Total hadronic cross-section of photon-photon interactions at OPAL

ELSEVIER

PROCEEDINGS SUPPLEMENTS

Nuclear Physics B (Proc. Suppl.) 82 (2000) 232-238

www.elsevier.nl/locate/npe

Total hadronic cross-section of photon-photon interactions at OPAL Frank Wiickerle a aFakult~it ffir Physik, Albert-Ludwigs-Universit~it Freiburg, Germany The total hadronic cross-section a77 for the interaction of real photons, 3'3' -+ hadrons, is extracted from a measurement of the cross-section of the process e+e - -+ e+e-3'*7 * ~ e+e - + hadrons using a luminosity function for the photon flux and form factors for extrapolating to Q2 _- 0. The data was taken with the OPAL detector at LEP at e+e - centre-of-mass energies VfSee = 161 GeV, 172 GeV and 183 GeV. In the energy range 10 < W g 110 GeV the total hadronic 3'3' cross-section az~ is consistent with the Regge behaviour of the total cross-section observed in 7P and hadron-hadron interactions.

1. I N T R O D U C T I O N At high 77 centre-of-mass energies W = V ~ the total cross-section for the production of hadrons in the interaction of two real photons is expected to be dominated by interactions where the photon has fluctuated into an hadronic state. Measuring the W dependence of the total hadronic 77 cross-section aT~ should therefore improve our understanding of the hadronic nature of the photon and the universal high energy behaviour of total hadronic cross-sections. Before L E P the total hadronic 77 cross-section has only been measured for 77 centre-of-mass energies W below 10 GeV by P L U T O [1], T P C / 2 7 [2], P E P / 2 7 [3] and the MD1 experiment [4] where the high energy rise of the total cross-section could not have been observed. Using LEP data taken at e+e - centre-of-mass energies V~ee ---- 1 3 0 - 161 GeV, L3 [5] has demonstrated that the total hadronic 3'7 cross-section in the range 5 _< W _< 75 GeV is consistent with the universal Regge behaviour of total cross-sections. We present a measurement of the total hadronic 77 cross-section in the range 10 < W < 110 GeV using OPAL data taken a t V/See = 161 GeV, 172 GeV and 183 GeV.

incoming photons and by the square of the invariant mass of the hadronic final state, W 2 = (ql + q2) 2 [6]. Events with detected scattered electrons (single-tagged or double-tagged events) are excluded from the analysis. This anti-tagging condition defines an effective upper limit Qmax 2 on the values of Q2 for both photons. This condition is met when the scattering angle 0 t of the electron is less than the angle 8max = 33 mrad between the beam axis and the inner edge of the acceptance of the detector or if the energy of the scattered electron is smaller than the minimum energy of 20 GeV required for the tagged electron. 3. M O N T E

CARLO SIMULATION

The leading order (LO) QCD Monte Carlo generators P Y T H I A 5.722 [7] and P H O J E T 1.05c [8] are used to simulate photon-photon interactions. P Y T H I A is based on a model by Schuler and SjSstrand [9] and P H O J E T has been developed by Engel based on the Dual P a r t o n model (DPM) [10]. The SaS-1D parametrisation of the patton distribution functions [11] is used in P Y T H I A and the leading order GRV parametrisation [12] in P H O J E T . The fragmentation and decay of the parton final state is handled in both generators by the routines of J E T S E T 7.408 [7]. #

2. K I N E M A T I C S The kinematics of the process e+e - ~ e+e - + hadrons at a given v~ee can be described by the negative square of the four-momentum transfers, Q/2 = _ q 2 carried by the two (i = 1,2)

4. E V E N T

SELECTION

Two-photon events are selected by requiring that the visible invariant mass WECAL measured in the electromagnetic calorimeter (ECAL), has

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E W?ickerle/Nuclear Physics B (Proc. Suppl.) 82 (2000) 232-238

to be greater thaza 3 GeV. At least 2 tracks must have been found in the event and the sum of all energy deposits in the ECAL and the hadronic calorimeter (HCAL) has to be less than 45 GeV. The missing transverse energy of the event measured in the ECAL and the forward calorimeters (FD) has to be less than 5 GeV. No track in the event has a momentum greater than 30 GeV/c. Finally, to remove events with scattered electrons in the FD or the silicon tungsten calorimeter (SW), the energy measured in the FD has to be less than 40 GeV and the energy measured in the SW less than 20 GeV (anti-tagging condition). Additional cuts are applied to reject beam-gas and beam-wall background and leptonic events in the case where only 2 tracks were found in an event. We use data corresponding to an integrated luminosity of 9.9 pb -1 at V/-See = 161 GeV, 10.0 pb -1 at V~e~ = 172 GeV and 54.4 pb -~ at v/-See : 183 GeV. After applying all selection cuts 193040 events remain. From the Monte Carlo (MC) it is estimated that after all cuts about 1.5% of the remaining events are deep-inelastic e~ (= ~"7) processes with max{Q12, Q22} > 4.5 GeV 2 at V'~ee : 183 GeV. The background from other processes apart from beam-gas and beam-wall interactions amounts to less than 1.6%.

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6. U N F O L D I N G O F CROSS-SECTION

THE

HADRONIC

The differential cross-section daee/dW for the process e+e - --+ e+e - + hadrons has to be obtained from the W~is distribution. The relation between Wvis and the generated invariant mass W for all selected P H O J E T and PYTHIA events is shown in Fig. 2. The relation is not very good due to hadrons which are emitted at small polar angles 0. These hadrons are either lost in the beam pipe or they are only detected with low efficiency in the electromagnetic calorimeters in the forward regions (FD and SW). The selec-

5. W R E C O N S T R U C T I O N For measuring a~.~(W) the value of W must be reconstructed from the hadronic final state. After the event selection a matching algorithm is applied in order to avoid double counting of particle momenta. The matching algorithm uses all the information of the ECAL, the HCAL, the FD and the SW calorimeters, as well as the tracking system. The four-momenta of the detected particles are used to calculate the visible invariant m a s s Wvis. The Wvis distribution dNsel/dWvis measured at 183 GeV is shown in Fig. 1 where N~l is the number of selected events. They are well described by the MC simulations which have been normalized to the number of data events after background and e~/events have been subtracted.

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E Wdckerle/Nuclear Physics B (Proc. Suppl.) 82 (2000) 232-238

234

tion efficiency for PYTHIA is about 15% lower than for PHOJET at W ~ 40 GeV and it approaches the PHOJET acceptance of about 60% at W ~ 80 GeV (Fig. 3). The background de-

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termined by the Monte Carlo is first subtracted from the data. The subtracted background does not include the remaining beam-gas and beamwall interactions. Then, the regularized unfolding of the resolution effects, as well as the correction for the detector acceptance and the selection cuts are done with the program GURU [13]. The differential cross-sections for ,the three beam energies, daee/dW, after unfolding can be seen in Fig. 4. Since the chosen bin size is not much larger than the resolution, bin-to-bin correlations are still sizeable. The differential cross-section daee of the process e+e - --+ e+e - + hadrons can be translated into the cross-section a ~ for the process 7"/--+ hadrons using the luminosity function L ~ for the photon flux [14] daee dyldQ2dy2dQ~ = a,~,~(W, Q2, Q2) dy 1: Q_ _12~y~2dQ 2'

where Yl and Y2 denote the fraction of the beam energy carried by photons with yly2 "~ W2/see (neglecting Q2). The cross-section for real photons (Q: = 0) is derived by using appropriate

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form factors F(Q 2) which describe the Q2 dependence of the hadronic cross-section:

a,~,~(W, Q1Q , 2)2 2 = F(Q2)F(Q2)a,~,~(W,O,O) The luminosity function L ~ and the form factors F(Q 2) for the various W bins are obtained from the program PHOLUM [8] which performs a numerical integration for each W bin over the unmeasured phase space (Q2, Q2 and y ranges). PHOLUM takes into account both transverse and longitudinally polarized photons. The difference between the extrapolation to Q2 = 0 and Q22 = 0 is about 7% of a ~ if the GVMD model is compared to a simple p0 form factor [8]. This uncertainty is not included in the systematic error of the measurement. For the determination of a ~ , the e~ events simulated by HERWIG [15] are subtracted from the data and the photon flux is therefore calculated with a cut on max{Q 2,Q~}. In order to check this procedure, the analysis was also performed without subtracting the Monte Carlo e'y events. In this case, the photon flux has to be calculated without a cut on max{Q 2,Q2}. The uncertainty is estimated by comparing these pro-

E Wdckerle/Nuclear Physics B (Proc. Suppl.) 82 (2000) 232-238 cedures and by using PYTHIA instead of HERWIG for the modelling of the e7 background. The resulting uncertainty on a-r~ is about 1% and it is therefore neglected.

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7. S Y S T E M A T I C E R R O R S The three data samples at vrSee = 161 GeV, 172 GeV and 183 GeV were independently analysed and the results of a,~,v(W ) are found to be in good agreement and are therefore averaged using as weight the corresponding integrated luminosities. Several distributions of the data are compared to the PYTHIA and P H O J E T simulations after detector simulation in order to study whether the general description of the data by the MC is sufficiently good to use it for the unfolding of the cross-section. The MC distributions are all normalized to the number of selected data events after the background including the e7 events have been subtracted from the data. In both MC models about 20% of the crosssection is due to diffractive and elastic events (e.g. 77 -~ PP). This fraction is almost independent of W for W > 10 GeV. The selection efficiency for the diffractive and elastic events is very small and, although the rate is almost the same in both models, the selection efficiencies are very different, For a generated W of 50 GeV only about 6% of all generated diffractive and elastic events are selected in PYTHIA, whereas about 20% are selected in P H O J E T (Fig. 3). Due to the small acceptance the detector correction has to rely heavily on the MC simulation for this class of events. Significant discrepancies are found in the distribution of the charged multiplicity rich measured in the tracking chambers (Fig. 5). Both MC models significantly underestimate the fraction of lowmultiplicity events with n c h < 6 and overestimate the fraction of high-multiplicity events in comparison to the data. Based on these observations the following systematic errors are taken into account in the measurement of the total cross-section: • In most of the distributions, both MC models describe the data equally well. We there-

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fore average the results of the unfolding. The difference between this cross-section and the results obtained by using PYTHIA and P H O J E T alone are taken as systematic error. This yields relative systematic errors of the cross-sections of 6% to 11%. An additional error due to the uncertainties of the modelling of the diffractive processes in the Monte Carlo is taken into account. Since there is large uncertainty on the diffractive 77 cross-section derived from the HERA measurements [16-18], we have increased the percentage of diffractive events from 18% to 27% in P H O J E T which leads to an increase of a ~ by 6%. Increasing the selection efficiency for diffractive events by a factor 2 leads to a decrease of a ~ by 6%. These variations of -I-6% are used as systematic error. The systematic error due to the uncertainty in the energy scale of the ECAL was estimated by varying the reconstructed ECAL energy in the MC by 5:3%. This yields relative systematic errors of the cross-sections of 4% and smaller. The electromagnetic calorimeters in the forward direction, SW and FD, are used in the Wvis measurement. A possible uncertainty in the energy scale and the detector

236

E Wiickerle/NuclearPhysics B (Proc. Suppl.) 82 (2000) 232-238 simulation for hadrons reconstructed in SW or FD was studied by calculating and unfolding Wvi s without SW and FD information, respectively. The difference between a.y~(W) obtained without SW or FD information and a.~.~(W) obtained with the full detector is taken as the systematic error. This yields relative systematic errors of the cross-sections of less than 9% and 2% for FD and SW respectively.

• On average the trigger efficiency for the lowest W range, 10 < W < 35 GeV, is greater than 96% and it approaches 100% for larger values of W. The lower limit on the trigger efficiency is taken into account by an additional systematic error. • It is estimated that about 2% of the selected events could be due to beam-gas or beamwall interactions. Hadronic photon-photon events, however, in coincidence with an offmomentum beam electron which was scattered upstream and hitting SW or FD are rejected by the SW and FD energy cuts. The fraction of photon-photon events rejected due to these coincidences is estimated to be less than 2%. Taking into account both effects, a value of 2% is therefore taken as additional systematic error. • Since the distribution of the charged multiplicity rich is not well described by the Monte Carlo models, we have studied the influence of this discrepancy by unfolding the two-dimensional (Wvis,nch) distribution. No significant difference from the one-dimensional unfolding of the Wvis distribution is found. Therefore no additional systematic error has been taken into account. • Since the background rate taken from Monte Carlo is only about 1.6%, a possible systematic error is neglected. • The overall normalisation error due to the uncertainty on the luminosity measurement is less than 1% and is therefore also neglected.

For the total error the statistical and the systematic errors are added in quadrature. 8. R E S U L T S A N D MODEL COMPARISONS The total hadronic cross-section a.~.r(W ) for the process 7"~ --+ hadrons is shown in Fig. 6. In

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Figure 6. a ~ as a function of W. The OPAL measurement is compared to the measurements by PLUTO [1], TPC/2~ [2], PEP/2"r [3], MD1 [4] and L3 [5]. The data are compared to model predictions based on a Donnachie-Landshoff fit to total cross-sections [19]. The solid line gives the prediction using equation 2. The dashed-dotted line is the eikonalised mini-jet model by Godbole and Panchieri [22], the dotted line is the model of Schuler and SjSstrand [9]. The model of Engel and Ranft [8] used in PHOJET is shown as dashed line.

the region W < 20 GeV, the OPAL measurement is consistent with the results from PLUTO [1], TPC/2-), [2] and PEP/2"r [3] within the large

E Wiickerle/Nuclear Physics B (Proc. Suppl.) 82 (2000) 232-238

237

spread and experimental errors of these measurements. The OPAL measurements exhibit the rise in the W range 10 < W < 110 GeV which is characteristic for hadronic cross-sections in this energy range. A similar rise was first observed by the L3 experiment [5], but their values of cr~-~ are about 20% lower than the OPAL measurement. L3 used PHOJET only for the unfolding, whereas for the OPAL measurement presented here the unfolding results of PHOJET and PYTHIA are averaged. The OPAL result obtained using only PHOJET is about 5 - 10% lower than the averaged result. cr~ is compared to several theoretical models. Based on the Donnachie-Landshoffmodel [19], we test the assumption of a universal high energy behaviour of hadronic 7% 7P and pp cross-sections (o-~'r, O--~pand app). The total cross-sections cr for hadron-hadron and photon-proton collisions have been found to be well described [20,21] by a Regge parametrisation of the form

as conservative estimate of the theoretical band of uncertainty. We also plot the prediction of Engel and Ranft [8] which is implemented in PHOJET and an eikonalised mini-jet model by Godbole and Panchieri [22] which uses the GRV parton densities of the photon and a transverse momentum cut-off of 2 GeV/c for mini-jet production. In order to quantify the slope of the high energy rise of O-77 in comparison to other hadronic crosssections like C%p and O-pp, we performed some fits of an extended form [23] of equation 1

O-AB ----X1AB 8el -b Y1AB 8-rll -~- Y2AB8 -~2 ,

obtained by the fits to our data are compatible with the values

CrAB : X 1 A B S e' -t- YIABS - r h -- Y2AB 8-rl2,

(1)

where A and B denote the interacting particles and the centre-of-mass energy squared, s, is taken in units of GeV 2. The first term in the equation is due to soft pomeron exchange and the other terms are due to C-even and C-odd reggeon exchange, respectively [21]. The exponents el, 71 and Y2 are assumed to be universal, whereas the coefficients XIAB and YiAB are process dependent. There values for crop and app are taken from Ref. [21]. Assuming factorisation of the Pomeron term X1AB, a~.y can be related to crop and crpp at high centreof-mass energies v ~ = v~.rp = vfSpp where the Pomeron trajectory should dominate by

O-~ =

crop (Tpp

(2)

This simple ansatz gives a reasonable description of O-~. Schuler and SjSstrand [9] give a total cross-section for the sum of all possible event classes in their model of V')" scattering where the photon has a direct, an anomalous and a VMD component. They consider the spread between this prediction and the simple factorisation ansatz

(TAn : XIAB sel + X2AB8 ~2 + Y1ABS-m

(3)

to our measured a ~ ( W ) data. The first term of equation 3 describes a possible second hard pomeron making a stepper slope (Y2-y~ = 0). The results of the fits are summarized in table 1. Within the errors the values -t-0.025

el = 0.101 =t: 0.004(stat)_0.019(sys )

and

X2.~7 = (0.5 :t= 0.2(stat)+l:oS(sys)) nb

e1=0.0954-0.002

and

X277-=0

of Ref. [21], which were determined by fits to the pp, pp, rr~:p, K+p, 7P and "),'),total hadronic cross-sections. 9. C O N C L U S I O N S We have measured the total cross-section a ~ of the process V')' ~ hadrons in the range 10 < W < 110 GeV using the OPAL detector at LEP. Both MC models used fail to describe several distributions related to the hadronic final state like the charged multiplicity distribution. Further improvements of the description of the hadronic final state are necessary to reduce the systematic error of the measurement. It will also be important to gain a better understanding of the diffractive and elastic processes for which the detection efficiency is found to be small. With the LEP2 data the high energy behaviour of a.y7(W) can be studied for the first time, extending the accessible W values by one order of magnitude up to W = 110 GeV. We observe the

E Wiickede/Nuclear Physics B (Proc. Suppl.) 82 (2000) 232-238

238

Table 1 Results of the various fits of Regge type parametrisations to the total hadronic 77 cross-section. If no error is given, the parameter was fixed in the fit. The values of X2 per number of degrees of freedom (ndf) are calculated based on the covariance matrix of the statistical errors.

11 Xl~, [nb] fit 1 fit 2 fit 3 PDG [21]

q 188 :t: 1+2~ 0.095 *--21 180±~+a° 0.101+nnaA+°'°~5 v_32 182 + vR+2" 0.095 --22 156 + 18 0.095 + 0.002 v.'-,'..,"* _ 0.019

II

rise of a ~ (W) characteristic for the high energy behaviour of total hadronic cross-sections. A simple model based on Regge factorisation and a universal Donnachie-Landshoff fit to the total crosssections of 7P and pp data describes the data reasonably well. Within the energy range and uncertainty of the measurement no significant evidence for a steeper rise of a.r~ with energy than other hadronic cross-sections in hadronic interactions or the existence of a hard pomeron can be found. REFERENCES

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