Muryn, B

Slominski, W

Szwed, J

CERN Document Server

DELPHI Collaboration DELPHI 2002-067 CONF 60110 July, 2002Measurement of the Electron Structure Functionat Zo peakBogdan MurynFaculty of Phys. and Nucl. Techniques,Technical University of Mining and Metallurgy, Cracow, PolandWojciech S lominski, Jerzy SzwedInstitute of Computer Science,Jagellonian University, Cracow, PolandAbstractThe hadronic part of the Electron Structure Function (ESF) has been measuredfor the first time using the e+e− data at electron scattering energy√s = 92.5GeV .The data analysis is simpler than that of the photon structure function. The ESFdata are compared to phenomenological models. The GRVLO and SAS parametriza-tions follow the data whereas GRVHO and LAC1 do not. It is shown that quasi-realphoton virtuality is important. The ESF data can serve as a cross-check of bothanalyses and help in refining existing parametrizations.Contributed Paper for ICHEP 2002 (Amsterdam)1 IntroductionThe single tag e+e− collisions can be used to determine both the photon [1] and electron[2, 3] hadronic structure functions. The case of the photon is studied both theoreticallyand experimentally since long [1, 4]. The experimental results on the electron structurefunction are presented for the first time in this paper.e(k)e(k')θtage(p) e(p')γγ*(q)}Xe(k)e(k')θtage(p)e(p')γ*(q)(1a) (1b)Figure 1: Deep inelastic scattering on a photon target (1a), and on an electron target(1b)Although both analyses start from the same set of events the procedures are quitedifferent mainly due to different kinematics. In the photon case (Fig. 1a) the spectrum ofvirtual photons emitted by the (untagged) electron is strongly peaked at small virtualitiesP 2, so one approximates the photon to be real, however one has to keep in mind thatnonzero virtuality plays a role [3]. In the electron case (Fig 1b.) one is dealing with areal particle so the problem does not appear. Another difference is the determination ofthe Bjorken variable x (for the photon) and z (for the electron). In the first case, sincethe photon momentum is not known, one is forced to use the total hadronic mass W todetermine x,x ∼= Q2Q2 + W 2(1)where Q2 is the negative momentum squared of the deeply virtual (probing) photon.The z variable for the electron is determined simpler - as in the classical deep inelasticscattering i.e. from the deeply scattered electron variables only (see below). A certaindrawback of the electron structure function is its expected shape: it contains the sharplypeaked photon distribution and is thus dominated by this shape. Having at disposal twomethods of analysis it is interesting to compare them and cross-check. We also expectthat the data on both the electron and photon structure functions will help to improvephenomenological parametrisations of quark content inside photon and electron.Let us concentrate on the measurement of the electron structure function. As illus-trated in Fig. 1b the upper (tagged) electron emmits a photon of high virtuality Q2 = −q2and scatters off the target electron constituents. The cross-section for such process underassumption that Q2  P 2, reads:d2σee→eXdzdQ2=2piα2zQ4[(1 + (1− y)2)F e2 (z, Q2)− y2F eL(z, Q2)], (2)1wherey = 1− (Etag/E) cos2(θtag/2) (3)with E, Etag and θtag being the beam electron initial energy, final energy and polar angle,respectively. The parton momentum fraction z is defined in the standard (deep inelastic)way:z =Q22pq=sin2(θtag/2)E/Etag − cos2(θtag/2) (4)and is measured, by means of the tagged electron variables only. The structure functionF e2 (z, Q2), which dominates the cross-section at small y, has a simple partonic interpre-tation:F e2 (z, Q2) = z∑i=q,q¯e2i fei (z, Q2) , (5)where ei and fei are the i-th quark/anti-quark fractional charge and density. In moste+e− experiments additional constraints are imposed on the target electron. Since theusual analyses express the same cross-section (2) in terms of the real photon structurefunctions, one requires this electron to have momentum transfer less than certain valueP 2max (P2max  Q2). This procedure leads to “less inclusive” measurement and in practicemeans that the electron structure functions depend additionally on P 2max.In a series of papers [2, 3] the construction of the electron structure function has beenpresented together with the Q2 evolution equations and their asymptotic solutions. Thisapproach has been also compared with the “photon structure“ approach.Although the determination of the electron and photon structure functions is quitedifferent the functions are simply interrelated:F e2 (z, Q2, P 2max) =1∫zdyγP 2max∫P 2mindP 2f eγ (yγ, P2) F γ2 (z/yγ, Q2, P 2) (6)where the photon flux f eγ reads:f eγ (yγ, P2) =α2piP 2[1 + (1− y2γ)yγ− 2yγ m2eP 2](7)and α is the fine structure constant, me — the electron mass and P2min = m2ey2γ/(1− yγ).The above formula means among others that any existing parametrisation of the pho-ton structure function, both real (P 2 = 0) and virtual (integrated over P 2), can be testedon the measured electron structure function.2 Data SelectionA detailed description of the DEPLHI detector and its performance can be found elsewhere[5]. The analysis has been carried out with the data sample collected by DELPHI at theLEP-1 collider during the 1994-1995 annual runs at a centre-of-mass energies ranging from88.6GeV to 94.6GeV and corresponding to an integrated luminosity of 70pb−1.The essential criterium to select γγ events is that one of two scattered electrons 1 wasfound in the DELPHI luminometer STIC (tag-condition) which covers angular region from1electron is used for both - electron and positron.243mrad to 166 mrad, whereas the second electron was asssumed to be undetected (antitagcondition). Such an event is reffered to as a single-tag event. The energy deposited bytagged electron in the STIC was greater than 0.6 ·Ebeam and no additional energy clustersexceeding 0.3·Ebeam has been detected. The measured energy and an angle of the scatteredelectron allow to determine transverse squared momentum Q2.The further step was to select γγ induced hadronic final states - with charged trackmultiplicity greater than 2. Charged particles were defined as a reconstructed trackswith momenta above 200 MeV , extrapolating to within 4 cm from the primary vertex intransverse (Rφ) plane and within 10 cm along the beam direction (z-axis). The relativemomentum uncertainty for charged particle candidate ∆pphad to be smaller than 1, itspolar angle with respect to the beam axis was between 20◦ and 160◦ and its measuredtrack length in the TPC was greater than 40 cm. To satisfy the trigger condition at leastone of charged tracks had to have momentum larger than 0.7 GeV and the total energyof all charged tracks was greater than 3 GeV . The minimum of the visible invariant massof all tracks was fixed at 3 GeV .In order to supress the Z0 hadronic background events and τ events the following cutswere implemented:• The vector sum of the transverse momenta of all charged particles, normalised tototal beam energy Ebeam was greater than 0.12.• The normalised (like above) sum of absolute values of longitudinal momenta of allparticles (including tagged electron) was greater than 0.6.• The angle between transverse momenta of tagged electron and that of charged par-ticles system had to be greater than 120◦.• The maximum of the visible invariant mass was 40 GeV .In order to cut off a background of the off-energy electrons the minimum of the taggedparticle energy was increased to 30 GeV .Among 21 430 events with one high energy deposit in the STIC calorimeter, 2340events were selected passing the above criteria.The main background originates from the two-photon production of ττ and their con-tribution estimated from the simulated data with the same integrated luminosity provided78 events. The next possible contributions to the background from the four-fermion finalstates and Z0 hadronic decays was investigated yielding 13 and 20 events.3 Simulated eventsIn order to evaluate the electron structure function one needs to measure two, indepen-dent variables, the polar angle θtag of the scattered (tagged) electron and its energy. Boththese quantities are very well measured in the DELPHI experiment using the STIC lumi-nometer. The effective θtag measurement in STIC ranges from 2.5◦ to 10◦ what at LEP-1energies corresponds to a |Q2| interval starting effectively from 4.5 to 45 (GeV/c)2. Thesquared-momentum Q2 and the energy resolutions (that areσQ2Q2= 2.5% and σEE= 2%respectively), assure very precise measurement in the full range of considered variables.These directly measured quantities lead to an exact evaluation of z and Q2 variables3describing the electron structure function (see formula (2)). In order to determine adetector response the measured cross-sections have been corrected using a detector effi-ciency, which is obtained on the basis of the comparison of a generated sample to a samplethat passed the detector simulation program with the same reconstruction program as theexperimental data. In general, the efficiency function is model dependent. Therefore itis very important to use an event-generator that descibes correctly the real data events.In this analysis TWOGAM event generator together with the JETSET Parton Showeralgoritms for the quark and gluon fragmentation have been used. This generator testedfor years with good results in DELPHI turned out to be a reliable tool to determine thecorrect detector efficiency. The TWOGAM cross-sections are expressed in terms of threeindependent components:• soft-hadronic part described by the Generalized Vector Dominance Model• point-like component, QPM• resolved photon interaction, RPCSince there is a freedom in choice of the photon structure function the GRVLOparametrization was adopted. More detailed description of TWOGAM package can befound [6]. It was established that such description guarantees the relatively good agree-ment of the simulated sample with the real data.The selection criteria presented in sect.1, imposed on real data sample has also beenused for the simulated sample. In that way one obtains two sets of distributions which canbe compared. For instance visible cross-sections for real data of the: 1/scattered electronangle cos(θtag), 2/ the probing photon virtuality Q2, 3/ the scattered electron energy E ′and finally 4/ visible hadronic invariant mass Wvis are compared to those obtained fromsimulated sample at the same luminosity (see Fig. 2). All compared distributions showgood agreement. Such above stated equalities confirm simultaneously good agreementbetween reconstructed (e.g. corrected by the corresponding efficiencies) real data cross-sections and those obtained from model (generated sample).4 Determination of the Electron Structure FunctionThe ESF, a function of two variables z and Q2, can be extracted from formula (2) andreads (one follows a usual practice to present structure function in a logarithmic scale ofthe z variable)F e2 (ξ, Q2) = CQ4(1 + (1− y)2)d2σee→eXdξdQ2(8)where ξ = log10(z) and C is a product of all constant factors.The measured function F e2 (ξ, Q2)meas has to be corrected in each ∆ξi∆Q2k binby the corresponding detector response function E(ξ, Q2), yielding reconstructed ESFF e2 (ξ, Q2)rec,F e2 (ξ, Q2)recik = Fe2 (ξ, Q2)measik E(ξ, Q2)ik (9)whereE(ξ, Q2)ik =F e2 (ξ, Q2)genikF e2 (ξ, Q2)simik(10)4Such a procedure is quite justified since migration effect of events generated in any ofthe (z, Q2) bins to neighbouring bins, after passing the detector simulation, is small. InFig. 2 and Fig. 3 one can see a smearing caused by the detector for both, the standardphoton x-variable Eq.(1) and z-variable Eq.(4), where events with single value of x=0.1and z=0.01 have been generated and next passed through the detector simulation program.In opposition to the z distribution that shows typical narrow gaussian-type resolution, thex distribution is shifted to higher values and spread over the whole region of x. For thatreason the x distributions have to be treated in a special way by means of an unfoldingprocedure. The one-dimensional unfolding requires a knowledge on theoretical shape ofthe photon-photon invariant mass distribution in order to convert Wvis into Wrec, whereasthe determination of the ESF is not sensitive to that distribution.Next, the Electron Structure Function is averaged over Q2 in considered region of thephoton virtuality leaving only the ξ dependence. In this analysis the ESF for three Q2intervals, Q2 ∈ (4.5, 30) GeV 2 , Q2 ∈ (4.5, 15) GeV 2 and Q2 ∈ (15, 30) GeV 2, has beenplotted (Fig. 5-7) and displayed in Table 1. The lower value for Q2 = 4.5 GeV 2 is akinematical limit caused by a cut on minimum θtag = 2.5◦ angle of the tagged electron.One should stress that in the last two ξ-bins, (-2.0,-2.4) and (-2.4,-2.8), the kinematicallyavailable Q2 intervals are (4.5, 20) GeV 2 and (4.5, 8.0) GeV 2 respectively, what has beentaken into account.Both, statistical and systematic uncertaintes contribute to the error bars displayed inFig. 5-7 and Table 1. The statistical is dominated by an effect of the limited number ofevents in the real data sample after all selection cuts. Since the simulated sample waslarger, the contribution from uncertaintes of the detector efficiency are much smaller. Thesystematic uncertainty has the following contributions which were added in quadratureto the statistical one:• Uncertaintes due to the energy (σEE= 2%) and scattering angle (σθ = 0.05◦) of thetagged electron measurements. To estimate this effect one standard deviation ofthe energy resolution distribution has been added to the energy Etag for each event,and one standard deviation has been subtracted from this value. The same wasperformed for the θtag variable. For each, out of four combinations of the angles andenergies, the ESF has been determined. This source of systematics was evaluatedas the maximum of the differences among the four F e2 (z, Q2)simulik values.The maximum value of all differences has been taken as a contribution to systematicuncertainty.• Uncertainty due to binning variation. This has been estimated evaluating the ESFfor three different bin widths.It should be amphasised that on average about 50 percent of the total uncertainty orig-inates from the systematic one. There is still possible to reduce the total error increasingnumber of data events (for instance with LEP2 data). Given any parametrization of thePhoton Structure Function one can convert it into Electron Structure Function accordingto formula (6). In Fig. 5-7 set of the ESF corresponding to GRVLO,GRVHO,SAS andfinally LAC1, photon parametrizations is superimposed on the data points. In additionto the above real photon structure parametrisation we also show the SaS virtual photonstructure parametrisation, marked as SAS-INT. It has been integrated over the virtuality5of the probed photon P 2 according to Eq. (6) up to P 2max = 3 GeV2 equal to the anti-tagcondition value.Table 1: Results for measurement of the electron structure functionQ2[GeV 2] 〈Q2〉 −log10(z) F e2 σstat σsystem(4.5-30.) 12.0 0.0-0.4 0.0 ± 0.00 +0.00−0.000.4-0.8 0.51 ± 0.11 +0.44−0.410.8-1.2 3.04 ± 0.33 +0.24−0.321.2-1.6 5.09 ± 0.32 +0.20−0.351.6-2.0 6.53 ± 0.25 +0.21−0.242.0-2.4 7.61 ± 0.17 +0.31−0.382.4-2.8 6.50 ± 0.14 +0.17−0.222.8-3.2 0.00 ± 0.00 +0.00−0.00(4.5-15) 8.5 0.0-0.4 0.00 ± 0.00 +0.00−0.000.4-0.8 0.18 ± 0.13 +0.43−0.440.8-1.2 1.75 ± 0.38 +0.25−0.361.2-1.6 3.61 ± 0.37 +0.22−0.231.6-2.0 5.52 ± 0.29 +0.19−0.242.0-2.4 7.10 ± 0.19 +0.34−0.412.4-2.8 6.69 ± 0.16 +0.15−0.222.8-3.2 0.00 ± 0.00 +0.00−0.00(15-30) 21.5 0.0-0.4 0.00 ± 0.00 +0.00−0.000.4-0.8 0.72 ± 0.17 +0.48−0.490.8-1.2 3.91 ± 0.50 +0.31−0.481.2-1.6 5.66 ± 0.49 +0.29−0.151.6-2.0 7.93 ± 0.38 +0.21−0.292.0-2.4 9.02 ± 0.25 +0.43−0.602.4-2.8 0.03 ± 0.14 +0.18−0.252.8-3.2 0.00 ± 0.00 +0.00−0.0065 ConlusionThe hadronic part of the electron structure function has been measured for the first time.The proposed method is explicit and simpler as compared to the photon structure analysis- it does not use the unfolding procedure. It also allows to take the virtuality of theprobed photon into account. In general the analysis shows consistency of both (electronand photon) approaches. It is demonstrated that the migration of events between z-bins(electron) is much smaller than between x-bins (photon). The statistical uncertainties arewell understood since in each bin of the measured ESF they reflect a Poisson error whereasstatistical uncertainties obtained from the unfolding procedure seem to be underestimated.Out of all presented models the GRVLO, SaS and P 2-dependent SaS follow the datawhereas GRVHO and LAC1 do not. It should be stressed that the inclusion of the photonvirtuality is important - the difference between two SaS parametrisations (P 2-dependentand P 2 = 0) are of the same order as between SaS and GRVLO ( both with P 2 = 0).Acknowledgements We are greatly indebted to our technical collaborators, to the mem-bers of the CERN-SL Division for the excellent performance of the LEP collider and tothe funding agencies for their support. We acknowledge the State Commitee for ScientificResearch, Poland, SPUB-M/CERN/P-03/DZ 296/2001 and grant/2P03B06116.References[1] E. Witten, Nucl. Phys. B120, 189 (1977);C.H. Llewellyn-Smith, Phys. Lett. 79B, 83 (1978);R.J. DeWitt et al., Phys. Rev. D19, 2046 (1979);T.F. Walsh and P. Zerwas, Phys. Lett. 36B, 195 (1973); R.L. Kingsley, Nucl. Phys.B 60, 45 (1973).[2] W. S lomin´ski and J. Szwed, Phys. Lett. B387, 861 (1996); Acta Phys. Polon. B271887 (1996); ibid B28 1493 (1997); ibid B29 1253 (1999). W. S lomin´ski, Acta Phys.Polon. B30, 369 (1999).[3] W. 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B458, 152 (1999).[5] DELPHI Collab., P.Aarnio et al., Nucl. Instr. and Methods., A378, 57 (1996)7[6] S. Nova, A. Olshevsky, T. Todorov, DELPHI-90-35 (unpublished).8Figure 2: The ∆σvis∆(1−cos(θ), ∆σvis∆Q2∆σvis∆Etagand ∆σvis∆Wvisible cross sections for real and simulateddata9Figure 3: The detector simulated z-distribution obtained from the sample generated atz=0.0110Figure 4: The detector simulated x-distribution obtained from the sample generated atx=0.1110246810-4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0Figure 5: The electron structure function averaged over Q2 ∈ (4.5, 30) GeV 2 (see alsotext)120246810-4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0Figure 6: The electron structure function averaged over Q2 ∈ (4.5, 15) GeV 2 (see alsotext)13Figure 7: The electron structure function averaged over Q2 ∈ (15, 30)GeV 2 (see also text)14

Measurement of the Electron Structure Function at Zo peak

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