The photon structure function at PHOTON'95, Sheffield, April 1995

P. Aurenche

Laboratoire de Physique Theorique ENSLAPP B.P.I 10, F-74941 Annecy-Le-Vieux Cedex, France

Abstract

We discuss some of the highlights of the Sheffield conference with special emphasis on the determination of the photon structure function.

Resume

On passe en revue les resultats concernant la fonction de structure du photon presentes a la conference de Sheffield, 8-13 Avril 1995.

1. Introduction the TeV energy range: as illustrated by G. Belanger [2], the 6 b and c c production rate via the one-resolved PHOTON '95 belongs to the series of conferences and two-resolved processes is several order of magnitude devoted to "Two-photon physics" initiated by P. Kessler larger than the H —• bb signal. Using polarized photon in 1973. For the first time, however, the conference beams as well as various kinematical cuts will however covered the related fields of deep-inelastic scattering reduce this background [3]. and photo-production experiments and, in particular, In the following, I discuss first the deep-inelastic the recent HERA results were extensively discussed. It scattering of a photon where the structure function became clear during the discussions that the scattering is usually defined. Then, the large p? processes and of real or virtual photons off nucleons are an essential heavy flavor production are presented in photon induced ingredient to the study of the deep structure of the reactions. photon. [1] From a theoretical point of view the photon 2. Deep-inelastic scattering and the photon structure function is as fundamental as or, perhaps, even structure function more fundamental than the proton structure function. Despite this fact it is known much less precisely: the 2.1. The data proton structure function has been probed through a variety of processes and it is now measured in the range The basic process where the photon structure 10~4 < XBJ < 1 with a precision which can reach function is introduced is the reaction e+e" —• e+e~ +X, a few %. As, we shall see below, the situation is as shown in fig. 1, where X is the hadronic system much less favorable in the case of the photon. Besides produced by the annihilation of the two photons. One providing a fundamental test of QCD, the knowledge of lepton is detected (energy E\, angle ©i) so that the the partonic structure of the photon is crucial for the emitted photon has a large virtuality Q2, while the calculation of the background to the production of an other lepton goes undetected or is constrained to be at intermediate mass Higgs in gamma-gamma colliders in a small angle (anti-tagging condition defined by ®max) by the 7* - 7 annihilation. Because of the limited acceptance of the detectors experimentalists can only measure

where WVi, is the visible invariant mass; - the target mass is not fixed and this causes uncertainties in the extraction of the structure function [5] which is very sensitive to its value. Indeed, one has Figure 1. The basic deep inelastic scattering process on a roughly photon target

corresponding to a small virtuality P2 of the other where mCut-off is identified to an infra-red cut-oif which (target) photon. The observable is related to the photon depends on the model used to perform the analysis structure functions F^ and F% via, (mcut-0ff - mq or AQCD or Q0). Using the analogy of the production mechanism of pairs with that of hadrons at the lowest order in QCD (i.e. via qq pairs) one can gain some information on the effect of the P2 dependence. For example, an effective value of P2 = .04 GeV2 has a 5% effect on the extraction of with the relations F] at LEP1 [5]. It is clear from the above discussion that the experimental analysis of F% requires very good Monte- Carlo event generators in order to reconstruct the events and where N(z Q ) is the Weiszacker-Williams 1 rnax and thus be able to unfold the x value from the measured spectrum of the target photon. Experimentally, x i . Until now the program developped by Field, the variable y is rather small so that, to a good v $ Kapusta and Poggioli [6] was used in most experimental approximation, one can use analysis. It appeared at this conference that the well- known Monte-Carlo codes developped for the analysis of hadronic collisions have been adapted to photon-photon collisions [7, 8, 9] and one should soon be able to better It is worth mentioning that at LEP2 it will not be understand the systematic errors of the data analysis. possible to go to large y values (or equivalently small New sets of data have been presented at Sheffield: E\ values) due to beam-gas background [4] and thus while the Amy [10] and Opal [11] data cover large x Fl cannot be measured. Azimuthal correlation studies and large < Q2 > values (up to 390 GeV2 in the case using final state jets may, however, yield information on of Amy) which do not allow to distinguish between the the longitudinal structure function (see below). available parton parametrizations, the new Delphi data Compared to proton structure function studies one [5] data reach x ~ .03 and like previous Opal data [12], encounters here several difficulties: with which they are compatible within the large error - the energy of the target photon is not fixed but it is bars, they marginally rule out the Lacl parametrization integrated over the Weizsacker-Williams spectrum: [13]. A word of caution should be said about the consistency of data sets: although the latest Delphi data concern only light quark production the value of F% is the same as that obtained by Cello [14] which As a consequence, include charm quark production! Let us note that LEP2 - the scaling variable x is not easily measurable and data should be able to reach values of x = .001 for 2 2 cannot be obtained only from the leptonic variables: < Q >= 6 GeV with about five times the presently analysed statistics at LEP1.

2.2. The theory

where the expression on the right end side involves Despite the rather large uncertainties in presently the invariant mass W of the hadronic system produced available data, several parton parametrizations exist at

20 the next-to-leading logarithmic order (NTL) [15, 16] and have been discussed at this conference [17, 18]. This is briely discussed here insisting on the specificity of the photon case as opposed to the proton structure A similar decomposition also holds for the gluon. The function. In principle, the data reviewed above should motivation for this form is the following. At low values 2 allow to extract the quark and the gluon content of the of Q ) i.e. in the non-perturbative regime, it is known photon. With these distributions one can then predict that the photon behaves like a hadron and its interaction jet or heavy flavor production in both 77 or 7p reactions is well described by the VDM hypothesis: the photon and thus have a stringent test of perturbative QCD. In behaves as a vector meson whose parton distributions fact, as in the proton case, the gluon is not sufficiently are often identified with those of a T. This is shown by constrained from the deep-inelastic experiments only, the last term of the above equation which also contains and all experiments are necessary to extract the parton the large Q2 evolution of this hadronic component. densities in the photon. Only if all available (mutually Above some Qo scale the perturbative component comes consistent) data sets can be reproduced with the same into play and asymptotically dominates the parton set of parton distributions in the NTL approximation distributions because of its logarithmic growth in Q2. do we have a quantitative test of QCD. As we shall see Depending on the parametrizations Q2 varies from below we are far from this idyllic situation! (.3 GeV2) [15] to a few GeV2 [18]. Let us start with some technicalities. The relation As always when working in the NTL approximation, between the observable, JP^(X,Q2) and the parton one has the freedom to choose the factorization scheme J 2 1 2 at which the collinear singularities are absorbed in the distributions q (x}Q ) and G (x,Q ) is (one quark flavor is assumed for the sake of the discussion) parton distributions. A further degree of freedom occurs

here related to the treatment of the direct term Cy(x)

in eq. (2.8). When working in the MS scheme, Cy(x) ~ (3a/7r)(ln(l — x) — 1), at large x, and it becomes very large and negative near x = 1: if one identifies naively

had VMD 2 q to q at Q = Q0, this causes F](x,Q ) to be negative at large x values, an unphysical result. To cure

this problem, one may define [15] the DIS1 scheme by The coefficient functions Bq(x), BQ{^) and C7 are absorbing C in the quark distribution: known, while the parton distributions we are trying to 7 determine satisfy the evolution equations

This immediately leads to new evolution equations, with

a modified kq at the next-to-leading order, as can be

1 seen by substituting q])IS to q via eq. (2.11). These evolution equations can be solved and no problem arises

then because, in this scheme, Cy(x) is now vanishing in eq. (2.8). This approach implicitely assumes that the VMD input is identified to the quark distribution in

the DIS7 scheme without any justification. Another approach [16], based on a careful analysis of the lowest

2 2 2 order QCD diagrams, shows that the dominant part of The functions kq(x,Q ), kG{x,Q ), Pxj(x,Q ) are

2 known to order a,(Q ) in QCD. Except for the functions the direct term Cy(x) should in fact be included in the written in boldface, eqs.(2.8), (2.9) are similar to the non-perturbative input so that at QQ one has, in the had 2 VDM 2 homogeneous equations governing the evolution of the MS scheme, q {x,Q ) = q {x,Q ) - <70(x), with

partons in the proton. The general solution can be C0 a known function such that C^(x) — C0 is regular as written as a sum of two terms: the first one, denoted x —• 1. In that way, the definition of the hadronic input ganom, is a particular solution to the full set of equations, is universal, independent of the considered observable. linearly growing in InQ2 (and usually chosen to vanish All NTL parton distributions lead to rather similar at some Qo value), while the second term qhad is the results in the presently available x and Q2 range of . general solution of the homogeneous (hadron-like) set They may differ violently at very small x values [19] of equations exhibiting the normal pattern of scaling but one should remember that extrapolations in x are violations. This is expressed as meaningless when working only in the framework of the Altarelli-Parisi equations. An interesting point concerns the importance of the hadronic (VDM) input which dominates the parton distributions in the photon at

21 Figure 3. Definition of the azimuthal angle between the lepton scattering plane and the jet production plane

The structure functions A{ correspond to convolutions Figure 2. The iinglet and the gluon distributions in the photon. of amplitudes in states of definite helicity for the 7* — 7 The crosses indicate the full contributions while the dots system as indicated in fig. 4 [21], [22]. It turns indicate the anomalous component only. out that for the production of spin 1/2 partons one has, for a properly chosen normalization, the identity FL = As [23] so that the experimental determination small x as seen in fig. 2 [16]. The somewhat paradoxical of the coefficient of the cos2# term in eq. (2.12) gives consequence is that at higher energies, where usually a measure of the longitudinal structure function. This the smaller values of x are probed, the sensitivity to the method has already been used by the L3 experiment in non-perturbative input will persist. its study of the pure QED process e+e~ —• e+e~/z+/x~ The role of the heavy flavor contribution to and A2 and A$ were experimentally extracted [24] in and Fl at the NTL order needs a special mention agreement with the theoretical calculations. When [20]. One of the most interesting point is that the working with hadronic final states care has to be taken charm contribution to F% is reliably predictable at large that kinematical cuts do not distort the predicted enough x, without any of the usual factorization scale azimuthal distribution [23]. A similar analysis has been ambiguity, because of the dominance of the direct term has been considered at Hera [25]. where the target photon couples directly to the heavy A domain of very interesting future research quark. At LEP2 for example, this occurs in the range concerns the structure function of a virtual photon 2 x > 3 10~ . The contribution of the gluon in the photon F](x,Q2]P2) with P2 « Q2. This is an old problem is negligeably small in that range but will dominate at [26] but the possibility to measure the structure function smaller x values. with P2 ~ 1. GeV2 at LEP2 or to study hard processes As mentioned above F% will not be directly with P2 at still larger values should trigger more measured at LEP2 when working only with the theoretical studies on this topic. It is a particularly observable eq. (2.1). However measuring azimuthal useful quantity to understand the transition from the distributions may open a window on this quantity. perturbative to the non-perturbative regime since at Going to the rest frame of the 7* — 7 system, in the large P2 everything should be perturbatively calculable see process of fig. 1, and defining % ( fig- 3) as the angle while at P2 = 0 we have seen that the non-perturbative between the electron scattering plane and the plane term is important. The function JF^(X,Q2;P2) still defined by the 7* - 7 axis and the outgoing jets (we obeys the eqs. (2.9) and therefore the solution can consider the lowest order diagrams only) one can write be expressed as the linear sum of an " anomalous" [21], [22] and a "hadronic" pieces as in eq. (2.10). A simple approach consists in using the real photon solution and multiply each term by appropriate form factors (logarithmic factor for the perturbative term and the usual pole-like VDM factor for the hadronic piece)

22 Figure 4. Simplified representation of the azimuthal structure functions Figure 5. Rapidity distribution of jets in photo-production: the Zeus data are compared to the NTL theory (thick solid lines)

[27, 28]. A more elaborate method [29] is based on using a dispersion relation-like approach for the P2 dependence and leads to a complete parametrization of sensitive to the renormalization and factorization scale quark and gluon distributions in a virtual photon. ambiguities at 0(a2) since the calculation is carried

out at 0{at). What should be stressed however is 3. Hard processes in 77 and jp collisions that each component on the right-hand side of eq. (3.13) is not a physical quantity as the dependence The production of jets at large pr will first be reviewed of each term on the factorization scale occurs at the before attempting to summarize the rather confused leading order. Considering for example the D and the experimental situation concerning charm production SF terms, they receive contributions from the same in both types of reactions. In both instances it Feynman diagrams and the factorization scale is just should be said that the comparison between theory and a cut-off which separates which contribution should go experiment has not yet reached the quantitative level. in the higher order corrections to the D term from what is included in the lowest order SF term. 3.1. Jet studies: inclusive results at the NTL order A similar discussion can be given concerning jet production in photoproduction and, in that case, only Several complete calculations exist for single inclusive two components appear as only one photon is involved jet cross-section . In 77 collisions the cross section for [30]-[32]. The theoretical situation is rather satisfactory the production of a jet of a given pr and pseudorapidity as the intrinsic theoretical uncertainties due to scale 77 can be decomposed as variations have been estimated to be in the ±20% in the kinematical range covered by TRISTAN, LEP and HERA for both 7 — 7 and 7 — p reactions. New preliminary data on jet production in 7 — 7 This form reflects the fact that the photon can couple collisions at TRISTAN have been presented [33] covering to the hard sub-process producing the large pr parton a pr range up to 9 GeV/c with very high statistics. either directly or through its quark or gluon content: Previous data by the same collaboration [33] have daD arises when both photons are involved in the hard been compared with theory and very good agreement sub-scattering, daSF refers to the case when one of the has been found showing that the structure function photon interacts through its quark and gluon content extracted from DIS data can explain jet production (i.e. via the structure function discussed above) and is in 77 collisions [27]. The new data will be very often referred to as the single-resolved component while useful to further constrain the non-perturbative input do~DF involves the structure function of each photon as well as the gluon density function in the photon (double resolved case). Each of these terms is known in since jet production in the covered kinematic range the NTL approximation [27]. As in all perturbatively is very sensitive to both quantities. Data on large calculated cross sections the result eq. (3.13) is pr jets at HERA are also becoming available [34,

23 35] and agreement with NTL theoretical predictions appears to be very good as far as the pr spectrum is concerned [31, 32]. However this agreement is fortuitous since the experimental rapidity distribution of the jets is not at all accounted for by the theoretical predictions [36] as illustrated in fig.elative to the Zeus data [35]. The NTL predictions fall below the data in the central rapidity region but are well above the data in the photon fragmentation region (backward rapidity range). In the central region the discrepancy may be qualitatively understood due to the probable importance of rescattering effects, between the remnants Figure 6. The kinematics of two-jet production in of the photon and the proton (see below), which increase photo-production the observed jet transverse energy compared to the partonic jet energy used in the theoretical calculations. In the backward region no such effect is expected or seen since most of the photon energy is used in the hard pr collision. It should be noted that, usually perturbative calculations tend to underestimate the experimental results because the parton pr is in general less than the hadronic jet pr • It is also quite interesting to observe that the discrepancy between theory and experiment does not disappear as the jet pr is increased. The discrepancy cannot be removed by varying the QCD parameters in a reasonable range nor by changing the parton distributions in the photon: in fact it can be checked that the predictions in the photon fragmentation region are not very sensitive to the non perturbative input in the photon nor to the gluon distribution. On the other hand they are quite sensitive to the gluon in the proton since the data probe Figure 7. Rate of di-jet production as a function of x7. The the range xp ~ .02 to .05 in the case of HI for example. quark initiated process is shown by the solid line while the gluon To help understand the observed discrepancy it would initiated process is expected to explain the difference between data and model at small x be interesting to have data on the rapidity dependence of 7 single hadron or single photon production as these data are free from jet definition ambiguities which may be the cause of the problem. Finally the NTL calculation One can then study the di-jet distribution as a function of di-jet production is still lacking and it would yield a of xy and one expects the region xy ~ 1 to be dominated rich quantitative phenomenology as we are going to see by the direct process, while for smaller xy values the at the leading logarithmic level. dynamics will be dominated by the hard interaction of the partons in the photon, with the gluon induced processes dominating the smallest x domain: this is 3.2. Di-jet production in the leading logarithmic 7 nicely illustrated by fig. 7 from HI [37] where the analysis data have been corrected to reconstruct, at the leading Di-jet production turns out to be a very useful logarithmic level, the parton momenta initiating the observable to access specific features of the photon jets. From these data, one can extract [37] the gluon

structure and impressive results have been presented distribution in the photon in the range .05 < x7 < 1. by both HERA collaborations. The basic idea is to in good agreement with standard leading order parton

use the more exclusive kinematics to reconstruct the x7 distributions but excluding the Lacl parametrization variable, i.e. the scaled momentum of the parton in the which is too high at small x . Zeus [38] performs photon which takes part in the interaction (see fig. 6). a similar analysis not correcting for jet momentum Conservation of momentum implies and therefore the theoretical predictions tend to fall below the data. Let us note that in the future, it will be possible to tag the electron so as to select events with photons of virtuality P2 and thus study

24 partonic transverse energy from the hadronic jet energy: the data seem to indicate that rescattering effects in the central and forward regions are important and make this reconstruction difficult.

3.3. Heavy flavor production

Similarly to the jet case, the cross section for the production of heavy flavors in 77 collisions has three components: the direct, the single resolved and the double resolved ones [41]. This is obvious since the diagrammatic structure is the same. But in Figure 8. Study of multiple scattering effects: Phojet (dash-dotted line) agrees with the data while models without contrast to the jet case the direct cross section is rescattering (dashed line) do not calculable unambiguously from perturbative QCD as the mass of the heavy quark acts as a cut-off of the potential collinear singularities. The main parameter controling the size of the cross section is therefore

2 2 F^ix.Q ] P ) with the hard scale being set by the jet the mass of the heavy quark (as well as at if the transverse momentum Q2 = p\\ combined with the DIS calcultation is performed in the NTL approximation). measurements on a slightly virtual photon a full study The factorization scale ambiguity appears only in the of the virtual photon structure function will be possible. SF and DF components, the latter component being In further studies, it is possible to isolate the photon negligible up to LEP2 energies. From the theoretical remnant which, in two large pr jet events, appears as a point of view the predictions are rather stable, at least third jet with low pr in the backward rapidity region up to LEP energies, for the following reasons [41]: (typically a cut 773 < —1 is imposed). Preliminary - the direct cross section dominates; typically it accounts results of Zeus [39] show that the pr as well as the for 70% of the total cross section at LEP1 and even rapidity distribution of this jet are in better agreement more at TRISTAN but decreases to 50% at LEP2. No with a model where the photon remnant is generated large uncertainties from the photon structure function with a power 1 jp2^ law rather than an exponential fall- are therefore expected. off, in qualitative agreement with the existence of an - the size of the higher order corrections is about 20% anomalous component in the photon structure function. to 30% with a standard choice of scales. A 15% As mentioned above, jet energy profile studies in uncertainty can be attributed to scale ambiguities. At

2 both HI and Zeus have shown a distorsion of the jet higher energies large In(5/771^) or ln(p r/rriQ) may have shape related to a higher level of transverse energy to be ressummed but these should not be a problem up outside the jet in the positive rapidity region [37, 38]: to LEP2. this is attributed to secondary scatterings between the The data concern only charm production as the photon and the proton fragments. To study this effect rate for bottom production is too small (

58 GeV the remaining transverse energy density (i.e. the energy Amy [42], Topaz [43] at V^e+C- = well outside the two-jet system) and study its dependence as from Aleph [44] were presented at this conference. as a function of x7: small xy values mean energetic Different experimental methods were used. In the case photon remnants and therefore important rescattering of Amy and Topaz the electron (or muon) inclusive effects. Fig. 8 illustrates this effect [40]: models without method is used where the lepton from the decay c —> IX multiple interactions do not reproduce the data while is obtained after subtracting the background. Amy also Phojet [9] which has a built-in mechanism for multiple introduces the "soft pion" method to identify D*'s: in scattering is in very good agreement with the data. the decay D*± —• D0^ the charged TT has a small In conclusion to these jet studies it is clear that, transverse momentum compared to the jet axis and the at the qualitative level, all charateristic features of the signal appears as an excess near the pr — 0 end of the photon hadronic structure are seen to be necessary to transverse momentum spectrum of the TT with respect account for experimental data: one needs both a quark to the jet. Finally, Aleph uses the more conventional and gluon component in the photon and the anomalous "AM method": the signal appears as a sharp peak at component is clearly seen. On the other hand the 145 MeV in the distribution in AM = MQ*± — M/30. NTL phenomenology based on jet distributions is not The comparison between theory and experiments can convincing, partly because the jet pr values available be roughly summarized by saying that the TRISTAN are rather low and it is not clear how to reconstruct the results on charm production at large pr (typically > 2. GeV/c) are compatible with NTL theoretical presently available is not high enough to be sensitive predictions assuming a charm quark mass mc ~ 1.3 GeV only to the perturbative or point-like structure of the and standard parton distributions [15]. The Topaz data, photon. Much more data from HERA as well as from including the low p? sample are even higher and would LEP2 will grandly improve the situation and hopefully require the larger (at low x) Lacl distributions. In we will soon reach a level of quantitative understanding contrast, Aleph requires a much higher charm mass, of as it is already the case for the proton structure function. the order 1.7 to 1.9 GeV depending on the choice of scales in the theoretical calculation. Extrapolating the Aknowledgements experimental data to estimate the total cross section of charm production [45], it appears that the rate of I thank R. Engel, M. Erdmann, J. Field, A. Finch, production is higher at TRISTAN than at LEPl! All M. Fontannaz, H. Hayashii, F. Kapusta, U. Karshon, the data show the need for a QCD component beyond M. Kienzle-Foccaci, E. Laenen, T. Nozaki, S. Soldner- the lowest order 77 —• cc component (the so-called Rembold and many of the speakers at Sheffield for their quark parton model). However it is fair to say that patience and for several enlightning discussions. I also no single set of QCD parameters can reproduce all the thank D. Poencier for some of the art work.

experimental data in the range y/s€+€- 29 to 90 GeV despite the large error bars in the data! Turning now to HERA data the initial yp energy is now much higher and the predictions of open charm production [47] are sensitive to the parton distributions in the photon (as well as in the proton). Results presented by U. Karshon [46], based both on the lepton References inclusive method and the AM method are consistent [1] Proceedings of PHOTON '95, Sheffield, England, 8-13 April with QCD extrapolations of lower energy data using 1995, B. Cartwright, D.J. Miller and V.A. Khoze cds. standard structure functions and a charm mass of [2] G. B clanger, see [l], 1.5 GeV. Hidden charm, i.e. production has also M. Baillargeon, G. Belanger and F. Boudjema, Phys. Rev. been measured at Zeus [46] at large inelasticities so that D51 (1995) 4712. [3] V.A. Khoze, see [1]. the dominant mechanism involves the direct coupling of [4] D.J. Miller, Proceedings of the Workshop on Two-Photon the photon to the charm quark pair. The experimental Physics at LEP and HERA, Lund, May 1994, G. Jarlskog results tend to exceed the NTL theoretical predictions and L. Jonsson eds. [48]. [5] I. Kronkvist, Delphi collaboration, see [l]; P. Abreu et al., Delphi collaboration, CERN-PPE-95-087. Based on present results it is clear that much more [6] J.H. Field, F. Kapusta and L. Poggioli, Phys. Lett. B181 work is necessary to reach a quantitative understanding (1986) 362; Z. Phys. C36 (1987) 121. of heavy flavor production. Large errors exist in the [7] L. Lonnblad, see [1]. [8] M. Seymour, see [l]; determination of the quark mass making the extraction G. Marchesini, B.R. Webber, G. Abbiendi, I.G. Knowles, of the gluon structure function in both the proton M.H. Seymour and L. Stanco, Comp. Phys. Com. 67 (1992) and the photon not very realistic. Clearly much more 465. statistics are necessary. When comparing theory and [9] R. Engel and J. Ranft, preprint ENSLAPP-A-540/95; R. Engel, Z. Phys. C66 (1995) 203. experiments one often extrapolates the experimental [10] T. Nozaki, Amy collaboration, see [l]; predictions to the whole phase space so as to compare S.K. Sahu et a/., Amy collaboration, KEK-Preprint-95-18. with the predictions for total cross section or more [11] B. Kennedy, Opal collaboration, see [l]. inclusive quantities. This certainly introduces extra [12] R. Akers, et aL, Opal collaboration, Z. Phys. C61 (1994) 199. errors. It would be advisible to have exclusive NTL [13] H. Abramowicz, K. Charchula and A. Levy, Phys. Lett. Monte-Carlo generators for a more reliable comparison B269 (1991) 458. between theory and experiments. [14] H.J. Behrend, Cello collaboration, XXVth International Conference on High Energy Physics, Singapore 1990, K.K. Phua and Y. Yamaguchi eds., World Scientific, 4. Conclusions Singapore. [15] M. Gluck, E. Reya and A. Vogt, Phys. Rev. D46 (1992) It is fair to say that our understanding of photon induced 1973. [16] M. Fontannaz, Orsay preprint LPTHE-93-22, talk given reaction has not yet reach a quantitative understanding at the 21st International meeting on Fundamental Physics, and whether we study jet production or heavy flavor Miranores de la Sierra, Spain, May 1993; production a lot of theoretical and experimental work P. Aurenche, M. Fontannaz and J.Ph. Guillet, Z. Phys. C64 is still needed. This is because this field of study is (1994) 621. [17] L.E. Gordon, see [1]; L.E. Gordon and J.K. Storrow, Z. relatively new and also because the photon appears to Phys. 56 (1992) 307. have a very complex partonic structure: the energy [18] H. Kan, see [l].

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