The total hadronic cross-section for the interaction of real photons is
extracted from a measurement of the cross-section of the process e+e->e+e- +
hadrons using a luminosity function for the photon flux and form factors for
extrapolating to Q**2=0. The data was taken with the OPAL detector at LEP at
e+e- centre-of-mass energies of 161 GeV and 172 GeV. In the energy range 10 < W
< 110 GeV the total hadronic photon-photon cross-section is consistent with the
Regge behaviour of the total cross-section observed in \gamma p and
hadron-hadron interactions.Comment: 7 pages, 7 figues, needs espcrc2.sty, to be published in proceedings
  of the XXVII INTERNATIONAL SYMPOSIUM ON MULTIPARTICLE DYNAMICS, INFN,
  Frascati (Rome), Italy, 8-12 September 199

Acciarri

Aihara

Baru

Berger

Blobel

Budnev

Capella

Donnachie

Engel

Frank Wäckerle

Glück

Kolanoski

Schuler

Sjöstrand

English

arXiv

Crossref

Nuclear Physics B - Proceedings Supplements

Total hadronic cross-section for photon-photon interactions at LEP

The total hadronic cross-section for the interaction of real photons is extracted from a measurement of the cross-section of the process e+e->e+e- + hadrons using a luminosity function for the photon flux and form factors for extrapolating to Q**2=0. The data was taken with the OPAL detector at LEP at e+e- centre-of-mass energies of 161 GeV and 172 GeV. In the energy range 10 < W < 110 GeV the total hadronic photon-photon cross-section is consistent with the Regge behaviour of the total cross-section observed in \gamma p and hadron-hadron interactions

Wäckerle, F

CERN Document Server

FREIBURG-EHEP-97-17 1Total Hadronic Cross-Section for Photon-Photon Interactions at LEP Frank Wa¨ckerleaaFakulta¨t fu¨r Physik, Albert-Ludwigs-Universita¨t Freiburg, GermanyThe total hadronic cross-section γγ for the interaction of real photons, γγ ! hadrons, is extracted froma measurement of the cross-section of the process e+e− ! e+e−γγ ! (e+e− + hadrons) using a luminosityfunction for the photon flux and form factors for extrapolating to Q2 = 0. The data was taken with the OPALdetector at LEP at e+e− centre-of-mass energiespsee = 161 GeV and 172 GeV. In the energy range 10  W 110 GeV the total hadronic γγ cross-section γγ is consistent with the Regge behaviour of the total cross-sectionobserved in γp and hadron-hadron interactions.1. IntroductionAt high γγ centre-of-mass energies W =psγγthe total cross-section for the production ofhadrons in the interaction of two real photons isexpected to be dominated by interactions wherethe photon has fluctuated into an hadronic state.Measuring thepsγγ dependence of the totalhadronic γγ cross-section γγ should thereforeimprove our understanding of the hadronic na-ture of the photon and the universal high energybehaviour of total hadronic cross-sections.Before LEP the total hadronic γγ cross-sectionhas only been measured for γγ centre-of-massenergies W below 10 GeV by PLUTO [1],TPC/2γ [2] and the MD1 experiment [3] wherethe high energy rise of the total cross-sectioncould not have been observed. Using LEP datataken at e+e− centre-of-mass energiespsee =130 − 161 GeV, L3 [4] has demonstrated thatthe total hadronic γγ cross-section in the range5  W  75 GeV is consistent with the univer-sal Regge behaviour of total cross-sections. Wepresent a measurement of the total hadronic γγcross-section in the range 10 < W < 110 GeVusing OPAL data taken atpsee = 161 GeV and172 GeV.Talk given at the XXVII INTERNATIONAL SYMPO-SIUM ON MULTIPARTICLE DYNAMICS, LaboratoriNazionali di Frascati - INFN, Frascati (Rome), Italy, 8-12 September 19972. KinematicsThe kinematics of the process e+e− ! (e+e−+hadrons) at a givenpsee can be described by thenegative square of the four-momentum transfers,Q2i = −q2i , carried by the two (i = 1; 2) incom-ing photons and by the square of the invariantmass of the hadronic nal state, W 2 = sγγ =(q1 + q2)2 [5]. Events with detected scatteredelectrons (single-tagged or double-tagged events)are excluded from the analysis. This anti-taggingcondition denes an eective upper limit Q2max onthe values of Q2i for both photons. This conditionis met when the scattering angle 0 of the electronis less than the angle max = 32 mrad between thebeam axis and the inner edge of the acceptanceof the detector or if the energy of the scatteredelectron is smaller than the minimum energy of35 GeV required for the tagged electron.3. Monte Carlo simulationThe leading order (LO) QCD Monte Carlo gen-erators PYTHIA 5.722 [6] and PHOJET 1.05c [7]are used to simulate photon-photon interactions.PYTHIA is based on a model by Schuler andSjo¨strand [8] and PHOJET has been developed byEngel based on the Dual Parton model (DPM) [9].The SaS-1D parametrisation of the parton distri-bution functions [10] is used in PYTHIA and theleading order GRV parametrisation [11] in PHO-JET. The fragmentation and decay of the partonnal state is handled in both generators by theroutines of JETSET 7.408 [6].2 FREIBURG-EHEP-97-174. Event selectionTwo-photon events are selected by requiringthat the visible invariant hadronic mass, WECAL,measured in the electromagnetic calorimeter(ECAL), has to be greater than 3 GeV. At least3 tracks must have been found in the event andthe sum of all energy deposits in the ECAL andthe hadronic calorimeter (HCAL) has to be lessthan 45 GeV. The missing transverse energy ofthe event measured in the ECAL and the forwardcalorimeters (FD) has to be less than 5 GeV. Notrack in the event has a momentum greater than30 GeV/c. Finally, to remove events with scat-tered electrons in the FD or the silicon tungstencalorimeter (SW), the energy measured in the FDhas to be less than 50 GeV and the energy mea-sured in the SW less than 35 GeV (anti-taggingcondition).Additional cuts are applied to reject beam-gasand beam-wall background. On average the trig-ger eciency for the lowest W range, 10 < W <30 GeV, is greater than 97% and it approaches100% for larger values of W .We use data corresponding to an integrated lu-minosity of 9.9 pb−1 atpsee = 161 GeV and10.0 pb−1 atpsee = 172 GeV. After applying allpreselection cuts 55169 events remain. From theMonte Carlo (MC) it is estimated that after allcuts about 4% of all remaining events are eγ pro-cesses with Q2 > 1 GeV2. The background fromother processes apart from beam-gas and beam-wall interactions amounts to less than 1%.5. W reconstructionFor measuring the total hadronic γγ cross-section γγ the value of W must be reconstructedfrom the hadronic nal state. After the eventselection a matching algorithm is applied in or-der to avoid double counting of particle momenta.The matching algorithm uses all the informationof the ECAL, the HCAL, the FD and the SWcalorimeters, as well as the tracking system. Thefour-momenta of the detected particles are usedto calculate the visible invariant mass Wvis.A cut Wvis > 6 GeV is applied to all prese-lected events. The Wvis distribution dN=dWvismeasured at 172 GeV is shown in Fig. 1 where Nis the number of selected events. They are welldescribed by the MC simulations which have beennormalized to the number of data events.11010 210 30 50 100Wvis [GeV]dN/dWvis [1/GeV] OPAL Preliminarydata-bg at 172 GeV(b)PHOJETPYTHIAbackgroundFigure 1. Wvis distribution for all selected eventswith Wvis > 6 GeV after background (bg) sub-traction atpsee = 172 GeV compared to MCpredictions. Statistical errors only are shown.6. Unfolding of the hadronic cross sectionThe dierential cross-section dee=dW for theprocess e+e− ! (e+e− + hadrons) has to be ob-tained from the Wvis distribution. The correla-tion between Wvis and the generated invariantmass W for all selected PHOJET and PYTHIAevents is shown in Fig. 2. The correlation isnot very good due to hadrons which are emit-ted at small polar angles . These hadrons areeither lost in the beam pipe or they are onlydetected with low eciency in the electromag-netic calorimeters in the forward regions (FD andSW). The acceptance for PYTHIA is about 15%lower than for PHOJET at W = 40 GeV and itapproaches the PHOJET acceptance of 60{65%FREIBURG-EHEP-97-17 30501000 50 100 150 200W [GeV]Wvis [GeV] OPAL Preliminary√see = 172 GeV(b)PHOJETPYTHIAFigure 2. Correlation between Wvis and the gen-erated invariant mass W atpsee = 172 GeV forMC events. The vertical bars show the standarddeviation (spread) of the Wvis distribution in eachbin. For illustration purposes the points havebeen shifted by 2 GeV.for W > 80 GeV (Fig. 3). The unfolding ofthese resolution eects, the correction for the de-tector acceptance and the background subtrac-tion is done by applying the unfolding programRUN [12]. The subtracted background does notinclude the remaining beam-gas and beam-wallinteractions. Since the chosen bin size is not muchlarger than the resolution, bin-to-bin correlationsare still sizeable.The dierential cross-section dee of the pro-cess e+e− ! (e+e− + hadrons) can be trans-lated into the cross-section γγ for the processγγ ! hadrons using the luminosity function Lγγfor the photon flux [7],[13],[14]deedy1dQ21dy2dQ22=γγ(W;Q21; Q22)d4Lγγdy1dQ21dy2dQ22;where y1 and y2 denote the fraction of the beamenergy carried by photons with y1y2  W 2=see(neglecting Q2). The cross-section for real pho-tons (Q2 = 0) is derived by using appropriateform factors F (Q2) which describe the Q2 depen-00.510 50 100 150W [GeV]Nsel/NgenOPAL Preliminary√see = 172 GeV(b)PHOJETPYTHIA(all)↑(diff.+el.)↓Figure 3. The ratio of the number of selectedevents, Nsel, to the number of generated events,Ngen, at a given generated invariant mass W atpsee = 172 GeV for MC events. The lower curvesgive this ratio for the diractive and elastic eventsseparately.dence of the hadronic cross-section:γγ(W;Q21; Q22) = F (Q21)F (Q22)γγ(W; 0; 0)The luminosity function Lγγ and the form factorsF (Q2) for the various W bins are obtained byapplying the program PHOLUM [7]. PHOLUMtakes into account both transverse and longitudi-nally polarized photons. The uncertainty of theextrapolation toQ2 = 0 is estimated to be 5{7.5%by comparing the GVDM model with a simple 0form factor [7]. This uncertainty is not includedin the systematic error of the measurement.7. Systematic errorsThe two data samples atpsee = 161 GeV and172 GeV were independently analysed and theresults for the total hadronic two-photon cross-section γγ are found to be in good agreementand are therefore averaged.Several distributions of the data are comparedto the PYTHIA and PHOJET simulations af-4 FREIBURG-EHEP-97-17ter detector simulation in order to study whetherthe general description of the data by the MCis suciently good to use it for the unfolding ofthe cross-section. The MC distributions are allnormalized to the data luminosity and the back-ground including the eγ events with Q2 > 1 GeV2is subtracted from the data.In both MC models about 20% of the cross-section is due to diractive and elastic events(e.g. γγ ! ). This fraction is almost inde-pendent of W for W > 10 GeV. The selectioneciency for the diractive and elastic events isvery small and, although the rate is almost thesame in both models, the selection eciencies arevery dierent. For a generated W of 50 GeV onlyabout 6% of all generated diractive and elasticevents are selected in PYTHIA, whereas about20% are selected in PHOJET (Fig. 3). Due tothe small acceptance the detector correction hasto rely heavily on the MC simulation for this classof events.Signicant discrepancies are found in the distri-bution of the charged multiplicity nch measuredin the tracking chambers (Fig. 4). Both MC mod-els signicantly underestimate the fraction of low-multiplicity events with nch < 6 and overestimatethe fraction of high-multiplicity events in compar-ison to the data.The energy EFD measured in the forward de-tectors (FD) is shown in Fig. 5 for all selectedevents with EFD > 2 GeV. The good agreementof data and MC at largeEFD shows that the back-ground from multihadronic Z0 events and deep-inelastic eγ events is small and that this remain-ing background is reasonably well described bythe MCFinally we plot the ratio PL=Evis of the lon-gitudinal momentum vector PL to the visible to-tal energy Evis (Fig. 6). The ratio PL=Evis ispeaked around 0.9 due to the Lorentz boost ofthe hadronic system. Data and MC are in rea-sonable agreement, dierent from the observa-tion in Ref. [4]. Studies of beam-gas and beam-wall events show that most of these events havePL=Evis > 0:85. The excess of the data over theMC seen at large PL=Evis is therefore consistentwith 2% remaining background from beam-gasbeam-wall events.010002000300040000 10 20 30nchdN/dn chOPAL Preliminarydata-bg at 172 GeV(b)PHOJETPYTHIAbackgroundFigure 4. nch distribution for all selected eventswith Wvis > 6 GeV after background subtractionatpsee = 172 GeV compared to MC predictions.Statistical errors only are shown.Based on these observations the following sys-tematic errors are taken into account in the mea-surement of the total cross-section: Both MC models describe the data equallywell. We therefore average the results ofthe unfolding. The dierence between thiscross-section and the results obtained by us-ing PYTHIA and PHOJET alone are takenas systematic error. For data and MC the cut on the chargedmultiplicity nch was increased from nch  3to nch  5. This systematically shiftsthe cross-sections to lower values, mainlyat small W . The unfolding was also re-peated using only data and MC events with3  nch  9. This variation systematicallyincreases the cross-section especially at highW where the average charged multiplicity ishigher than at low W . The shifts are usedas systematic errors. The systematic error due to the uncertaintyin the energy scale of the ECAL was esti-FREIBURG-EHEP-97-17 511010 210 310 20 30 40 50EFD [GeV]dN/dE FD [1/GeV] OPAL Preliminarydata-bg at 172 GeV(b)PHOJETPYTHIAbackgroundFigure 5. The distribution of the energy in theforward calorimeter, EFD, for all selected eventswith Wvis > 6 GeV after background subtractionatpsee = 172 GeV compared to MC predictions.Statistical errors only are shown.mated by varying the reconstructed ECALenergy in the MC by 5%. An overall normalisation uncertainty of 1%is due to the error on the luminosity mea-surement. The lower limit on the trigger eciency istaken into account by an additional system-atic error of 3% in the range 10 < W <38 GeV. It is estimated that about 2% of the selectedevents could be due to beam-gas or beam-wall interactions. This value is thereforetaken as additional systematic error.For the total error the statistical and the system-atic errors are added in quadrature. The valuesare given in Table 1.8. ResultsThe total hadronic cross-section γγ for theprocess γγ ! hadrons is shown in Fig. 7. In50001000015000-1 -0.5 0 0.5 1PL/EvisdN/d(PL/E vis)OPAL Preliminarydata-bg at 172 GeV(b)PHOJETPYTHIAFigure 6. The distribution of the ratio PL=Evisfor all selected events with Wvis > 6 GeV afterbackground subtraction atpsee = 172 GeV com-pared to MC predictions. Statistical errors onlyare shown.the region W  10 GeV the OPAL measurementis in agreement with the measurements at lowerenergies by PLUTO [1], TPC/2γ [2] within theexperimental errors.The OPAL measurement shows the rise in theW range 10 < W < 110 GeV which is characteris-tic for hadronic cross-sections. A similar rise wasobserved by the L3 experiment [4], but the valuesfor γγ are about 20% lower than the OPAL mea-surements. Several things should be noted whichcan explain parts of this discrepancy: First, theerrors are strongly correlated between the W binsin both experiments. Secondly, L3 has used PHO-JET for the unfolding, whereas for the OPALmeasurement the unfolding results of PHOJETand PYTHIA are averaged. The unfolded cross-section using PHOJET is about 5% lower thanthe central value. In both experiments the cross-sections obtained using PHOJET are lower thanthe cross-section obtained with PYTHIA.The total cross-section γγ is compared to sev-eral theoretical models. Based on the Donnachie-6 FREIBURG-EHEP-97-17W range (GeV) 10 { 16 16 { 26 26 { 38 38 { 56 56 { 80 80 {110γγ [nb] 385 394 398 433 485 536stat.error  4  3  4  6  8 15MC model 26  4 20 21 21 43nch cut+ 5− 42+ 13− 37+ 24− 25+ 45− 21+ 74− 27+ 95− 34ECAL scale 37 28 13  6  6  7luminosity  4  4  4  4  5  5trigger +12 +12 +12beam-gas − 8 − 8 − 8 − 9 −10 −11total syst. + 47− 62+ 34− 48+ 37− 36+ 50− 32+ 78− 36+105− 56total error + 47− 62+ 34− 48+ 37− 36+ 50− 32+ 78− 37+106− 58Table 1The total hadronic two-photon cross-section γγ and the contributions from the various systematic errors.Landsho model [15], we test the assumptionof a universal high energy behaviour of γγ, γpand pp cross-sections. The total cross-sections for hadron-hadron and γp collisions are well de-scribed by a Regge parametrisation of the form = Xs + Y s−; (1)whereps is the centre-of-mass energy of thehadron-hadron or γp interaction. The rst termin the equation is due to Pomeron exchange andthe second term is due to Reggeon exchange [16].The factors  = 0:07900:0011 and  = 0:46780:0059 are assumed to be universal and have beentaken from Ref. [16] together with the process de-pendent t values of the parameters X and Y forthe total hadronic γp and pp cross-sections. As-suming factorisation of the Pomeron term X , thetotal γγ cross-section can be related to the pp (orpp) and γp total cross-sections at high centre-of-mass energiespsγγ =psγp =pspp where thePomeron trajectory should dominate byγγ =2γppp: (2)This simple ansatz gives a reasonable descrip-tion of γγ . Schuler and Sjo¨strand [8] give a to-tal cross-section for the sum of all possible eventclasses in their model of γγ scattering where thephoton has a direct, an anomalous and a VMDcomponent. They consider the spread betweenthis prediction and the simple factorisation ansatzas conservative estimate of the theoretical band ofuncertainty. We also plot the prediction of Engeland Ranft [7] which is implemented in PHOJET.It is in good agreement with the L3 measurementand signicantly lower than the OPAL measure-ment. The steeper rise predicted by Engel andRanft is in agreement with both measurements.9. ConclusionsWe have measured the total cross-section of theprocess γγ ! hadrons in the range 10 < W <110 GeV using the OPAL detector at LEP.Both MC models used fail to describe severaldistributions related to the hadronic nal statelike the charged multiplicity distribution. Furtherimprovements of the description of the hadronicnal state are necessary to reduce the systematicerror of the measurement. It will also be impor-tant to gain a better understanding of the dirac-tive and elastic processes for which the detectioneciency is found to be small.With the LEP2 data the high energy behaviourof the total γγ cross-section can be studied for therst time, extending the accessible W values byone order of magnitude up to W = 110 GeV. Weobserve the rise of the total γγ cross-section char-acteristic for the high energy behaviour of totalhadronic cross-sections. A simple model based onRegge factorisation and a universal Donnachie-Landsho t to the total cross-sections of γp andFREIBURG-EHEP-97-17 7020040060080010001 10 10 2W [GeV]σγγ  [nb]OPAL PreliminaryL3PLUTO 1984TPC/2γ 1990MD-1 1991σγp2 /σppSchuler and SjöstrandEngel and Ranft (PHOJET)Figure 7. γγ as a function of W . The OPALmeasurement is compared to the measurementsby PLUTO [1], TPC/2γ [2], MD1 [3] and L3 [4].The inner error bars, which are sometimes smallerthan the symbol size, give the statistical er-rors and the outer error bars the total errors.The data are compared to model predictionsbased on a Donnachie-Landsho t to total cross-sections [15]. The solid line gives the predictionusing equation 2. The dotted line is the modelof Schuler and Sjo¨strand [8]. The model of En-gel and Ranft [7] used in PHOJET is shown asdashed line.pp data describes the data reasonably well.AcknowledgementsI want to thank R. Engel for many useful dis-cussions and for providing the program PHOLUMand the organizers for the nice and interestingconference.REFERENCES1. PLUTO Collaboration, Ch. Berger et al.,Phys. Lett. B149 (1984) 421.2. TPC/2γ Collaboration, H. Aihara et al.,Phys. Rev. D41 (1990) 2667.3. S. E. Baru et al., Z. Phys. C53 (1992) 219.4. L3 Collaboration, M. Acciarri et al., CERN-PPE/97-48 (1997).5. For a general review see: H. Kolanoski,Two-Photon Physics at e+e− Storage Rings,Springer-Verlag (1984).6. T. Sjo¨strand, Comp. Phys. Commun. 82(1994) 74; LUND University Report, LU-TP-95-20 (1995).7. R. Engel and J. Ranft, Phys. Rev. D54 (1996)4244;R. Engel, Z. Phys. C66 (1995) 203 and privatecommunications.8. G. A. Schuler, T. Sjo¨strand, Z. Phys. C73(1997) 677.9. A. Capella, U. Sukhatme, C. I. Tan, J. TranThanh Van, Phys. Rep. 236 (1994) 225.10. G. A. Schuler and T. Sjo¨strand, Z. Phys. C68(1995) 607.11. M. Glu¨ck, E. Reya, A. Vogt, Phys. Rev. D46(1992) 1973; Phys. Rev. D45 (1992) 3986.12. V. Blobel, DESY-84-118 (1984); Proc. 1984CERN School of Computing, Aiguablava,Spain, CERN 85-09 (1984); The RUN man-ual, unpublished.13. V. M. Budnev et al, Phys. Rep. 15 (1975)181-282.14. G. A. Schuler, CERN-TH/96-297 and hep-ph/961040 (1996).15. A. Donnachie and P. V. Landsho,Phys. Lett. B 296 (1992) 227.16. Review of Particle Physics, Phys. Rev. D54(1996) 191.

Total Hadronic Cross-Section for Photon-Photon Interactions at LEP

Total Hadronic Cross-Section for Photon-Photon Interactions at LEP

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