We compute the ratio between the direct and the resolved photon components of
single jet and dijet production in $ep$ collisions for the kinematical range
covered by the most recent ZEUS data. We analyse the phenomenological
consequences of different models for the structure of virtual photons in these
observables and compare them with the available data. We also comment on the
correlation between the so called $x_{\gamma}^{obs}$ and the `true'
$x_{\gamma}$, that can be inferred from the data.Comment: epsfig, 5 figure

Canal, C. Garcia

de Florian, D.

Sassot, R.

English

arXiv

We compute the ratio between the direct and the resolved photon components of single jet and dijet production in $ep$ collisions for the kinematical range covered by the most recent ZEUS data. We analyse the phenomenological consequences of different models for the structure of virtual photons in these observables and compare them with the available data. We also comment on the correlation between the so called $x_{\gamma}^{obs}$ and the `true' $x_{\gamma}$, that can be inferred from the data.We compute the ratio between the direct and the resolved photon components of single jet and dijet production in $ep$ collisions for the kinematical range covered by the most recent ZEUS data. We analyse the phenomenological consequences of different models for the structure of virtual photons in these observables and compare them with the available data. We also comment on the correlation between the so called $x_{\gamma}~{obs}$ and the `true' $x_{\gamma}$, that can be inferred from the data

Garcia Canal, C.

CERN Document Server

CERN-TH/96-234Photoproduction of jets and the virtual structure ofthe photonD.de Florian 1Theoretical Physics Division, CERN, CH 1211 Geneva 23, Switzerlande-mail: deflo@na47sun05.cern.chC.Garca CanalLaboratorio de Fsica Teorica, Universidad Nacional de La Plata,C.C. 67 - 1900 La Plata - ArgentinaR.SassotDepartamento de Fsica, Universidad de Buenos AiresCiudad Universitaria, Pab.1 (1428) Bs.As. - ArgentinaAbstractWe compute the ratio between the direct and the resolved photon components ofsingle jet and dijet production in ep collisions for the kinematical range coveredby the most recent ZEUS data. We analyse the phenomenological consequences ofdierent models for the structure of virtual photons in these observables and com-pare them with the available data. We also comment on the correlation betweenthe so called xobsγ and the ‘true’ xγ, that can be inferred from the data.CERN-TH/96-234August 19961On leave of absence from Departamento de Fsica, Universidad de Buenos Aires, Ciu-dad universitaria Pab.1 (1428) Bs.As., ArgentinaIntroduction:In recent years, dierent inclusive photon-photon experiments have con-tributed to unveil the parton content of photons in a program similar to thatpursued for the proton. Several sets of parton distribution functions for thephoton have been proposed and are periodically rened attaining increasinglevels of precision. For a comprehensive review see references [1, 2].The photoproduction of jets with large transverse energy at HERA [3],has opened the possibility of testing the gluon content of photons and the ac-curacy of these experiments allows also a clear discrimination between eventsgenerated by quasi-real and virtual photons [4]. These improvements makepossible the testing of dierent hypothesis about the photon structure andits dependence on the virtuality scale, such as how the hadronic componentof the photon is supressed at high virtuality, as it is usually expected. Thedetails of this dependence were originally thought to be obtainable by meansof a purely perturbative approach [5, 6], at least for a restricted kinematicalregime. More recently it has been analized with non perturbative models forthe hadronic structure of the photon at some denite energy scale [7, 8]. Theabove mentioned models are the subyacent motivation of the most recentparton distribution parametrizations, whose energy scale dependence is thendriven by the inhomogeneus Altarelli-Parisi evolution equations [5].Both the perturbative and nonperturbative approaches generate photonicparton distributions which dier not only in the dependence on the virtualityscale but also in its quark and gluonic content. They can be compared andtheir consequences in dierent observables analysed.Recently, the ZEUS collaboration have produced for the rst time dataon dijet photoprodution in ep collisions for dierent values of the photonvituality [4]. The preliminary data coming from this measurement allows aninteresting test for the current ideas on the virtual photon structure in therange of virtualities spanned between 0:10 and 0:55 GeV2.In this paper we compute the ratio between the resolved and the directphoton components of dijet photoproduction in ep collisions, already mea-sured at HERA, using dierent models for the photon content. In doing so,we take into account the non-trivial kinematical cuts inherent to the experi-1mental data. Particularly, we show how the magnitude and the dependenceof this ratio in the photon virtuality is fairly reproduced by model depen-dent parametrizations for the photon, but not by the perturbative approach,at least at leading order, mainly due to the poor gluon content of this lastapproximation. We also determine the value of xthresholdγ , the exact photonenergy fraction threshold used to dene the ratio, that provides the bestagreement between theoretical estimates and experiment. This procedureis necessary due to the fact that the data points are obtained using an ex-perimentally dened threshold fraction, xobsγ , which is not straightforwardlyrelated to the theoretically dened one. In doing this, we nd a rather sen-sible agreement between the determinations coming from the most realisticparametrizations.We also compute predictions for the same ratio but for single jet crosssections, as suggested in ref [7], but in an integrated kinematical range, simi-lar to that covered by ZEUS data analyses. For this single jet cross sections,we nd a clear increase in the ratio, i.e. in the resolved component, due tolow xγ contributions, which would suggest an increased sensitivity on thegluon component. However, the dependence on the virtuality scale is similarto that of dijet production.In the following section we dene the cross sections to be analysed, specif-ing the kinematical range over which these are integrated in order to becompared with the experimental data. Then, we make a short summaryabout the photonic parton distributions to be used and compare their mainfeatures. In the third section we show theoretical estimates, compare themwith the available data and discuss about the xthresholdγ choices that bring thebest accord between them. Finally we sumarize our results and present ourconclusions.Jet Cross Sections:In leading order the dierential cross section for two jet production inep collisions takes a very simple form when written in terms of the fractionof the photon energy intervening in the hard process, xγ, the fraction ofthe proton energy carried by the participating parton, xp, and that of the2electron carried by the photon, z [9]ddxγ dxp dz dpT dP 2= ~fγ=e(z; P2)fγ(xγ; Q2; P 2)fp(xp; Q2)d^dpT(1)Here, pT is the transverse momentum of the jets, P 2 is the photon virtuality,and Q2 is the relevant energy scale of the proccess, in this case taken to beequal to p2T . d^=dpT represents the hard parton-parton and parton-photoncross sections [10].The functions fγ(xγ; Q2; P 2) and fp(xp; Q2) denote the parton distribu-tion functions for the photon and the proton, respectively. The rst onereduces to (1 − xγ) -the probability for nding a photon in a photon- fordirect contributions, i.e. those in which the photon participates as such inthe hard process. ~fγ=e(z; P2) is the unintegrated Weizsa¨cker-Williams distri-bution [11]~fγ=e(z; P2) =21P 21 + (1− z)2z(2)which has been shown to be a very good approximation for the distributionof photons in the electron, provided the photon virtuality is much smallerthan the relevant energy scale [7].The dierential cross section in eq.(1) can also be written in terms ofthe (pseudo) rapidities 1 and 2, which are constrained by the experimentalsettings, and the electron and proton energies Ee and Ep [12]. Both pairs ofvariables are related to the energy fractions byxp =pT2Ep(e1 + e2)xγ =pT2zEee−1 + e−2(3)Kinematical restrictions constrain xγ to lay in the interval [p2T =xpzEeEp; xmaxγ ], xp in [p2T=zEeEpxmaxγ ; 1] and z in [p2T=EeEp; 1]. In the ZEUS data thereare also additional constraints involved such as those coming from the cutsapplied to the rapidities −1:125    1:875, and the ones for the Jacquet-Blondel variable 0:15  yJB  0:75, which corresponds to 0:20  z  0:80[3]. In order to analyse the P 2 dependence of the total cross section, thevariables xγ, xp, z, and pT , must be integrated taking into account both setsof constraints.3Switching from the (1; 2) plane (gure 1a) to the (~xp; ~xγ) (gure 1b)where ~xp = xp2Ep=pT and ~xγ = xγ2zEe=pT , the triangle ABC is mappedinto the area A0B0C 0 in gure 1b; the triangle ADC is also mapped into thesame region, due to the indistinguishability of events related by an exchangeof 1 and 2. This implies that when integrating over xp and xγ, two partonicevents must be considered for each point, the two partonic cross sectionscoming from the exchange of the Mandelstam variables u and t [13],d^dpT=d^dpT(s; u; t) +d^dpT(s; t; u) (4)For dijet process the  cuts applied determine the regions A0B0C 0 and A0D0C 0in the (xp; xγ) plane which have to be further constrained with the abovementioned kinematical cuts. For single jets events, due to the  restrictions,only the areas where neither of the jets can be detected are excluded so thexp; xγ region is extended with the areas limited by the prolongation of thecurves A0B0 and B0C 0Experimentally, the ratio between the resolved and the direct contribu-tions is dened as the number of events with photon energy fractions xγlower than certain threshold value xthresholdγ divided by the number of thoseevents with greater energy fractions. Naively, one would expect the directcontribution sharply peaked at xγ = 1, i.e. the photon participating withall its energy in the hard process, so the most natural threshold for deningthe ratio would be this, however, the detector resolution smears the distri-bution and also complicates the determination of xγ, which is then approx-imated by a measurable fraction xobsγ , dened in terms of the two highesttransverse energy jets. Previous analyses have shown [3] that a threshold ofabout xobsγ = 0:75 provides a good discrimination between direct and resolvedevents, however it is not possible to determine to which value of the xthresholdγit corresponds [4].With these elements in mind, one is able to estimate the yield of anexperimental determination of the ratio, been the set of photonic parton dis-tributions and the value of xthresholdγ the main uncertainties left.Photonic Parton Distributions:4In recent years, several sets of parton distributions for the real photonhave been proposed [1, 2]. The scale dependence of these distributions isdriven by the inhomogeneus Altarelli-Parisi evolution equations [5] with in-put distributions coming from either plausible dynamical assumptions orphenomenological ts to the photon structure function data, as for partondistributions in hadrons. For virtual photons a similar procedure can befollowed, provided a dependence on the virtuality scale is somehow imple-mented. In reference [13], for example, this dependence is introduced, for thequark distributions, by an interpolating factor multiplying the real photonparton distributionsr = 1−ln(1 + P 2=P 2c )ln(1 +Q2=P 2c )(5)where Pc is a typical hadronic scale. For gluons, the factor is chosen to bethe square of the former. One can, for example, implement this approach inany of the available real photon parton distributions. Reference [7] proposesa decomposition between a perturbative and a nonperturbative componentin the input parton distributions of virtual photons. The former coming fromthe photon-photon box diagram, whereas the later is related to the partoncontent of pions. Both contributions are weighted by factors that guarantee asmooth transition to the real photon description. A dierent decompositionis proposed in reference [8], where the vector meson dominated contributionand the anomalous component are multiplied by certain dipole dampeningfactors, designed to take into account the P 2 dependence.Altenatively, virtual photons oer another possibility which consists inobtaining the input parton distributions by a perturbative approach whichalso takes into account the dependence on the virtuality [6]. The caveat ofthis approach is that it is only applicable in a restricted kinematical region,(2QCD << P2 << Q2), where the photon exhibits hard pointlike behaviourand higher twist corrections can be neglected. In leading order, the resultingparton distributions can then be approximated byqγi (x;Q2; P 2) ’23e2i [x2 + (1− x)2] lnQ2P 2gγ(x;Q2; P 2) ’ 0 (6)Next to leading order corrections to these distributions have also been com-puted nding moderate corrections in the photon structure function but largeones for large values of x [6].5In references [7, 8] it has been noticed that most of the model dependentresults for photonic parton distributions are considerably larger than thoseobtained perturbatively, even in the restricted kinematical region. In orderto illustrate this dierence, in gure (2a) we show the ratio between the re-solved and direct components of dijet photoproduction imposing a thresholdvalue of xγ = 1:0 for a xed value of pT (pT = 4GeV ), computed with dif-ferent parametrizations. The abbreviation ‘uem’ stands for the perturbativeparton distributions of reference [6], ‘SaS 1D’ and ‘SaS 2D’ for those of [8],‘GRS’ for [7], and ‘WHIT#’ for those of reference [15] with the implementedP 2 dependence of reference [13]. Clearly, the perturbative distributions yieldconsiderably smaller ratios, the main dierence coming from the gluon con-tent, as can be seen in guere (2b) where the perturbative result is comparedwith the quark component of the nonperturbative expectation for the ratio.Experimental Data.In order to compare theoretical expectations with the available data ondijet photoproduction, it is necesary to nd out the xγ threshold value forthe theoretical calculation that corresponds to the xobsγ of the experiment. AtP 2 = 0:01GeV 2 one would expect photons to behave almost as real photonsand the corresponding photonic parton distributions strongly constrainedby the real photon data. The model dependence implemented to take intoaccount the virtuality, and the corresponding uncertainty, is then minimisedso one can try to nd the value of xthresholdγ that provides the best accordbetween the data and the estimates. In gure (3) we show the dijet ratiosintegrated in pT and at P 2 = 0:01GeV 2, as a function of xthresholdγ for dierentsets against the experimental value obtained with xobsγ = 0:75 (the thick solidline). The conventions for the other lines are the same as in gures (2a) and(2b). The gure shows that the best value for xthresholdγ lays between 0:85and 0:95. The residual uncertainty in the photonic parton distributions andthe experimental errors prevents a more precise determination, however thevalues coming from most of the distributions are perfectly consistent with thedenition of xobsγ , which implies 0:75  xthresholdγ  1:0. The comparison alsorules out some ‘extreme’ distributions, such as the set WHIT4 [15], whichhas an enormous gluon component and would require xthresholdγ << 0:75, or6the perturbative set with almost null gluon content (xthresholdγ >> 1).In gure (4) we compare the experimental data on dijet with the theoret-ical expectations coming from dierent parametrizations as a function of P 2.The lines correspond to the extreme estimates (xthresholdγ = 1:0 and 0:75, asdashed lines) and to an intermediate value (xthresholdγ = 0:85, as a solid line).The gures favor distributions with stronger dependence on the virtuality,such as SaS2D and GRS, both of which, incidentally, prefers xthresholdγ ’ 0:85.No choice of xthresholdγ adjust the estimates coming from other paramentriza-tions to the data whith similar accuracy. Plausibly, future high statistics dataon dijet photoproduction will allow a more stringent discrimination betweenparton distributions.In gure (5) we show estimates for single jet ratios. There, the low xγcontributions coming from the extra integration regions increase the resolvedcomponent and thus the value for the ratio. However, the dependence onthe virtuality scale and that on the xthresholdγ , seem to be analogous to thoseof dijet ratios, implying a similar behaviour of each component inside andoutside the restricted A’B’C’ region. Apart form this, single jet data wouldnot highlight individual characteristics of the sets, dierent to those shownby dijet data. However, it can help increasing the statistics of global ts.7Conclusions:We have analysed dierent estimates for the ratio between direct and re-solved contributions for single and dijet photoproduction. We have found afairly good agreement between the estimates coming from most of the pho-tonic parton distributions available and the data produced by ZEUS, andthe impossibility to conciliate these data with the estimates coming from‘extreme’ parton distributions, such as those of perturbative origin or withunlikely large gluon content. The P 2-dependent data show greater agreementwith estimates coming from parametrizations with stronger P 2 dependence,a large gluon component, and a xthresholdγ value of about 0:85, correspondingto xobs:γ = 0:75. Single jet ratios show slightly larger resolved components,but a similar P 2 dependence. Future experiments on single jet and dijetphotoproduction would be able to further constrain the dierent proposalsfor the parton structure in the virtual photon.Acknowledgements:We warmly acknowledge F. Barreiro for driving our attention to dijetphotoproduction data and for kind comments and suggestions.8References[1] M.Drees, R.Godbole, BU-TH 95/02, hep-ph 9508221, (1995).[2] T.Sjo¨strand, J.K.Storrow, A.Vogt, LU-TP 96-5, hep-ph 9601351, (1996).[3] M.Derrick et al., Phys.Lett.B322 (1994) 287; B348 (1995) 665;T.Ahmed, et al., Nucl.Phys.B445, (1995) 195.[4] M.L.Utley, GLAS-PPE/95-03, hep-ex 9508016 (1995).[5] M.Witten, Nucl.Phys.B120, (1977) 189,W.A.Bardeen, A.Buras, Phys.Rev.D20, (1976) 166.[6] T.Uematsu, T.F. Walsh, Phys.Lett. B101, (1981) 263, Nucl.Phys.B199,(1982) 93.[7] M.Gluck, E.Reya, M.Stratmann, DO-TH 96/08 hep-ph 9605297 (1996).[8] G.Schuler, T.Sjo¨strand, CERN-TH/96-04, hep-ph 9601282 (1996).[9] M.Drees, R.Godbole, Phys.Rev.D39, (1984) 169.[10] B.L.Combridge et al., Phys.Lett.B70, (1977) 234;D.W.Duke, J.Owens, Phys.Rev.D26, (1982) 1600.[11] S.Frixione, et al., Phys.Lett.B319, (1993) 339.[12] M.Klasen, G.Kramer, DESY 95-226 (1995).[13] M.Drees, R.Godbole, Phys.Rev.D50, (1994) 3124.[14] M.Drees, R.Godbole, Phys.Lett.61, (1988) 683.[15] K.Hagiwara et al., Phys.Rev.D51, (1995) 3197.9Figure Captions:Fig.1a Integration regions for the variables 1 and 2.Fig.1b Integration regions for the variables ~xp and ~xγ.Fig.2a The ratio between the resolved and direct components of dijet photo-production (xthresholdγ = 1:0 and pT = 4GeV ), computed with dierentparametrizations.Fig.2b The same as in Figure (2a) but only for the quark component in thephoton.Fig.3 The dijet ratios integrated in pT and at P 2 = 0:01GeV 2 as a function ofxthresholdγ and for dierent sets. The experimental value obtained withxobsγ = 0:75 is also shown for comparison.Fig.4 The data on dijet ratios against the theoretical expectations comingfrom dierent parametrizations as a function of P 2.Fig.5 Estimates for single jet ratios as a function of P 2.10Figure 1: a. Integration regions for the variables 1 and 2. b. Integrationregions for the variables ~xp and ~xγ.11Figure 2: a. The ratio between the resolved and direct components of dijetphotoproduction (xthresholdγ = 1:0 and pT = 4GeV ), computed with dierentparametrizations. b. The same as in Figure (2a) but only for the quarkcomponent in the photon.12Figure 3: The dijet ratios integrated in pT and at P 2 = 0:01GeV 2 as afunction of xthresholdγ and for dierent sets. The experimental value obtainedwith xobsγ = 0:75 is also shown for comparison.13Figure 4: The data on dijet ratios against the theoretical expectations comingfrom dierent parametrizations as a function of P 2.14Figure 5: Estimates for single jet ratios as a function of P 2.15

Photoproduction of jets and the virtual structure of the photon

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