The inclusive one- and two-jet cross-sections are measured in collisions of
quasi-real photons at e+e- centre-of-mass energies of 130 and 136 GeV using the
OPAL detector at LEP. Jets are reconstructed with a cone jet finding algorithm.
The jet cross-sections are compared to next-to-leading order (NLO) perturbative
QCD calculations. Transverse energy flows in jets are studied separately for
direct and resolved two-photon events.Comment: 4 pages, 6 Postscript figures, uses stwol.st

Soldner-Rembold, Stefan

English

arXiv

The inclusive one- and two-jet cross-sections are measured in collisions of quasi-real photons at e+e- centre-of-mass energies of 130 and 136 GeV using the OPAL detector at LEP. Jets are reconstructed with a cone jet finding algorithm. The jet cross-sections are compared to next-to-leading order (NLO) perturbative QCD calculations. Transverse energy flows in jets are studied separately for direct and resolved two-photon events

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arXiv:hep-ex/9609018v1  27 Sep 1996FREIBURG-EHEP-96-01 1JET PRODUCTION IN PHOTON-PHOTON INTERACTIONS ∗STEFAN SO¨LDNER-REMBOLDAlbert-Ludwigs-Universita¨t Freiburg, Fakulta¨t fu¨r Physik, D-79104 Freiburg im Breisgau, GermanyOn behalf of the OPAL collaborationThe inclusive one- and two-jet cross-sections are measured in collisions of quasi-real photons at e+e− centre-of-mass energies√see = 130 and 136 GeV using the OPAL detector at LEP. Jets are reconstructed with a conejet finding algorithm. The jet cross-sections are compared to next-to-leading order (NLO) perturbative QCDcalculations. Transverse energy flows in jets are studied separately for direct and resolved two-photon events.1 IntroductionWe present measurements of jet production in γγinteractions at√see of 130 and 136 GeV. The jetcross-sections are compared to predictions of per-turbative QCD which use different parametrisa-tions of the photon structure function.In the Quark Parton Model (QPM) jets areproduced by the interaction of bare photons, γγ →qq. This is called the direct process. The largestpart of the total cross-section, however, is mod-elled by interactions where the photon fluctuatesinto a hadronic state. The processes are calledsingle-resolved if one photon couples directly to aparton in the other photon and double-resolved ifpartons from both photons interact.2 Data analysis andMonte Carlo simulationTwo-photon events are selected by requiring thatthe sum of all energy deposits in the calorime-ters is less than 50 GeV. The hadronic invariantmass, WECAL, measured in the electromagneticcalorimeter has to be greater than 3 GeV; themissing transverse energy of the event has to beless than 5 GeV; at least 5 charged tracks musthave been found and no track may have a momen-tum greater than 15 GeV/c.To remove events with scattered electrons inthe forward detectors, the energy measured inthese detectors has to be less than 40 GeV (20GeV) depending on the angular range, corre-sponding to an effective maximum photon virtual-ity, Q2max, of 0.8 GeV2 (“anti-tagging condition”).For an integrated luminosity of 4.9 pb−1, 7808∗To be published in the proceedings of ICHEP’96,Warsawevents remain after all cuts. The average vis-ible hadronic invariant mass Wvis is about 18GeV. The total background from other processesis about 1 %.OPALx+gEventsPYTHIAPHOJETdirect010203040506070800 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Figure 1: The number of two-jet events as a function ofx+γ compared to PHOJET and PYTHIA. Statistical errorsonly are shown. The hatched histogram is the direct con-tribution to the PYTHIA events.The leading order (LO) QCD generatorsPYTHIA 5.721 1 and PHOJET 1.05 2 are usedfor the γγ event simulation. The fragmentationis handled by JETSET 7.408 1.3 Jet reconstruction and backgroundsIn the cone jet finding algorithm a jet is definedas a set of particles, i. e. partons or hadrons gen-erated in a Monte Carlo program, or tracks andcalorimeter clusters, whose momenta lie within acone of size R, such that the axis of the cone co-incides with the momentum sum of the particlescontained. The cone size R, which is chosen to beR = 1, is defined as R =√(∆η)2 + (∆φ)2, withη = − ln tan(θ/2) being the pseudorapidity and φthe azimuthal angle in the laboratory frame. ∆ηand ∆φ are the differences between the cone axisand the particle direction. The total transverseenergy EjetT of the jet (defined with respect to thebeam axis) is the scalar sum of the transverse en-ergies ETi of its components. The pseudorapidityηjet and the azimuthal angle φjet are defined asthe sum over the ηi and φi of the jet componentsweighted by their transverse energies ETi :ηjet =∑iETiηi∑i ETiand φjet =∑i ETiφi∑iETi.All results are given for jets with EjetT > 3 GeVand |ηjet| < 1.4 Energy flow in jet eventsIn γp scattering, direct and resolved two-jetevents, which correspond to the single- anddouble-resolved events in γγ scattering if the pro-ton is substituted in the place of a VMD-like pho-ton, have been identified by measuring the fractionxγ of the photon energy participating in the hardscattering3. In γγ scattering two photons interact,therefore a pair of variables is defined 4x±γ =∑jets(E ± pz)∑hadrons(E ± pz), (1)where pz is the momentum component along thez axis of the detector and E is the energy. Ide-ally, the total energy of the event is containedin the two jets for direct events without remnantjets, i. e. x±γ = 1, whereas for resolved events atleast one of the x±γ values is expected to be muchsmaller than one. The variables x±γ are measuredusing all tracks and calorimeter clusters that wereused in the jet finding algorithm. In addition, theenergies in the forward detectors, which are notused for jet finding and for the energy flow distri-butions, are added in the denominator of Eq. 1.This improves the separation of direct and re-solved events.Figure 1 shows the number of two-jet eventsas a function of x+γ , together with the PYTHIAand PHOJET samples, after the detector simula-tion. The x−γ distribution, which is not shown, isconsistent with the x+γ distribution within the sta-tistical errors. The peak expected for direct eventsat x+γ = 1 is smeared out due to higher orderQCD, hadronisation and detector resolution ef-fects. Only statistical errors are shown, since sys-tematic effects largely cancel in the ratio (Eq. 1).The direct events, which are shown sepa-rately for the PYTHIA sample, mainly contribute024681012141618-2 -1 0 1 2-2 -1 0 1 202468101214-2 0 2Dh¢1/Njet dET/dDh¢ [GeV](a)min(x+g,x-g)<0.8OPAL (b)min(x+g,x-g)>0.8OPAL DataPHOJETPYTHIADh¢Df1/Njet dET/dDf [GeV](c)min(x+g,x-g)<0.8OPAL (d)min(x+g,x-g)>0.8OPALDf-2 0 2Figure 2: Transverse energy flow measured relative to thedirection of the jet in two-jet events. Jets from eventswith min(x+γ , x−γ ) < 0.8 (a,c) and min(x+γ , x−γ ) > 0.8 (b,d)are shown separately. The energy flow is integrated over|∆φ| < pi/2 for the ∆η′ projection (a,b) and over |∆η′| < 1for the ∆φ projection (c,d). Statistical errors only areshown.in the region x+γ > 0.8. Experimentally, sam-ples with large and small direct contributions areseparated by requiring min(x+γ , x−γ ) > 0.8 andmin(x+γ , x−γ ) < 0.8, respectively. About 95 % ofall events in the region min(x+γ , x−γ ) > 0.8 origi-nate from direct interactions in PYTHIA.Figure 2 shows the transverse energy flows1NjetdETd(∆η′)and1NjetdETd(∆φ)(2)with respect to the jet direction for two-jet eventswith min(x+γ , x−γ ) < 0.8 (low xγ) and withmin(x+γ , x−γ ) > 0.8 (high xγ), separately. Theshape of the selected jet is seen clearly in both ∆η′and ∆φ. No detector correction has been applied.The same tracks and clusters which are used forjet finding are included, with∆η′ = k(η − ηjet) and ∆φ = φ− φjet. (3)The rapidity difference is multiplied by a factork = ±1. The factor k is chosen event-by-event tobe k = +1 for events with x+γ > x−γ and k = −1for events with x+γ < x−γ . Due to the choice of k,there is always more energy flow at ∆η′ < 0.2In Fig. 2, a pedestal is observed which couldindicate the existence of a photon remnant. Asexpected, this enhancement in the region around|∆φ| ≈ pi/2 and at |∆η′| > 1 is more pronouncedfor low xγ events. The jets in high xγ events aremuch more back-to-back in ∆φ (Fig. 2d) than inlow xγ events (Fig. 2c). The pedestal in the ∆φ re-gion between the two jets at |∆φ| ≈ pi/2 is not ob-served in the high xγ events. Jets in high xγ eventsare also observed, on average, to have more aver-age transverse energy and to be more collimated.This is as expected for direct events, where all theavailable energy is used in the hard subsystem.Both Monte Carlo models describe the transverseenergy flow reasonably well, except for an under-estimate in the central region around the jet axis.Nevertheless the overall modelling is sufficientlygood to justify using the Monte Carlo models forunfolding the detector resolution effects in the jetcross-section measurements.5 Inclusive jet cross-sectionsThe one- and two-jet cross-sections shown in Fig. 3are corrected to the hadron level using the methodof regularised unfolding. The main systematic un-certainty on the jet cross-sections originates fromvarying the energy scale of the ECAL in the MonteCarlo simulation by ±5 % and from the unfoldingprocedure. The model dependence of the unfold-ing is taken into account by adding to the system-atic error the difference between the results ob-tained with PYTHIA, which are taken to be thecentral values, and PHOJET.The EjetT distribution is compared to a NLOperturbative QCD calculation of the inclusive one-jet cross-section by Kleinwort and Kramer 5 whouse the NLO GRV parametrisation of the pho-ton structure function 6. Their calculation wasrepeated for the kinematic conditions of this anal-ysis. All scales are chosen to be equal to EjetT .The strong coupling αs is calculated from the two-loop formula with Λ(5)MS= 130 MeV. The ratioof the NLO to the LO inclusive one-jet cross-section decreases from about 1.19 to 1.03 betweenEjetT = 3 GeV and EjetT = 16 GeV.The direct, single- and double-resolved partsof the one-jet cross-section and their sum areshown separately. The agreement between dataand the calculation is good. The resolved cross-sections dominate in the region EjetT<∼ 5 GeV,whereas, at high EjetT the direct cross-section islargest. The EjetT distribution falls less steeplythan expected in γp and pp interactions, becausethe fraction of hard interactions rises from pp toγp to γγ interactions, due to the additional directphoton interactions. It should be noted that theNLO QCD calculation gives the jet cross-sectionfor massless partons, whereas the jet cross-sectionsare measured for hadrons.The inclusive two-jet cross-section is measuredfor events with at least 2 jets using the two jetswith the highest EjetT in an event. The EjetT distri-bution is also compared to the NLO calculations5,which have been extended to include the full NLOcalculation for the double-resolved two-jet cross-section. The increase of the NLO compared to theLO inclusive two-jet cross-section is less than 10 %in the calculation.The inclusive one- and two-jet cross-sectionsas a function of |ηjet| are shown in Fig. 4. Withinthe uncertainties of the measurement, the distri-butions are nearly independent of |ηjet| in agree-ment with the expectations of the Monte Carlomodels.The total cross-sections, which are dominatedby the low EjetT events, depend on the photonstructure function. In Fig. 4 the total jet cross-sections predicted by the two Monte Carlo mod-els differ significantly even if the same photonstructure function (here SaS-1D) is used. Thismodel dependence reduces the sensitivity to theparametrisation of the photon structure function.Different parametrisations were used as input tothe PHOJET simulation. The GRV-LO and SaS-1D parametrisations describe the data equallywell, but the LAC1 parametrisation 7 overesti-mates the total jet cross-section by about a factorof two.6 ConclusionsWe have measured jet production in γγ interac-tions with the OPAL detector at√see of 130 and136 GeV, using a cone algorithm with R = 1,EjetT > 3 GeV and |ηjet| < 1.Two-jet events originating from direct andresolved photon interactions were separated ex-perimentally using x±γ . Jets in events withmin(x+γ , x−γ ) > 0.8 are expected to be produced3ETjet [GeV]ds/dE Tjet  [pb/GeV] OPAL|h jet| < 1NLO QCDdirectsingle-res.double-res.10-111010 24 6 8 10 12 14 16ETjet [GeV]ds/dE Tjet  [pb/GeV]|h jet1|,|h jet2| < 1OPALNLO QCDdirectsingle-res.double-res.10-111010 24 6 8 10 12 14 16Figure 3: The inclusive one-jet (upper plot) and two-jet(lower plot) cross-sections as a function of EjetTcomparedto the NLO calculation by Kleinwort and Kramer5. The di-rect, single-resolved and double-resolved cross-sections andthe sum are shown separately.|h jet|ds/d|hjet | [pb]OPAL ETjet > 3 GeVPHOJET SaS-1DPHOJET LAC1PHOJET GRVPYTHIA SaS-1D01002003004005006000 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1|h jet|ds/d|hjet | [pb]OPAL ETjet1,ETjet2 > 3 GeVPHOJET SaS-1DPHOJET LAC1PHOJET GRVPYTHIA SaS-1D0501001502002500 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Figure 4: The inclusive one-jet (upper plot) and two-jet(lower plot) cross-sections as a function of |ηjet| comparedto the LO QCD calculations of PYTHIA and PHOJET.mainly from direct interactions. These jets areobserved to have, on average, more average trans-verse energy and to be more collimated thanjets in resolved events with min(x+γ , x−γ ) < 0.8.In resolved events a pedestal is observed in thetransverse energy flows which may be related tothe photon remnant. The Monte Carlo modelsPYTHIA and PHOJET describe the transverseenergy flow distributions reasonably well.The inclusive one-jet and two-jet productioncross-sections were measured as a function of EjetTand |ηjet|. The measurement extends the EjetTrange of previous measurements 8 up to EjetT =16 GeV. The EjetT dependent one- and two-jetcross-sections are in good agreement with NLOQCD calculations 5.Within the uncertainties of the measurements,the jet cross-sections are nearly independent of|ηjet| for |ηjet| < 1. The total jet cross-sectionis dominated by the resolved cross-section. Giventhe model dependence of the jet cross-sections inPYTHIA and PHOJET, the GRV-LO and SaS-1Dparametrisations describe the data equally well.The LAC1 parametrisation overestimates the to-tal jet cross-section by about a factor of two.References1. T. Sjo¨strand, Comp. Phys. Commun. 82(1994) 74; G. A. Schuler and T. Sjo¨strand,CERN-TH/96-119.2. R. Engel and J. Ranft, ENSLAPP-A-540/95and SI 95-08 (1995), to be publ. in Phys.Rev. D; R. Engel, Z. Phys. C66 (1995) 203.3. ZEUS Collab., M. Derrick et al., Phys. Lett.B322 (1994) 287; H1 Collab., T. Ahmedet al., Nucl. Phys. B445 (1995) 195.4. L. Lo¨nnblad and M. Seymour (convenors),γγ Event Generators, in “Physics at LEP2”,CERN 96-01, Vol. 2 (1996) 187.5. T. Kleinwort and G. Kramer, DESY-96-035(1996); Phys. Lett. B370 (1996) 141 andprivate communication.6. M. Glu¨ck, E. Reya, A. Vogt, Phys. Rev. D46(1992) 1973; Phys. Rev. D45 (1992) 3986.7. H. Abramowicz, K. Charchula, A. Levy,Phys. Lett. B269 (1991) 458.8. AMY Collab., B. J. Kim et al., Phys.Lett. B325 (1994) 248; TOPAZ Collab., H.Hayashii et al., Phys. Lett. B314 (1993) 149.4

Jet Production in Photon-Photon Interactions

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