully applied to the evaluation of the thrustdistribution in e+e− collisions, but can in prin-ciple be extended to other processes. Grazzinireported on progress in perturbative calculationsbeyond the one-loop approximation. In partic-ular, he described studies of the collinear lim-its of three partons, where generalizations of theAltarelli-Parisi splitting vertices appear. Suchlimits are one of the building blocks for next-to-next-to-leading calculations, the next frontier ofperturbative QCD.

2. HEAVY QUARK PRODUCTION

Experimental results, both on charm and onbottom production, were presented by the ZEUSand H1 collaborations. Many D∗ productiondata were updated from previous measurements.Heavy quarks can provide particularly interest-ing tests of perturbative QCD since, due to theirlarge mass acting as a cutoff for infrared singular-ities, their total production rate can be predictedon rigorous theoretical grounds with no free pa-rameters other than their mass, the parton dis-tribution functions and the strong coupling.The H1 collaboration showed that a generally

good, albeit not perfect, agreement with NLOQCD predictions can be observed [ 1]. It isalso worth noticing that the gluon distributionfunction in the proton has been extracted fromcharm data in both photoproduction and DIS.The two results show good agreement with each

3

other and with the indirect determination fromF2, as shown in Fig. 1.

0

10

20

-4 -3 -2 -1 00

10

20

-4 -3 -2 -1 0log xg

x gg(

x g)

H1 NLO

QCD fit to F2

D* (DIS)

D* (γp)

CTEQ4F3

µ2=25 GeV2

Figure 1. Gluon densities obtained from D∗ anal-yses in photoproduction and DIS.

ZEUS D∗ data were shown in a new lowphoton-proton energy region, 80 GeV < Wγp <120 GeV [ 2]. As shown in Fig. 2, the experimen-tal data tend to be generally higher than the NLOQCD predictions, especially in the forward (pro-ton) direction. Comparisons with the so-calledmassless approach show better agreement, butthis kind of approach is probably not fully reli-able at these low transverse momentum values [3].Bottom production data, given in terms of ob-

served leptons coming from semileptonic decays,were also presented by both ZEUS and H1 col-laborations. ZEUS observed electrons, finding across section larger by a factor of∼ 4 than the onepredicted by the HERWIG leading order (LO)plus parton shower Monte Carlo program [ 4]. H1performed two analyses, both using muons to tagthe heavy quark [ 5]. In these cases, the experi-mental results are about a factor of 5 and 3 largerthan the prediction of a different LO Monte Carloprogram, AROMA.Such large factors between theory and exper-

iment might seem important. However, oneshould keep in mind both the large errors stillpresent in the experimental determinations andthe fact that the theoretical prediction is given

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ηD*dσ

ep →

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/dηD

* (

nb)

(a) 2 < p⊥ D* < 8 GeVPeterson fragm., ε = 0.036PYTHIA fragm.

Figure 2. ZEUS differential cross sectionsdσ/dηD

∗

compared with NLO predictions for themassive approach. Full description of curves maybe found in [ 2].

here by a leading order Monte Carlo program. Itis well known that NLO calculations for heavyquarks greatly increase leading order predictions,usually by at least a factor of 2. However, acomparison with a NLO calculation is unfortu-nately not yet possible, since experimental resultsare only quoted for a “visible” cross section forwhich no full simulation at NLO is so far avail-able. Combining this fact with the experimentaluncertainty, it becomes apparent that it is stillpremature to talk of a discrepancy in the bot-tom production cross section at HERA. We areof course looking forward to more detailed com-parisons between theory and experiment, bottomproduction being better behaved in QCD pertur-bation theory than charm, and therefore provid-ing a better test of QCD predictions.Heavy quark production was also discussed for

the hidden flavour case, i.e. heavy quarkonia pro-duction. Elastic and inelastic J/ψ electroproduc-tion has been analysed by the H1 collaboration [6]. Results from an inclusive sample (elastic plusinelastic) were compared to predictions from theso-called soft colour interaction model as imple-mented in the Monte Carlo program AROMA.Most of the shapes of the differential distribu-tions can generally be reproduced, while the mag-nitude of the theoretical predictions is usuallytoo low. Results from an inelastic sample were

4

instead compared to predictions obtained withthe non-relativistic QCD (NRQCD) approach toquarkonium production. Such predictions can beseen to be at some variance with the data, bothin magnitude and, especially for the rapidity dis-tribution, in shape. It is however known that,especially at such a low scale as the one set bythe charm mass, NRQCD predictions can sufferfrom large uncertainties.

3. JETS IN DIS

The use of jet algorithms and the study of jet-related observables continue to be both a popularand powerful approach in order to characterizethe hadronic final state’s properties. The anal-ysis of multi-jet events in DIS has been used toextract the value of the strong coupling constantαs [ 7, 8, 9, 10]. These and many other importantanalyses have clearly shown the large potential ofQCD studies with jets at HERA but have alsorevealed important limitations. The latter arecaused by the difficulties of current QCD MonteCarlo models to describe the data precisely, bythe large renormalization scale uncertainties ofQCD predictions in NLO in the phase space cov-ered, or by the uncertainties of the proton’s par-ton density.

In this session various presentations of jet anal-yses were given, which addressed these issues.Most analyses profited from the large data samplecollected in particular during the very successful’97 data taking period of HERA. Thus, generallythe measurements were considerably extended, ei-ther into the region of high photon virtuality, Q2,or to harder jet structures corresponding to largetransverse jet energies, EBreitT , in the Breit frame.Three representative jet analyses are discussed inmore detail below.

In [ 11] a systematic comparison of various mea-sured jet distributions with model predictions wasperformed in dijet events at Q2 > 150 GeV2. InFig. 3 the xp distribution determined with themodified Durham algorithm (run in the labora-tory frame) is shown for three different ranges ofQ2. The precision of the data is high and signifi-cant deviations of the QCD Monte Carlo modelsARIADNE and LEPTO are observed. In contrast

to the MC models, the perturbative QCD predic-tions in NLO, which are also shown in Fig. 3,describe the measured jet distributions very well.The same conclusions are reached using the fac-torizable kT algorithm (run in the Breit frame).

modified Durham algorithm, y 2 > 0.005

0

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dxp

150 < Q2 < 275 GeV2

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dn/

dxp

575 < Q2 < 5000 GeV2

H1 preliminary data

NLO + hadr. ARIADNE 4.10 LEPTO 6.51

Figure 3. Distribution of xp = xBj/ξ in threeranges of Q2 measured with the modified Durhamalgorithm.

It is important to note that both Monte Carlomodels have recently been investigated in the con-text of the HERA Monte Carlo Workshop [ 12]and were considerably improved. In version 4.10of ARIADNE, the Q2 dependence of dijet eventshas been modified. In version 6.51 of LEPTO, anew model of soft-colour interactions has been im-plemented. Given the relative disagreement withthe data, further development of the models isdesirable.An excellent description of the data by QCD

in NLO is also observed in the preliminary in-clusive jet cross sections, d2σjet/dETdQ

2, in thekinematic region of Q2 > 150 GeV2 and for

5

transverse jet energy EBreitT > 7 GeV [ 13]. Inthis phase space region both perturbative andnon-perturbative uncertainties are expected to besmall.The corresponding dijet cross section measure-

ments were fitted simultaneously with F2 deter-minations to yield the gluon density of the proton[ 14]. This procedure extends the accessible rangeof the gluon momentum fraction, ξ, to larger val-ues with respect to the less direct determinationsof the gluon density from the scaling violation ofF2. The value of the strong coupling constant wasassumed to be known in this analysis, but a com-bined fit of both the gluon density and αs shouldbe possible in the future.A preliminary measurement of the dijet event

rate and the dijet cross section as a function of Q2

and a determination of αs were presented in [ 15].Jets of high transverse momentum EBreitT havebeen selected at Q2 > 470 GeV2. In the region oflarge Q2, corresponding to large parton momen-tum fractions, the proportion of gluon-initiatedscattering processes is minimal. Thus this anal-ysis is less sensitive to the uncertainties in thegluon density and may depend to a lesser extenton the details of parton density extractions fromthe world data than earlier αs determinations.Also, the renormalization scale uncertainties are(relatively) small, both owing to the large value ofQ2 and the high jet transverse energies required.Again, this nicely illustrates the quest for smaller(theoretical) uncertainties by selecting more re-strictive but safer phase space regions.

4. EVENT SHAPES AND POWER COR-

RECTIONS

The comparison of exclusive hadronic finalstate observables with the corresponding pertur-bative QCD predictions requires an estimation ofhadronization effects. Phenomenological models,such as the string or the cluster model imple-mented in Monte Carlo generators, are primarilyused for these estimates. Depending on the ob-servable under study, hadronization correctionsmay be large, however, and it is difficult to esti-mate their uncertainty rigorously.An alternative approach consists in applying

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H1 preliminary

NLO CTEQ5Mµ = ET,jet

Q2 / GeV2

7 10 20 50 100

[150 ... 200](× 100)

[200 ... 300](× 10)

[300 ... 600]

[600 ... 5000]

Figure 4. Inclusive jet cross section as a functionof the transverse jet energy ET in the Breit framein different regions of Q2.

analytical power corrections of the form ∼ 1/Qpwhen comparing perturbative QCD predictionswith measured hadronic distributions. The lead-ing power p and the exact form of the power cor-rections to the mean values of event shape dis-tributions have been calculated for a large num-ber of observables in both e+e− annihilation anddeep inelastic scattering. The size of the correc-tion depends on the value of an effective universalcoupling constant α0, on the strong coupling con-stant αs and, of course, on Q

2.The results of a 2-parameter fit of αs and α0 to

the mean values of various event shape distribu-tions recently measured at HERA [ 16] are shownin Fig. 5. These results consider the recent the-oretical developments of the calculation of two-loop corrections, leading to the so-called Milanfactor [ 17], and of an updated calculation of thecoefficient for the jet broadening variable [ 18].Also, the experimental precision has been consid-erably improved with respect to an earlier analy-sis [ 19]. The value of α0 is found to be ∼ 0.5 andit is independent of the variable studied to within

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0.1 0.11 0.12 0.13 0.14

αs(MZ)

α_ 0(µ

Ι = 2

GeV

)

τ

B

ρ

τc

C

H1 PreliminaryFits à la Dokshitzer, Webber et al.1σ- and 2σ-contours (stat. and exp. syst.)

pdf: MRSA’-115

Figure 5. Determinations of αs(MZ) and α0 forvarious event shape variables measured in DIS.

20%. The variation of the resulting αs values isvery large, however, which strongly suggests thatfurther theoretical studies are needed.

In e+e− annihilation similar fits to the meanvalues (as a function of the centre-of-mass energy√s) of thrust, wide jet broadening and heavy

jet mass yielded much better agreement in αsand similar agreement in α0 [ 20]. Predictionsof power corrections to distributions, in contrastto mean values, of event shape observables havealso been tested [ 20]. Fig. 6 shows the widejet broadening distribution measured at differ-ent centre-of-mass energies. Perturbative QCDpredictions with either hadronization correctionsfrom Monte Carlo models (full line) or power cor-rections (dashed line) are fitted to the data andyield fits of similar quality to those without thepower corrections but systematically lower valuesof αs. The differences are largest at low centre-of-mass energy where also the applied correctionsare sizeable.

In conclusion, the concept of power correctionshas led to a remarkable theoretical activity, oftenin close collaboration with experimentalists, and

Figure 6. Distributions of the wide jet broad-ening, BW , at different centre-of-mass ener-gies together with perturbative QCD predictionscombined with power corrections or traditionalhadronization corrections.

power corrections prove to be surprisingly suc-cessful. The approach is rather economical in thesense that only one additional universal param-eter α0 needs to be determined by experiment.A number of examples have recently been given,where also the limitations and difficulties becameapparent.

5. FRAGMENTATION IN DIS

In the above jet analyses, the emphasis isplaced on accessing the very rare multi-jet eventsat increasingly large jet ET to minimize soft non-perturbative effects in the subsequent compari-son to perturbative QCD predictions. Valuableinformation on the properties of QCD can alsobe gained from the study of charged particle pro-duction, however, which is obviously strongly in-fluenced by the non-perturbative hadronizationphase. A key question is: To what extent dothe measured hadrons reflect the underlying par-

7

ton spectra? These depend on the initial partonicconfiguration and the subsequent parton cascade.The typical observables are particle rates, mo-mentum distributions of the hadronic final stateparticles and multi-particle correlation variables.Increasingly refined perturbative predictions formore and more complex observables have beenderived within the framework of the ModifiedLeading Log Approximation (MLLA) [ 21]. Manyof those predictions have been compared withdata using the concept of Local Parton-HadronDuality (LPHD). The hypothesis of LPHD in con-nection with MLLA relates the average proper-ties of partons and hadrons by means of a simplenormalization constant. With these assumptions,the theoretical predictions depend essentially ontwo parameters only, an effective strong couplingconstant determined by the QCD scale Λ and anenergy cutoff parameter Q0. Both have to be de-termined by measurement.A recent measurement of scaled momentum

Figure 7. Evolution of the mean, width, and ofthe higher moments skewness and kurtosis, of theln(1/xp) distribution with Q

2.

distributions [ 23] is presented in Fig. 7, wherethe mean value and higher moments of the ξ dis-tribution are shown as a function of Q2 for dif-ferent ranges of x. The variable ξ is defined asln 1/xp = lnQ/2p

Breit. Only particles in the cur-rent hemisphere of the Breit frame are considered.This makes possible a direct comparison with re-sults from e+e− annihilation, which are also in-cluded in the figure.The fair agreement observed between the re-

sults of DIS and e+e− annihilation suggests thatthe main features of quark fragmentation areuniversal. While the mean value of the ξ dis-tribution as a function of Q2 is well describedby MLLA predictions, no consistent descriptionof mean, width, skewness and kurtosis can beachieved. The measurements benefit considerablyfrom the large range in Q2 that is now covered byHERA. Clearly, further studies, possibly consid-ering mass effects [ 25], are needed to understandthis disagreement.Measurements of the properties of particles in

the target hemisphere have also been made andthe correlation between the mean particle multi-plicity in the two hemispheres has been studied [23].A measurement of the charged particle xp dis-

tribution as a function of Q is shown in Fig. 8for different ranges in xp [ 24]. QCD calculationsin NLO combined with NLO fragmentation func-tions are compared to the measurement. For largevalues of xp and with increasing Q, a significantdecrease of the distributions is observed, whichis expected from scaling violations in the frag-mentation functions due to gluon radiation. Theagreement with the prediction is good, except atsmall values of xp where mass effects, which arenot considered in the calculations, are important.A simple power correction ansatz as proposed in[ 27] results in a surprisingly close description ofthe data. Detailed calculations of these powercorrections have been started and were discussedat this meeting [ 26].

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xp range

0.02 - 0.05 ( × 10 )

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0.10 - 0.20 ( × 3 )

0.20 - 0.30

0.30 - 0.40

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Figure 8. The inclusive charged particle distribu-tions 1/NDISdn

±/dxp in the current hemisphereof the Breit frame. The distribution is shownas a function of Q for different intervals of xp.Data from e+e− annihilation as a function of thecentre-of-mass energy E∗ are also shown.

6. FORWARD JET AND π0 PRODUC-TION IN DIS

The study of jet and particle production in thevery forward (proton) region in DIS is largely mo-tivated by the interest in the parton dynamics atsmall values of x. In particular, one would like toaccess a region where the validity of the BFKLequations could be tested.

Experimentally, measurements close to theedge of the detectors are challenging, but bothH1 and ZEUS [ 28] have nevertheless succeededto measure forward jet cross sections. They showa significant rise of the forward jet cross sectionwith decreasing values of x. The measurementsare in striking disagreement with the predictionsof Monte Carlo models based on the traditional

DGLAP parton showers. Furthermore, QCD pre-dictions in NLO disagree with the data [ 29].Recently, several ways to describe the measure-

ment have been found and were presented at thismeeting [ 30, 32, 31]. These are: the inclusion ofa resolved virtual photon contribution in the NLOcalculations performed by [ 30]; the inclusion of aresolved virtual photon component in the MonteCarlo model RAPGAP [ 28]; and the inclusion ofNLO effects in a recent BFKL calculation by ap-plying higher order consistency conditions [ 32].In addition, [ 31] obtained a good description offorward jets (and of F2) with a modified versionof the Monte Carlo program SMALLX based onthe CCFM parton evolution equation.An important new measurement of forward π0

cross sections was presented in [ 33]. Differentialdistributions in x, ηπ and pt,π have been mea-sured for three ranges of Q2. Given the difficultphase space region, the precision of the measure-ment is excellent and compares favourably withthe jet measurements. The inclusive π0 cross sec-tions as a function of x are shown in Fig. 9.Again, RAPGAP with a resolved virtual photoncontribution describes the data better than MCmodels based on DGLAP parton showers suchas LEPTO (shown). The best description is ob-tained by the modified BFKL calculation men-tioned above.In conclusion, significant theoretical progress

has been made in understanding the physics ofthe forward region. The precise measurementof the multi-differential π0 distributions will con-strain existing and future models considerably.

7. REAL PHOTON STRUCTURE

In a hard collision involving an incoming pho-ton, this photon may scatter directly, or it mayfirst fluctuate into a hadronic object. Although itis no longer considered possible to make a com-plete prediction of the photon’s structure withoutinput from experiment, measurements that aresensitive to the hadronic nature of the photon cannevertheless provide a test of some fundamentalhypotheses.In e+e− collisions, the photon’s structure func-

tion F γ2 is probed in deep inelastic scattering

9

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500

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1500

dσπ /

dx

/ nb

inclusive forward πo cross sections

H1 preliminarypT,π > 2.5 GeV

Q2 / GeV2

[ 2.0 ... 4.5 ]

[ 4.5 ... 15.0 ]

[ 15.0 ... 70.0 ]

LEPTO 6.5

RAPGAP 2.06

LO BFKL

0

200

400

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50

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10-4

10-3

x

Figure 9. The inclusive π0 cross sections as afunction of x for three ranges of Q2, together withthe predictions of MC models and the BFKL cal-culation of [ 32].

processes where one of the leptons is scatteredthrough a large angle. F γ2 is expressed as a func-tion of the fraction of the photon’s energy partic-ipating in the scatter, x, at the resolution scaleprovided by the square of the momentum trans-fer at the scattered lepton vertex, Q2. Fig. 10shows the latest world measurements of F γ2 (x)/αat medium Q2 [ 34]. The available photon par-ton density parametrizations are generally able todescribe the data.At HERA, the partons of the proton probe di-

rectly, not only the quark density, but also thegluon density of the photon. Here the resolu-tion scale of the probe is measured in terms ofthe transverse momenta of the jets or tracks pro-duced. In Fig. 11 an extraction of the leadingorder gluon density of the photon is shown [ 35].Here the probing resolution for the jet analysisis 〈P 2T 〉 = 74 GeV2 and for the track analysis〈P 2T 〉 = 38 GeV2. The different experimental ap-

proaches both indicate a rise of the leading ordergluon density as xγ falls.At high values of the resolution power it be-

comes possible to describe the high-x quark com-ponent of the photon’s structure using quark par-ton model predictions alone, as shown in Fig. 12 [34]. The experimental constraint on the pho-ton’s structure coming from the e+e− experi-ments, however, grows weak here.ZEUS has measured dijet cross sections

in photoproduction in this high scale region(EjetT leading, second > 14, 11 GeV) as shown inFig. 13 [ 36]. Next-to-leading order perturbativeQCD calculations using current photon partondensities are unable to describe these data whenboth jets are in the central region, 0 < ηjet1,2 < 1.As other uncertainties are expected to be low inthis kinematic regime, it would be a good testof our understanding of photon-induced processesto check whether a parton density can be foundwhich allows the ZEUS data to be described whileremaining consistent with the available high-Q2

F γ2 measurements from LEP.An interesting alternate process, which may re-

veal information on the photon’s structure, comesfrom prompt photon production in γγ and γpcollisions. Prompt photon cross sections have

〈Q2〉 = 11 GeV2 L3(Phojet)

OPAL(Herwig)

Fγ 2(x

)/α

〈Q2〉 = 15 GeV2 DELPHI(Twogam)

ALEPH(Herwig)

GRV-HO

〈Q2〉 = 23 GeV2

SaS-1d

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Figure 10. F γ2 /α at medium Q2 from LEP.

10

xγ

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Figure 11. Measurement of the gluon densityin the real photon from dijet and high pT trackevents.

L3 〈Q2〉 = 120 GeV2Prel

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0

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Figure 12. F γ2 /α at high Q2 from LEP.

the potential to be free of theoretical uncertain-ties arising from hadronization effects. Both theZEUS [ 37] and TOPAZ [ 38] collaborations pre-sented early studies of prompt photon productionbut a considerable improvement in statistics isnecessary before any strong conclusions may bedrawn.

8. VIRTUAL PHOTON STRUCTURE

It is expected that as a photon’s virtuality in-creases, it will begin to lack the time to developa complex hadronic structure.From the total cross section for the double-tag

process, e+e− → e+e−γ∗γ∗ → e+e−X , there isan indication that the hadronic component of thephoton’s structure is still evident at sizeable pho-ton virtualities [ 39].ZEUS has measured the ratio of the low-xγ di-

jet cross section to the high-xγ dijet cross sec-tion as a function of the photon’s virtuality Q2 atthe probing scale provided by EjetsT > 5.5 GeV,Fig. 14 [ 36]. This ratio is flat for a parton den-sity that does not evolve with Q2 (GRV LO) andfalling for a parton density that is suppressed withQ2 (SaS 1D). Therefore the fall that is observedin the data indicates that the photon’s partondensity is suppressed as the photon’s virtualityincreases.H1 present the effective parton density of the

photon, f̃γ , as a function of Q2 in Fig. 15 [

35]. The data are consistent with parton den-sities which fall logarithmically with Q2 and areinconsistent with a pure vector meson dominance

Figure 13. Dijet cross section as a function of ηjet2in bins of ηjet1 and for 0.50 < y < 0.85.

11

0

0.5

1

1.5

2

2.5

3

3.5

4

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5

ZEUS Preliminary 1995Energy Scale UncertaintyHerwig with GRV LOHerwig with SaS1DLepto

Q2 (GeV2)

σ(x γ

< 0

.75)

/σ(x

γ > 0

.75)

Figure 14. Ratio of the dijet cross section forxOBSγ < 0.75 to the dijet cross section for x

OBSγ >

0.75.

α-1 xf~ γ

α-1 xf~ γ

Figure 15. Leading order effective parton den-sity of the photon as a function of Q2 at P 2T =85 GeV2.

ansatz for the photon’s structure.

9. JET SUBSTRUCTURE IN PHOTON-

INDUCED COLLISIONS

The measurement of jet substructure inphoton-induced collisions has been used to studyuniversal properties of fragmentation.Jet shapes measured in deep inelastic scatter-

ing and in γγ collisions are compared in the toprow of Fig. 16 [ 38]. The comparison is made

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

1.2

1.4

0 0.2 0.4 0.6 0.8 1r

ψ(r

)γp, 10

12

rapidity [ 37]. It is found that 〈nsubjet〉 increases

Figure 17. Number of subjets at ycut = 0.01 as afunction of ηjet.

as expected from the predominance of gluon jetsin the forward region.

10. INCLUSIVE PHOTONS IN pp̄ COL-LISIONS

Inclusive photon results from the Tevatron werepresented, where the CDF and DØ data were seento be consistent with each other [ 40]. The CDFdata reach lower photon pT values where the crosssection tends to be higher than theory calcula-tions. This shape difference is difficult to explainwith current NLO QCD calculations. Best fits areobtained with the kT smearing procedure used toexplain the E706 photon data. A kT smearingof about 3.5 GeV is needed to explain the data.The result is shown in Fig. 18. In the same talk ahigh statistics measurement of photon-muon pro-duction was also presented, which compares wellwith NLO QCD.

Figure 18. The CDF measurement of the inclu-sive photon pT spectrum.

11. JET RESULTS FROM THE TEVA-

TRON

Results were presented on subjet multiplicityin quark and gluon jets at DØ [ 41]. Jets areidentified using the kT jet algorithm, which hasthe advantage of being IR-safe and allows a moredirect comparison between theory and measure-ments. The gluon jet fraction was determined at√s = 1800 GeV and

√s = 620 GeV. The results

indicate that there are more subjets at√s = 1800

GeV as well as more subjets in gluon jets.In the joint session with the structure func-

tion working group, both CDF and DØ presentedresults on the inclusive jet cross section [ 42] [43]. When the CDF run IA results were pub-lished, they showed an excess of events at highET with respect to QCD expectations using par-ticular parton density functions. This excess gen-erated a lot of interest, and explanations rangedfrom quark substructure to modified parton den-sity functions. The preliminary CDF measure-ment from the IB run is based on an integratedluminosity of 87.7 pb−1 and is in agreement withthe Run IA measurement. DØ presented recentlypublished results which are consistent with QCDpredictions. Improved energy calibrations at DØallowed them to reduce the systematic errors to

13

10% at low ET and to about 30% at high ET . Acomparison of CDF data with DØ data is shownin Fig. 19, where the results are seen to be con-sistent. It appears that the behaviour at high ET

0

0.5

(Dat

a-T

heo

ry)/

Th

eory

CTEQ4HJ, µ = 0.5 ET max , Rsep= 1.3 0.1 < |ηjet| < 0.7

CDF (94-95) Data

DØ (94-95) Data

0

10

20

30

50 100 150 200 250 300 350 400 450ET (GeV)

Un

cert

ain

ty (

%)

CDF (94-95)

DØ

Figure 19. The CDF and DØ measurements ofthe inclusive jet cross section.

can be accommodated by enhancing the gluon athigh x as is done in the CTEQ PDFs. A more sen-sitive search for quark substructure can be con-ducted using either the dijet mass distribution ordijet angular distribution and will be discussedlater.A consistency check of αs from jet data was

presented by CDF [ 43]. The technique extractsαs from a third-order equation where the coeffi-cients are calculated assuming a particular PDFand value of αs. By varying αs one can checkfor a consistent solution where the extracted αsequals the input value. The method depends onthe choice of PDF since different PDFs result ina different αs. The results show the running ofαs in one experiment and yield a result consistentwith measured αs from other experiments.Both CDF and DØ presented the ratio of the

scaled cross section for a centre-of-mass energy of630 and 1800 GeV as a function of xT [ 42] [ 43].The ratio allows a reduction of the uncertainty

due to theory and experiment. Above values ofxT = 0.1 the CDF and DØ measurements agree,while at lower xT values the measurements di-verge. The DØ data tend to higher ratio valueswhile the CDF results tend to lower values as isshown in Fig. 20.

0

0.5

1

1.5

2

2.5

3

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5Jet Xt

Ratio

of S

cale

d Cr

oss

Sect

ions

CDF Preliminary Data 0.1 < |ηjet| < 0.7D0 Data |ηjet| < 0.5

Figure 20. Ratio of the scaled cross section forcentre-of-mass energies of 1800 and 630 GeV as afunction of xT as measured by CDF and DØ.

DØ also presented the rapidity dependence ofthe inclusive jet cross section for three differentη bins up to η < 1.5 [ 42]. Results were in goodagreement with NLO QCD calculations.Both CDF and DØ presented measurements on

the dijet mass distribution [ 44] [ 45]. Resultsfrom the two experiments are in good agreementin both shape and normalization. DØ has usedthe measurement to place limits on quark com-positeness as is shown in Fig 21. Dijet angu-lar distributions provide a sensitive test of newphysics and have the advantage that the distri-butions are less sensitive to the energy measure-ment uncertainty. Results were presented fromCDF and used to place limits on quark compos-iteness.DØ presents the differential dijet cross section

separately for opposite-side jets and same-side

14

0.5

0.75

1

1.25

1.5

200 400 600 800M (GeV/c

2)

Cro

ss s

ecti

on

rati

o

JETRAD: CTEQ3M, µ = 0.5ET

max, Rsep

=1.3R

Λ+ =1.5 TeV

Λ

+ =2.0 TeV

Λ+ =2.5 TeV

Λ+ =3.0 TeV

DØ Data

Figure 21. Limits placed on compositeness mod-els using the DØ dijet mass data

jets [ 44]. Both jets are required to sit in the sameη bin. Results were compared to the JETRADcalculation using different PDFs. Dijet differen-tial cross sections from CDF were shown wherethe central jet was used to measure the ET of theevent [ 45]. A second jet is allowed to fall in oneof four η bins. A quantitative comparison of dif-ferent PDFs is under way. The differential dijetmeasurement covers a plane in the x–Q2 space,making it more sensitive to the shape of the crosssection determined by different PDFs. The datawill provide a useful input to QCD fits in orderto determine refined PDFs.

12. CONCLUSIONS

At this meeting many beautiful, high-precisionexperimental results were presented and com-pared with theoretical predictions. QCD has beenclearly established as a successful theory for thedescription of hard scattering processes. It isnow increasingly important to better understandsoft non-perturbative phenomena and processeswhere more than one hard scale plays a part.The further development of power corrections andresummed calculations as well as the calculationof QCD cross sections at next-to-next-to-leadingorder is under way. This program will eventu-

Frac

tiona

l Diff

. fro

m N

LO

QC

D a)

ET(1) (GeV)

% e

rror

Systematic Uncertainty

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

50 100 150 200 250 300 350 400

0

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40

50 100 150 200 250 300 350 4000

20

40

50 100 150 200 250 300 350 400

Frac

tiona

l Diff

. fro

m N

LO

QC

D b)

ET(1) (GeV)

% e

rror

Systematic Uncertainty

-0.20

0.20.40.60.8

11.21.41.61.8

50 100 150 200 250 300 350 400

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20

40

50 100 150 200 250 300 350 4000

20

40

50 100 150 200 250 300 350 400

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tiona

l Diff

. fro

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LO

QC

D c)

ET(1) (GeV)

% e

rror

Systematic Uncertainty

-0.2-0.1

00.10.20.30.40.50.60.70.80.9

50 100 150 200 250

0

20

40

50 100 150 200 2500

20

40

50 100 150 200 250

Frac

tiona

l Diff

. fro

m N

LO

QC

D d)

ET(1) (GeV)

% e

rror

Systematic Uncertainty

-0.20

0.20.40.60.8

11.21.41.61.8

22.2

50 100 150 200

0

20

40

50 100 150 2000

20

40

50 100 150 200

Figure 22. Triple differential dijet cross section.

ally lead to an even more stringent comparisonof theory and experiment. The development ofthese concepts should benefit greatly from contin-ued close communication between theorists andexperimentalists.

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