PL3: Structure Functions⋆ OUNP-98-01 RobinDevenish (r.devenish@physics.ox.ac.uk) Physics Dept., Oxford University,UK Abstract. Recent measurements of unpolarised and polarised nucleon structure 8 functionsandFγ arereviewed.TheimplicationsforQCDandthegluonmomentum 2 9 distributionarediscussed.Thestatusoftheunderstandingofσγ∗p inthetransition 9 tot region between real photoproduction and deep-inelastic scattering is summarised 1 briefly. n a J 1 Introduction 4 1 Thistalkcoversthreeareas:unpolariseddeep-inelasticscattering(DIS)data, parton distributions and associated phenomenology (Sec.2); nucleon spin 1 structure(Sec. 3)andthestatusofFγ measurements(Sec.4).Newmeasure- v 2 3 ments from the Tevatronrelevantfor partondetermination suchas W decay 1 asymmetries,Drell-Yanasymmetries,directγ andinclusivejetcross-sections 0 are coveredby Weerts [1]. Diffractive DIS and the diffractive structure func- 1 tion are covered by Eichler[2], recent measurements of α by Ward[3] and 0 S thestatusofDISmeasurementsatverylargeQ2fromHERAaresummarised 8 9 by Elsen[4]. / x e 2 Unpolarised Deep Inelastic Scattering - p e The kinematic variablesdescribingDIS areQ2 =−(k−k′)2, x=Q2/(2p.q), h y = (p.q)/(p.k), where q = k −k′ and k, k′, p are the 4-momenta of the v: initial and final lepton and target nucleon respectively. At fixed s, where i s=(k+p)2,andignoringmassesthe variablesarerelatedbyQ2 =sxy.The X expression for the double differential neutral-current DIS cross-sectionis r a d2σ(l±N) 2πα2 dxdQ2 = Q4x Y+F2(x,Q2)−y2FL(x,Q2)∓Y−xF3(x,Q2) , (1) (cid:2) (cid:3) where Y =1±(1−y)2 and F (i=2,3,L) are the nucleon structure func- ± i tions. For Q2 values much below that of the Z0 mass squared, the parity violatingstructure functionxF is negligible.F is asignificantcontribution 3 L only at large y. At HERA both F and F are treated as calculated correc- 3 L tions andtheF dataquotedis thatcorrespondingto γ∗ exchangeonly.The 2 kinematic coverage of recent fixed target and HERA collider experiments is shown in Fig.1 and more details are given in Table 1. ⋆ Extended version of the writeup of the plenary talk given at the EPS HEP97 Conference, Jerusalem Aug. 1997. 2 R.Devenish Table 1. Summary of recent structure function experiments. All the data re- ferred in this table are available from the Durham HEPDATA database, at http://durpdg.dur.ac.uk/HEPDATAon theworld wide web. Beam(s) Targets Experiment Q2 (GeV2) x R Status e− p,d,A SLAC 0.6−30 0.06−0.9 yes complete µ p,d,A BCDMS 7−260 0.06−0.8 yes complete µ p,d,A NMC 0.5−75 0.0045−0.6 yes complete µ p,d,A E665 0.2−75 8·10−4−0.6 no compete ν,ν¯ Fe CCFR 1.−500. 0.015−0.65 yes complete e±, p - H1 0.35−5000 6·10−6−0.32 estimate running e±, p - ZEUS 0.16−5000 3·10−6−0.5 no running 2V) 105 HERA 94-96 Ge 2Q ( 104 HERA SVTX 1995 ZEUS BPC 1995 HERA 1994 y = 1 103 HERMES E665 102 BCDMS CCFR 10 SLAC NMC 1 10-1 y = 0.005 -6 -5 -4 -3 -2 -1 10 10 10 10 10 10 1 x Fig.1. Regions in the(x,Q2) plane for fixedtarget and collider DIS experiments. The vast bulk of nucleon structure function data is for F and here the 2 overall situation is rather pleasing. The fixed target programme is complete with the publication in the last 18 months of the final data from NMC [5] andE665[6]toaddtothe olderdatafromSLACandBCDMSthatstillplay an important role in global fits to determine parton distribution functions (PDFs). The first high statistics data from the 1994 HERA run were pub- PL3: StructureFunctions 3 Fig.2.Fp datafrom HERA(94)andfixedtargetexperimentsatfixedxasafunc- 2 tion of Q2. The curves shown are the NLO DGLAP QCD fit used to smooth the data duringunfolding. 4 R.Devenish F21.5 QCD Fit prel. 1 0.5 Q2=150GeV2 Q2=200GeV2 Q2=250GeV2 Q2=350GeV2 1.5 1 0.5 Q2=500GeV2 Q2=650GeV2 Q2=800GeV2 Q2=1200GeV2 1.5 H1 prel. 1 0.5 Q2=1500GeV2 Q2=2000GeV2 Q2=3000GeV2 Q2=5000GeV2 10-3 10-2 10-1 101-3 10-2 10-1 101-3 10-2 10-1 101-3 10-2 10-1 x1 Fig.3. Preliminary H1 F2 data: left 1 < Q2 < 100GeV2 from HERA 1995/6; right 150 < Q2 < 5000GeV2 from HERA 1995-97 runs. The curves show the Q2 evolution of a NLO QCD fit to H1data on theleft and evolved to higher Q2. lishedby H1 [7] andZEUS[8]lastyear.TheF datanow covering4 decades 2 in Q2 and 5 decades in x are summarised in Fig.2. The data from the fixed targetandHERAcolliderexperimentsareconsistentwitheachotherinshape and normalisation and show the pattern of scaling violations expected from perturbativeQCD(pQCD).Thesystematicerrorsforthe fixedtargetexper- iments are typically less than 5% and those for H1 and ZEUS around 5% for Q2 <100GeV2, above this value the errorsbecome statistics dominated. Fairly recently CCFR published an update of their high statistics FνFe and 2 xFνFe data[9], following an improved determination of energy calibrations. 3 The CCFR data and a determination of α are described in more detail by S De Barbaro[10]. H1hassubmittedpreliminaryvaluesofF frommorerecentHERAruns. 2 The data are shown in Fig.3: on the left for 1 < Q2 < 100GeV2 (the region covered by the improved H1 rear detector) is from 5.4pb−1 taken in 1995/96[11]; on the right for 150 < Q2 < 5000GeV2 is from 22pb−1 accu- mulatedoverthe period1995-97[12].AlsoshowninFig.3isaNLOQCDfit to H1 data with Q2 <120GeV2, which is evolved to cover the region of the higher Q2 data. All the new data are well described by the QCD curves and the characteristic steep rise of F as x decreases is seen up to the largest Q2 2 values. PL3: StructureFunctions 5 2.1 The low Q2 transition region One of the surprises of the HERA F data is the low scale from which NLO 2 QCD evolution seems to work. H1 and ZEUS have now measured the cross- sections and hence F from the safely DIS at Q2 ∼ 6GeV2 through the 2 transition region to Q2 =0, using a combination of new detectors very close to the electron beam line and by shifting the primary interaction vertex in theprotondirectionby70cm.ThedataareshowninFig.4andaredescribed indetailinrefs.[13,14,15].Alsoshowninthe figurearedatafromthe E665 experiment[6] which had a special trigger to allow measurements at small x and Q2. As Q2 → 0 F must tend to zero at least as fast as Q2, it is often 2 more convenient to consider σγ∗p(W2,Q2)≈ 4π2αF (x,Q2) (2) tot Q2 2 whichisvalidforsmallxandwhereW2 ≈Q2/xisthecentre-of-massenergy squared of the γ∗p system. For Q2 > 1GeV2, the steep rise of F as x 2 decreasesisreflectedinasteeperriseofσγ∗p withW2 thantheslowincrease tot shown by σγp and characteristic of hadron-hadrontotal cross-sections. tot Twoverydifferentapproaches,bothproposedbeforetheHERAmeasure- ments, may be taken as paradigms. Glu¨ck, Reya and Vogt (GRV) [16] have long advocated a very low starting scale as part of their approach to gener- atePDFs‘dynamically’usingNLOQCD.Predictionsfromtheirmostrecent parameterisation[17] are shown as the black solid line in Fig.4, starting in the Q2 = 0.4GeV2 bin and upwards. The data are in reasonable agreement withthe theorydownasfaras theQ2 =0.92GeV2 bin. Theother approach, thatofDonnachieandLandshoff(DL)[18],isanextensionofReggeparame- terisations that describe hadron-hadronand realphotoproduction data well. The form that DL use to describe σγ∗p is tot σ =A(Q2)(W2)αP−1+B(Q2)(W2)αR−1, (3) DL whereα andα aretheinterceptsofthePomeronandReggeontrajectories P R respectively with values α = 1.08, α = 0.05, determined from hadron- P R hadrondata. The DL model gives the trend of the energy dependence of the verylowQ2σγ∗pHERAdata,uptoQ2 ∼0.4GeV2,thoughthenormalisation tot ofthemodelisabitonthelowside.TheDLcurvesinFig.4arethesolidgrey lines. In[19] the ZEUS collaboration has investigated the transition region. From NLO QCD fits with starting scales of Q2 = 0.4, 0.8, 1.2GeV2 it is 0 found that only the latter two give acceptable descriptions of the data. For thelimitQ2 →0aDLformisused.Fromthesetwoapproachesthetransition to pQCD occurs in the Q2 range 0.8−1.2GeV2. The advent of accurate data from HERA has prompted many groups to try to model the behaviour of σγ∗p throughout the transition region. tot Very briefly: the model of Capella et al (CKMT)[20] uses a DL form at 6 R.Devenish ZEUS 1995 F20.4 Q2 = 0.11 GeV2 Q2 = 0.15 GeV2 Q2 = 0.20 GeV2 Q2 = 0.25 GeV2 0.3 0.2 0.1 F20.06 0.4 0.2 Q2 = 0.30 GeV2 Q2 = 0.40 GeV2 Q2 = 0.50 GeV2 Q2 = 0.65 GeV2 F2 0 1 0.75 0.5 0.25 Q2 = 0.92 GeV2 Q2 = 1.34 GeV2 Q2 = 1.90 GeV2 Q2 = 2.60 GeV2 F2 0 ZEUS BPC 1995 ZEUS SVTX 95 Prel. 1 ZEUS 1994 E665 H1 SVTX 1995 0.5 DL Q2 = 3.50 GeV2 Q2 = 4.65 GeV2 Q2 = 6.10 GeV2 CKMT 0 BK 10-5 10-210-5 10-210-5 10-2 GRV(94) x x x ABY Fig.4. F2 data from E665, H1 and ZEUS at very small values of Q2. The curves are described in thetext. low Q2 but allows the Regge intercepts α , α to become Q2 dependent, P R for Q2 > 2GeV2 DGLAP evolution gives the Q2 dependence; Abramow- icz et al (ALLM) [21] follow a similar approach but use a QCD inspired parameterisation at large Q2; Badelek & Kwiecinski (BK)[22] take F = 2 FVMD+Q2FQCD/(Q2+Q2) where FVMD is given by strict ρ, ω, φ VMD 2 2 0 2 andthe QCDscaleparameterQ2 is chosento be 1.2GeV2;Schildknechtand 0 Spiesberger(ScSp)[23]revivethe idea ofGVMD to fitdata for0

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