The structure of the photon is probed in photon-photon interactions at LEP
and in photon-proton interactions at HERA.Comment: 10 pages, submitted to proceedings of DIS2000, Liverpool, UK, 25-30
  April 200

Soldner-Rembold, Stefan

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arXiv

The structure of the photon is probed in photon-photon interactions at LEP and in photon-proton interactions at HERA.The structure of the photon is probed in photon-photon interactions at LEP and in photon-proton interactions at HERA

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Photon Structure

The LEP experiments measure the QED and QCD structure of the photon in deep-inelastic electron-photon scattering. The status of these measurements is discussed in this short review

Söldner-Rembold, S

For Publisher’s usePHOTON STRUCTURESTEFAN SO¨LDNER-REMBOLDCERN, CH-1211 Geneva 23, SwitzerlandE-mail: stefan.soldner-rembold@cern.chThe LEP experiments measure the QED and QCD structure of the photon in deep-inelastic electron-photon scattering. The status of these measurements is discussed in this short review.1 KinematicsAt LEP the virtuality of the \probing" pho-ton is Q2 = −q2 (the negative squared four-momentum of the photon) and the virtualityof the \probed" photon is P 2 = −p2  0.The deep-inelastic scattering cross-section iswritten asd2eγ!e+hadronsdxdQ2=22xQ4(1)(1 + (1− y)2F γ2 (x; Q2)− y2F γL (x; Q2);where  is the ne structure constant, x andy are are the usual dimensionless variables ofdeep-inelastic scattering and W 2 = (q + p)2is the squared invariant mass of the hadronicnal state. The scaling variable x is given byx =Q2Q2 + W 2 + P 2: (2)The term proportional to F γL (x; Q2) is smalland is therefore usually neglected. In leadingorder the structure function F γ2 (x; Q2) can beidentied with the sum over the parton den-sities of the photon weighted by the square ofthe parton’s charge.2 QED Structure FunctionsThe QED structure function F γ2 has beenmeasured in the process e+e− !e+e−+−.In addition, the measurement of the distri-bution of the azimuthal angle  between theelectron scattering plane and the plane con-taining the muon pair in the γγ centre-of-mass system gives access to the struc-ture functions F γA and FγB . They are re-lated to the transverse-longitudinal (A) and-0.3-0.2-0.100.10.20.30 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1xFγ A / Fγ 2OPAL Q2 = 5.4 GeV2Fγ A / Fγ 2L3 Q2 = 3.25 GeV2Fγ A / Fγ 2DELPHI prl. Q2 = 12.5 GeV2(a)x1/2 Fγ B / Fγ 2OPAL Q2 = 5.4 GeV21/2 Fγ B / Fγ 2L3 Q2 = 3.25 GeV21/2 Fγ B / Fγ 2DELPHI prl. Q2 = 12.5 GeV2(b)-0.0500.050.10.150.20.250.30 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Figure 1. The measured ratios F γA/Fγ2 and 1/2 ·F γB/Fγ2 compared to the QED prediction1.the transverse-transverse (B) interference inthe interaction of the transverse real photonwith the virtual photon. The LEP measure-ments 2;3;4 are shown in Fig. 1. Both struc-ture functions are found to be signicantlydierent from zero and the ratios are well de-scribed by QED 1.3 Hadronic Structure FunctionsThe measurement of hadronic structure func-tions is considerably more dicult due to thenecessity to reconstruct x from the hadronicnal state in the detector (Eq. 2). Signicantprogress has been made recently in reducingthe systematic errors due to unfolding andhadronisation uncertainties. ALEPH, L3 andOPAL have compared their combined datato the PHOJET and HERWIG generators 5.os: submitted to World Scientific on April 23, 2001 1For Publisher’s useAn unbiased tune using informations fromHERA has improved HERWIG signicantly.Furthermore new methods for regu-larised unfolding like the maximum entropymethod or the singular value decompositionmethod have been used. ALEPH and OPALhave introduced two-dimensional unfoldingand improved treatment of hadronic energyin the forward region. L3 is applying energy-momentum conservation using kinematic in-formation from both hadrons and the elec-trons. The uncertainty on the measurements00.10.20.30.40.500.20.40.610 -3 10 -2 10 -1 1Fγ 2(x)/α OPAL, <Q2>=1.9 GeV2L3, <Q2>=1.9 GeV2PLUTO, <Q2>=2.4 GeV2TPC-2γ, <Q2>=2.8 GeV2GRV LO Q2=1.9 GeV2GRV LO Q2=2.8 GeV2SAS1D Q2=2.8 GeV2QPM Q2=2.8 GeV2(a)xFγ 2(x)/α OPAL, <Q2>=3.7 GeV2L3, <Q2>=5.0 GeV2PLUTO, <Q2>=4.3 GeV2TPC-2γ, <Q2>=5.1 GeV2GRV LO Q2=3.7 GeV2GRV LO Q2=5.1 GeV2SAS1D Q2=5.1 GeV2WHIT1 Q2=5.1 GeV2QPM Q2=5.1 GeV2(b)Figure 2. The measured hadronic structure functionF γ2 compared to the GRV-LO8, SaS-1D 9 and theWHIT1 10 parametrisations and to the QPM model.In the case of L3 the values obtained using PHOJETand TWOGAM for unfolding are shown separately.shown in Fig. 2 are therefore considerably re-duced 6;7.The hadron-like component dominates atlow x and there could be a rst indication ofthe low x rise of the photon structure functionexpected from QCD evolution.The Q2 dependence of the structure func-tion F γ2 in bins of x is shown in Fig. 3 for allcurrently available measurements. The dataare compared to the GRV-HO and the SaS-1D parametrisation, and to the sum of theasymptotic prediction 11 for 3 light flavoursand the point-like part of the charm struc-ture function taken from GRV. Positive scal-ing violation of the photon structure function0.00.50.00.50.00.50.00.50.00.50.01.00.01.00.01.010 -1 1 10 10 2 10 3Q2 (GeV2)F 2γ (x,Q2 )/αem <x>0.0060.050.150.250.350.50.70.9SaS-1D (LO) GRV-HOasympt. (nf=3) + Fγ,PL2,cTPC/2γPLUTOJADETASSOTOPAZAMYALEPHDELPHIL3OPALFigure 3. The Q2 dependence of the hadronic struc-ture function F γ2 in bins of x compared to the GRV-HO, SaS-1D and the asymptotic prediction.is observed in all x ranges - dierent fromthe proton - due to the regular QCD evolu-tion at low x and due to the inhomogeneousterm (γ ! qq) at larger x. As expected,the asymptotic prediction fails to describe thedata at low x, where the non-perturbativehadron-like contribution dominates, whereasall models give a reasonable description of themedium to high x; Q2 region.4 Charm Structure FunctionIn Fig. 3 the charm threshold is clearly visi-ble. Above the kinematic threshold for charmproduction, the c and u contribution to thepoint-like part of the photon structure func-tion are of similar size. OPAL has measuredthe charm structure function of the photonfor the rst time using D decays 12. Theregion x > 0:1 - which is dominated by thepoint-like component - is in good agreementwith a NLO calculation 13. In the regionx < 0:1 the measurement suggests the ex-istence of a hadron-like component with cur-rently large errors. These uncertainties areexpected to be signicantly reduced in thefuture due to higher statistics and better MCos: submitted to World Scientific on April 23, 2001 2For Publisher’s use00.20.410 -3 10 -2 10 -1x Fγ 2,c (x,< Q2>) / αOPALNLO (Laenen et al.)NLO hadron-likeLOGRS-LOpoint-like<Q2> = 20 GeV2Figure 4. Charm structure function F γ2;c of the pho-ton as function of x for 〈Q2〉 = 20 GeV2.modelling of charm production.5 Virtual Photon StructureIn addition to the structure function of(quasi-)real photons, i.e. P 2  0, the eec-tive structure function of virtual photons canbe measured if Q2 >> P 2 >> 2QCD. Thiswas rst done by PLUTO 14. For real pho-0120 0.2 0.4 0.6 0.8 1xF effγ (x)/α a)  Q2 = 120 GeV2,  P2 = 3.7 GeV2 DATA QPM GRS L30120 2 4 6 8P2 (GeV2)<F effγ  /α>b) DATA QPMQ2 = 120 GeV2,  0.05 < x < 0.98Figure 5. Effective structure function of the virtualphoton as function of x and P 2.tons only the cross-sections LT and TT con-tribute, where the indices refer to the longi-tudinal and transverse helicity states of theprobe and target photon, respectively, i.e.F γ2 ’ LT + TT. For P 2 >> 0 other he-licity states have to be taken into account,leading to the denition of the eective struc-ture function F γeff ’ LT + TT + TL + LL(interference terms are neglected). This ef-fective structure function measured by L3 15is shown in Fig. 5. We expect the hadron-likepart of the parton densities at low x to de-crease with increasing virtuality of the pho-ton. In Fig. 5b the QPM approximation ofthe point-like part therefore fails to describethe data point at P 2 = 0. The shape of theP 2 dependence is consistent with the QPMansatz but the errors are still large. Muchmore precise data is to be expected from LEPon virtual photon structure in the next years.References1. R. Nisius, Phys. Rept. 332 (2000) 165.2. DELPHI note 2000-135, abstract 644submitted to this conference.3. L3 Coll., Phys. Lett. B438 (1998) 363.4. OPAL Coll., Eur. Phys. J. C11 (1999)409.5. ALEPH, L3 and OPAL Coll., CERN-EP-2000-109.6. L3 Coll., Phys. Lett. B447 (1999) 147;Phys. Lett. B436 (1998) 403.7. OPAL Coll., hep-ex/0007018.8. M. Glu¨ck et al., Phys. Rev. D46 (1992)1973; Phys. Rev. D45 (1992) 3986.9. G.A. Schuler et al., Z. Phys. C68 (1995)607.10. K. Hagiwara et al., Phys. Rev. D51(1995) 3197.11. E. Witten, Nucl. Phys. B120 (1977) 189;in the parametrisation of L.E. Gordonet al., Z. Phys. C56 (1992) 307.12. OPAL Coll., hep-ex/9911030, see alsoA. Bo¨hrer, hep-ph/0009121, these pro-ceedings.13. E. Laenen et al., Phys. Rev. D49(1994) 5753; E. Laenen, S. Riemersma,Phys. Lett. B376 (1996) 169.14. PLUTO Coll., C. Berger et al.,Phys. Lett. B142 (1984) 119.15. L3 Coll., Phys. Lett. B483 (2000) 373.os: submitted to World Scientific on April 23, 2001 3

Photon Structure

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