The measurements of hadronic structure functions of the photon based on the
reaction ee --> ee gamma^(*)(P^2) gamma^*(Q^2)--> ee hadrons are discussed.Comment: 9 pages, 6 figures, Conference contribution to DIS 2000, 25-30 April
  2000, Liverpool, England, to appear in the Proceeding

Grupen, Claus

Haas, Daniel

Nisius, Richard

English

arXiv

The measurements of hadronic structure functions of the photon based on the reaction ee --> ee gamma^(*)(P^2) gamma^*(Q^2)--> ee hadrons are discussed.The measurements of hadronic structure functions of the photon based on the reaction ee --> ee gamma^(*)(P^2) gamma^*(Q^2)--> ee hadrons are discussed

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HADRONIC STRUCTURE FUNCTIONS OF THE PHOTONMEASURED AT LEPRichard NisiusCERN, Email: Richard.Nisius@cern.chDaniel HaasUniversity of Basel, Email: Daniel.Haas@cern.chClaus GrupenUniversity of Siegen and CERN, Email: Claus.Grupen@cern.ch aThe measurements of hadronic structure functions of the photon based on thereaction ee → eeγ(?)(P 2)γ?(Q2) → ee hadrons are discussed. This review coversthe latest developments in the analysis and the most recent measurements at LEP.1 IntroductionOne of the most powerful tools to investigate the structure of quasi-real pho-tons, γ, is the measurement of photon structure functions in deep inelasticelectron-photon scattering at electron-positron colliders. A recent review onthis topic along with the references to the published results can be found in 1.The main idea is that by measuring the dierential cross-sectiond2eγ!eXdxdQ2=22xQ4(1 + (1− y)2 F γ2 (x; Q2)− y2F γL (x; Q2); (1)the photon structure function F γ2 is obtained. Here Q2 is the absolute value ofthe four momentum squared of the virtual photon, γ?; x and y are the usualdimensionless variables of deep inelastic scattering and  is the ne structureconstant.In the region of small y studied (y  1) the contribution of the termproportional to the longitudinal structure function F γL is small and it is usuallyneglected. In leading order F γ2 is proportional to the parton content, fi;γ , ofthe photon, F γ2 = xPe2q (fq;γ + fq¯;γ), where the sum runs over quarks qand antiquarks q of charge eq. The hadronic structure function Fγ2 receivescontributions both from the point-like and the hadron-like part of the photonstructure. The point-like part can be calculated in perturbative QCD, whereasthe hadron-like part is usually described based on the Vector Meson Dominancemodel.aInvited talks given at the DIS 2000 Conference, 25-30 April 2000, Liverpool, England, toappear in the Proceedings.1Because the energy of the quasi-real photon is not known, the value ofx = Q2=(Q2+P 2+W 2) has to be derived by measuring the invariant mass W ofthe hadronic nal state, which is a source of signicant uncertainties, especiallyat low values of x, and makes measurements of F γ2 mainly systematics limited.If both photons are virtual, Eq. (1) gets more complicated, however, inthe region Q2  P 2  2, where  is the QCD scale, an eective structurefunction F γeff of virtual photons can be determined1.This review concentrates on the recent developments to reduce the sys-tematic uncertainties, the newly evaluated radiative corrections to F γ2 , andthe latest measurements of F γ2 and Fγeff .2 New developments in the analysisIn previous analyses it had been seen that the dominant error in the measure-ment of F γ2 at low x is the imperfect modelling of the hadronic nal state by theMonte Carlo programs. To reduce this error two approaches have been taken.Firstly, the LEP experiments have measured distributions of the hadronic nalstate corrected for detector eects 2. For large regions in most of the distribu-tions studied the results of the dierent experiments agree with one another,and consequently the results have been combined while using the spread ofthe measurements as an estimate of the systematic uncertainty. Signicantdierences are found 2 between the combined data and the predictions of theHERWIG and PHOJET Monte Carlo models. Therefore the combined LEPdata serve as an important input to improve on the Monte Carlo models.Secondly, several experiments have used improved unfolding methods toreduce the sensitivity of the result to the dierent predictions. The main ideais the following. If one assumes that the structure function F γ2 is independentof the fragmentation of the hadronic nal state, then, in the one-dimensionalunfolding, using the variable x, the result is independent of the actual shape ofthe input distribution function fpart(x) used in the unfolding, and only dependson the transformation A(xvis; x) between the value of x and the measured valuexvis. This transformation partly depends on the Monte Carlo model used, butalso to a large extend on the detector capabilities which are independent of thechosen model. By using a second variable, v, the same argument applies to thisvariable. Now the result is largely independent of the joint input distributionfunction fpart(x; v) and only the transformation A(xvis; vvis; x; v) matters. Be-cause only the transformation of v but not its predicted distribution aects theunfolding result, part of the dependence on the Monte Carlo model is removed.A quantity which has proven to be very useful as the second unfoldingvariable is the forward energy. As an example from ALEPH 3, Figure 1(left)2[width=0.49]./g01a.eps [width=0.49]./g01b.epsFigure 1: Correlation between generated and measured quantities from ALEPH and L3.shows the correlation between x and xvis at hQ2i = 56:5 GeV2 for several binsof the energy observed in the forward region below a polar angle of 17 degrees,denoted with E17. If very little energy is observed under small polar angles,which means the hadronic system is well contained in the central detector, thereis a good correlation between x and xvis. In contrast, for large values of theforward energy the correlation severely deteriorates. Using two-dimensionalunfolding 4 the result for F γ2 is almost independent of the largely dierentpredicted distributions of the forward energy.At large Q2 more transverse momentum is transferred to the hadronic sys-tem which therefore is better contained in the detector. It has been shown byL3 that in this case already a kinematic t using energy momentum conser-vation gives a good correlation between the generated and measured hadronicinvariant mass 5. Based on a generator simulating the quark parton model(QPM) prediction, this is demonstrated in Figure 1 for hQ2i = 120 GeV2,for quasi-real target photons and also for virtual target photons with hP 2i =3:7 GeV2(lower right). Already without the kinematic t an acceptable reso-lution is found for quasi-real target photons (lower left), which improves afterthe t procedure has been applied leading to a good correlation (upper). Forthe virtual target photons the initial resolution is somewhat worse and conse-quently the t yields a bigger improvement (lower right).[width=0.8]./g02.epsFigure 2: The effect of radiative corrections on F γ2 for OPAL at 〈Q2〉 = 1:9 GeV2.Usually QED radiative corrections to Eq. (1) are neglected in the analysisof F γ2 . For this conference, OPAL for the rst time presented a measurementcorrected for this eect based on the prediction of the RADEG 6 program,which takes into account initial state radiation from the deep-inelastically scat-tered electron and the Compton scattering process. It has been found that theradiative corrections are x-dependent and largest at small values of x, suchthat the shape of F γ2 is changed when these corrections are applied7. Anexample of the size of the corrections is shown in Figure 2, where the arrowsconnect the values of F γ2 before and after the correction. With the presentlevel of accuracy of the measurements the corrections are comparable to thestatistical precision of the OPAL data.3A second eect, which is usually not corrected for is the predicted suppres-sion of F γ2 due to the fact that the quasi-real target photon is slightly o-shell.This P 2 suppression is theoretically uncertain and the predictions vary by asmuch as a factor of two at low values of x. Therefore, at present, this correc-tion should not be applied to the data, in order not to bias the experimentalresult towards a particular theoretical model 1.3 Recent Measurements[width=0.8]./g03.epsFigure 3: New measurements of F γ2 from OPAL.[width=0.8]./g04.epsFigure 4: New measurements of F γ2 from ALEPH.Several new or recently nalised measurements have been presented at thisconference. OPAL has updated and extended the measurements concentratingon the low x behaviour of F γ2 for hQ2i values ranging from 1.9 to 17.8 GeV2,examples of which are shown in Figure 3. By using improved Monte Carlomodels, improved reconstruction techniques to measure the visible invarianthadronic mass, and two-dimensional unfolding, the measurement errors havebeen considerably reduced 7, compared to the published analysis.In general the shape of the GRV LO parameterisation is consistent withthe OPAL data in all the accessible x and Q2 regions. The normalisation isalso consistent with the data, except at the lowest scale, hQ2i = 1:9 GeV2Figure 3(a), where GRV is too low. Within the precision of the OPAL mea-surement, the description of the data by SaS1D LO is of similar quality as forGRV LO. Also for L3 the shape of the GRV LO parameterisation is consistent,however, in this case GRV lies below the data at hQ2i = 5 GeV2 Figure 3(b).The LEP results extend the reach at low x compared to measurements of F γ2performed at lower e+e− centre-of-mass energies. The results from PLUTOnicely agree with the LEP data at high values of x, whereas the shape ofTPC/2γ is largely dierent from all other measurements.The new results on F γ2 from ALEPH are shown in Figure 4. Based on52.9 pb−1of data, taken at e+e− centre-of-mass energy of 183 GeV, F γ2 hasbeen obtained in two Q2 ranges of 7  Q2  24 GeV2 and 17  Q2  200 GeV2with average values as indicated in the gure. The inner error bars represent4the statistical errors while the outer ones include systematical uncertainties,mainly coming from the remaining model dependence and the details of thesmoothing and regularisation technique used in the unfolding procedure. Thenew ALEPH result clearly disfavours the strongly rising F γ2 prediction fromLAC1. The very same eect, namely that predictions of steeply rising F γ2 atlow x, driven by large gluon distribution functions of the photon are disfavouredby the data, had been seen previously 1.[width=0.49clip]./g05a.eps [width=0.49clip]./g05b.epsFigure 5: Measurement of F γefffrom L3.L3 has nalised the results for hQ2i = 120 GeV2 based on LEP datataken at e+e− centre-of-mass energies around the mass of the Z boson 5. Thestructure function F γ2 is not described by the quark parton model for x < 0:4,where the hadron-like component is expected to be largest. In this region thedata are even higher than the predictions of several parametrisations of F γ2which contain a hadron-like contribution 5.In addition, the structure function F γeff was measured for hQ2i = 120 GeV2and hP 2i = 3:7 GeV2, thereby ensuring Q2  P 2  2, Figure 5. As inthe case of the PLUTO result 8, the QPM prediction is too low comparedto the data. Also the GRS prediction falls short with respect to the data.However, this may be expected, because the GRS prediction only contains thecontribution from transverse virtual target photons. The QPM prediction ofthe P 2 evolution of F γeff is consistent in shape with the data, but too low,with the most signicant dierence stemming from F γ2 at P2 = 0 and forx < 0:4 5. The measurement at P 2 > 0 cannot rule out the quark partonmodel prediction, although the data are consistently higher. For more detailedcomparisons to be made the full statistics of the LEP2 programme has to beexplored.4 The present status of the measurementsIn the present investigations of the photon structure function F γ2 two distinctfeatures of the photon structure are studied. Firstly, the shape of F γ2 is mea-sured as a function of x at xed Q2. Particular emphasis is put on measuringthe low x behaviour of F γ2 in comparison to the proton structure function ob-tained at HERA. Predictions of strongly rising F γ2 at low x are disfavoured bythe data which show a rather flat behaviour of F γ2 at low x.Secondly, the evolution of F γ2 with Q2 is investigated. The present status ofthe measurements, including those discussed above, is shown in Figure 6. The5[width=0.95]./g06.epsFigure 6: The Q2 evolution of F γ2 in bins of x.positive scaling violation predicted by QCD for all values of x is clearly seen.In addition, it has been seen 1 that the slope of F γ2 increases for increasingvalues of x, and that the measurements can be described by an augmentedasymptotic prediction 9 (ASYM) for F γ2 as described in more detail in1.5 ConclusionsThe measurement of the hadronic structure of the photon is an active eld ofresearch. The newly available results indicate that the systematic error of themeasurements can be largely decreased when two-dimensional unfolding andimproved Monte Carlo models are used. With the analysis of the full data takenwithin the LEP2 programme, considerable improvement of our understandingof the hadronic structure of the photon can be expected.AcknowledgmentsWe wish to thank the organisers of this interesting workshop for the fruitfulatmosphere they created throughout the meeting. One of the authors (C. G.)wants to thank Klaus Aholderbach for his help in preparing the talk.References1. R. Nisius, hep-ex/9912049, to be published in Phys. Rep.2. ALEPH, L3 and OPAL Collabs., A.J. Finch et al., In PHOTON 99, Nucl.Phys. B (Proc. Suppl.) 82, 156 (2000).3. ALEPH Collab., K. Aholderbach, Ph.D. thesis, University of Siegen,June 2000; A. Bo¨hrer, In PHOTON 99, Nucl. Phys. B (Proc. Suppl.)82, 25 (2000).4. G.D. Cowan, Statistical Data Analysis, Clarendon Press, Oxford 1988;S. Cartwright, M.H. Seymour et al., J. Phys. G24, 457 (1998).5. L3 Collab., M. Acciarri et al., CERN-EP/2000-044.6. E. Laenen and G.A. Schuler, Phys. Lett. B374, 217 (1996);E. Laenen and G.A. Schuler, In PHOTON 97, World Scientic, 57 (1998).7. OPAL Collab., G. Abbiendi et al., CERN-EP/2000-.8. PLUTO Collab., C. Berger et al., Phys. Lett. 142B, 119 (1984).9. E. Witten, Nucl. Phys. B120, 189 (1977).6

Hadronic Structure Functions of the Photon Measured at LEP

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Hadronic Structure Functions of the Photon Measured at LEP

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