Measurements of diffractive processes at HERA Aharon Levy for the H1 and ZEUS Collaborations 3 0 0 1 Introduction 2 One of the main objectives of ep scattering is to study the structure of the n a proton. This is done by performing a deep inelastic scattering (DIS) process J in which the virtual photon probes the partonic structure of the proton. All 7 events are studied, like in a total cross section experiment. 2 If, however,the finalstate consists of events in which the protonremains intact,orthereis alargerapiditygap(LRG),wehavediffractiveevents,me- 2 diatedbyacolorsingletexchange.Thesecanbefurtherclassifiedasinclusive v 2 diffractiveevents,asdepictedin Fig.1,orasexclusive ones,showninFig.2. 2 In this talk, these two classes of processes will be studied. 0 1 0 e Q2 e 3 e (k’) e (k) 0 γ* V (γ) x/ Q2 X W e W - p e P P p (P) t p (P’) h t : Fig.2.Schematicdiagramforexclusive v Fig.1. Schematicdiagram forinclusive diffractive electroproduction of vector Xi diffractive DIS ep reaction, where the mesonsV,wheretherapiditygapisbe- LRGisbetweentheprotonandthefinal tween V and p. r state X. a In the Regge theory of strong interactions [1], the color singlet exchange isdue to the softPomeron,IP,introducedbyGribov[2],andthe parameters of its trajectory have been determined by Donnachie and Landshoff [3]. In contrast to the universal nature of this exchange, in the language of Quan- tum Chromodynamics (QCD), the color singlet exchange is described as a two gluon exchange [4]. Since its properties depend on the scale involved in the interaction,the QCD Pomeronhas a non-universalcharacter.We will discusstheresultswithrespecttothesoftandthehardbehaviorofthesetwo approaches, which manifest themselves in the energy behavior of the cross sections. 2 Aharon Levy 2 Kinematics of diffractive scattering The variables used in diffractive scattering can be defined using the four vectors presented in Fig. 3. The usual DIS variables are the negative of the masssquaredofthevirtualphoton,Q2 =−q2 =−(k−k′)2,thesquareofthe centerofmassenergyofthe γ∗p system,W2 =(q+p)2,the Bjorkenscaling Q2 variable,x= 2p·q,whichinthe QuarkPartonModelcanbe thoughtofthe fraction of the proton momentum carried by the interacting quark, and the q·p inelasticity, y = k·p. , k In addition to the above variables, the k e e variables used to describe the diffrac- q quark tive finalstate are β MX xIP = q·(qp·−pp′) ≃ QQ22++MWX22 x ,t LRG p IP p, Q2 Q2 p p β = ≃ 2q·(p−p′) Q2+M2 X Fig.3. Schematic diagram of diffrac- t = (p−p′)2. tiveep interaction. The fractional proton momentum which participates in the interaction with γ∗ is x , and β is the equivalent of Bjorken x but relative to the exchanged IP object. M is the invariantmass of the hadronic finalstate recoiling against X the leading proton, M2 =(q+p−p′)2. The approximate relations hold for X small t and large W. 3 Diffraction as soft or hard process IntheReggedescription,diffractionisasoftprocess.Itspropertiesaredeter- ′ minedbytheuniversalPomerontrajectory,α (t)=α (0)+α t,withα (0) IP IP IP IP = 1.081 and α′ = 0.25 GeV−2. Therefore the energy behavior of the total IP γ∗p cross section is expected to be σ ∼ (W2)αIP(0)−1 ≃ W0.16. Both the tot elasticandtheinclusivediffractioncrosssectionareexpectedtohaveafaster rise with energy ∼ (W2)2αIP(0)−2/b, where b is the slope of the differential cross section in t [5]. In the perturbative QCD picture, the diffractive process is viewed, in the proton rest frame, as follows: the virtual photon fluctuates into a quark- antiquarkpair,whichinteractdiffractivelywiththeprotonbyexchangingtwo gluons.Therefore,inthis case,the diffractivecrosssectionis proportionalto the square of the gluon density. Since the gluon density, xg(x,Q2) ∼ x−λ ∼ (W2)λ, where λ depends on the scale Q2, the diffractive cross section has an energy behavior ∼ (W4)λ(Q2). At Q2 = 10 GeV2, for example, λ≈ 0.2, and thus the cross section would have a W0.8 dependence. The abovediscussionshowsthatwe expecta transitionfromsoftto hard processes when the virtuality of the probing photon increases. Diffractiveprocesses at HERA 3 4 Inclusive diffraction Onecanexpresstheinclusivecrosssectionbyadiffractivestructurefunction FD which is a function of four variables, x ,t,x,Q2. It was shown [6,7,8] 2 IP that QCD factorization holds also in case of diffraction. Thus FD can be 2 decomposed into diffractive parton distributions, which would follow the same DGLAP evolution equation that apply in the DIS inclusive case. If, inaddition,one postulatesReggefactorization,inthe spiritofIngelmanand Schlein [9], FD may be decomposed into a universal IP flux and the struc- 2 ture function of the IP. One usually integrates over the t variable, and this decomposition is written as dFD(3)(x,Q2,x ) 2 dx IP =fIP(xIP)F2IP(β,Q2), IP where the x dependence of the flux is universal, independent of β and Q2 IP and is given by fIP(xIP)∼xI1P−2αIP(0). ZEUS xFD(3)IP20000....00002468 β=0.007 β=0.03 β=0.13 β=0.48 (Q2G.42eV2) DiffHHr11a pcrteilivme effeZZcEEtUUivSS epr eαlimIP(0) 0.008 0) 1.3 00..0046 3.7α(IP ALLM97 0.02 0.008 1.2 0.06 0.04 6.9 0.02 0 1.1 0.08 0.06 soft IP 0.04 13.5 0.02 1 100Z-4EUS (prel.1) 097-200..0068 39 10-310-210-1 1 Q120 [G1e0V22] 0.04 Regge fit 0.02 0 10-4 10-2 10-4 10-2 10-4 10-2x Fig.5. Q2 dependence of αIP(0) de- IP rived from measurements of diffractive Fig.4. xIP dependence of xIPF2D(3) at andtotalγ∗pcrosssections.Thecurve fixed β and Q2 values, as denoted in (ALLM97) is a representation of the thefigure. results obtained in inclusive DIS measurements. Fig. 4 shows the x dependence of x FD(3) at fixed β and Q2 values, as IP IP 2 measured by the ZEUS collaboration [10]. The curves are the best fit to the data(restrictedto x <0.01usingauniversalflux,asdescribedabove,with IP α =1.16±.01(stat)+.04(syst).Thisvalue,togetherwithacompilationfrom IP −.01 other measurements [11], is displayed in Fig. 5. For comparison, also shown is the Q2 dependence of α (0)derivedfrom the inclusive DIS measurements IP 4 Aharon Levy andconvenientlyrepresentedbytheALLM97parameterization[12].Clearly, theinclusiveDISdataarenotcompatiblewithauniversalIP trajectory.The diffractive measurements seem to point to some Q2 dependence, though the uncertaintiesaretoolargeforafirmconclusion.ForQ2 >10GeV2,thevalue of α (0) is significantly higher than that expected from the soft Pomeron. IP TheβandQ2dependenceofthePomeronstructurefunction,asmeasured by the H1 collaboration [11], are shown in Fig. 6. It is the Pomeron struc- turefunctionundertheassumptionthatthelongitudinaldiffractivestructure function is zero, FD = 0, and that Regge factorization holds, and therefore L one divides-out the Pomeron flux. One sees that, just like in the inclusive DIS case, as Q2 increases,the Pomeronstructure function is consistent with a risingbehaviortowardslowβ.However,unlike the inclusive DIScase,pos- itive scaling violations are observed up to large β values, and only for β > 0.6, the scaling violations turn negative. H1 preliminary H1 preliminary x)IP00.0.18 xQIP2==60.5.0 G0e0V23 xIP=Q02.=080.51 GeV2xIP=0.0Q02=312 GexV2IP=0.01Q2=15 GeV2 x)IP0.1 xβI=P0=.001.30003 xβ=IP0=.0020.001 βx=I0P.0=302.003 β=x0IP.0=430.01 β=0.050 (P0.06 (P0.05 / f3)I00..0024 / f3)I0.1 σD(r0.1 Q2=20 GeV2 Q2=25 GeV2 Q2=35 GeV2 Q2=45 GeV2 σD(r β=0.067 β=0.080 β=0.107 β=0.130 β=0.167 0.08 0.05 0.06 0.04 0.1 0.02 β=0.200 β=0.267 β=0.320 β=0.433 β=0.500 0.1 0.05 0.08 Q2=60 GeV2 Q2=90 GeV2 Q2=120 GeV2 10-2 10-1 0.06 β 0.1 0.04 β=0.667 β=0.800 0.02 0.05 H1 97 (prel.) y<0.6 H1 97 (prel.) y<0.6; M<2 GeV 10-2 10-1 10-2 10-1 10-2 10-1 H1 2002 σrD NLO QCDX Fit (FLD=0) H1 97 (prel.) y<0.6 10 102 10 102 HH11 9270 0(2p rσerlD.) N yL

Measurements of diffractive processes at HERA

Similar Measurements of diffractive processes at HERA