Understanding Direct Photon Production

J.F. Owens, Florida State University

Direct photon production is a process which provides us with a means of studying hard scattering processes with an electromagnetic probe in the final state. In this regard, the process is related to deeply inelastic scattering and photoproduction (initial state probes) and lepton pair production (final state probe). One of the great virtues of this process is that one of the two lowest order subprocesses involves an initial state gluon (q g ==> gamma q). Thus, especially in p-p or p-nucleus interactions, one has a process which can provide strong constraints on the gluon distribution. Unfortunately, there are disagreements between some experimental results and next-to-leading-order QCD calculations. These discrepancies have recently been reviewed as part of the Fermilab QCD and Weak Boson RUN II Workshop (Baur et al., 2000) . The situation is further confused by the lack of consensus as to whether or not there is a problem with the current theoretical treatment of this process. In a recent detailed analysis (Aurenche et al., 1998) of this situation a list of sources of theoretical and experimental uncertainties was presented. It was pointed out that if restrictions were placed on the choice of data sets (no nuclear targets, no isolated photon cross sections, and no pion beams) then there was general agreement between standard NLO QCD calculations and the surviving data sets. Moreover, with a minimum transverse momentum cut in place, the discrepancies with the excluded data sets were mostly just in overall normalization. This would seem to suggest that the problem is largely one of correctly determining the normalizations of various experiments. But which ones?

An alternative explanation is that one must take into account recoil corrections due to initial state gluon radiation. In conventional QCD calculations the incoming partons are treated as if they were collinear with the incoming hadrons. Initial state gluon radiation gives the incoming partons some transverse momentum which, in turn, can contribute to the transverse momentum of the observed photon. This gives rise to an enhancement of the cross section at fixed p_T. This issue has been investigated using a phenomenological k_T smearing model ( Apanasevich et al., 1998). For most experiments, the result of the smearing model is a normalization shift. For E706, the k_T corrections have some p_T shape dependence due to the wide kinematic coverage of the experiment. Additional details can be found in the Run II Workshop contribution referenced above. Recently, a formalism which combines both threshold and k_T resummation nas been developed ( Laenen et al., 2000 ) which shows promise for improving the theoretical description of the data.

Another source of uncertainty in the theoretical calculations is the treatment of isolation cuts used in triggers at collider experiments. Direct photon production in high energy hard scattering processes involves two rather different final state configurations. Often, these photons are well isolated from other partons, which appear in the final state as jets. Such contributions can be calculated perturbatively. However, sometimes the photon is produced as part of the evolution of a parton cascade or as part of the hadronization process. Such bremstrahlung contributions involve the nonperturbative fragmentation functions for a quark or gluon to produce a photon. These can be determined from measurements at, for example, electron-positron colliders. Now, in order to properly trigger on events which contain photons at the Tevatron or other high energy colliders, it is necessary to suppress events where the photon is closely accompanied by hadrons. The suppression is done by invoking isolation cuts on the electromagnetic trigger. Generally, these are of the form of an upper limit on the amount of hadronic energy which can accompany the electromagnetic trigger in some region about the trigger. Such an isolation cut suppresses, but does not totally remove, the above mentioned bremsstrahlung component. Therein lies the crux of the problem.

The question of the isolation cuts and the fragmentation or bremsstrahlung contribution has been studied theoretically. One suggestion (Frixione, 1998) has been put forward which would remove the fragmentation contribution from the isolated photon cross section altogether. Also, it appears that there are theoretical problems (Berger, Guo, and Qiu, 1995) associated with the current method of defining isolation cuts. This question has been studied in detail (Berger, Guo, and Qiu, 1996) for electron positron annihilation. Some theoretical work has also been done in an attempt to remove the problem. (Aurenche et al., 1996)

At low values of x_T the bremsstrahlung contribution can be quite sizeable. Thus, if a portion of this piece is removed by the isolation cut, it is important to know how well the effect of the cut is calculated. If, for example, the theoretical calculation overestimates the effect of the cut, then the result may be too low. To check the theoretical treatment of the isolation cuts, one would like to have cross sections measured with several different sets of isolation parameters. One could then see if the theoretical dependence on these parameters matched that of the theory. If so, then the confidence in the calculation would be increased. If not, then perhaps this would provide some clues which would help improve the theoretical description of the data.

On the experimental side, it would be interesting and useful to have information on the triple differential cross section for photon + jet production, i.e., measuring the photon p_T and the rapidities of the photon and the recoiling jet. This could help shed some light on the underlying dynamics and whether or not the recoil correction hypothesis is correct. In addition, wider rapidity coverage for the photon would be helpful. These topics are discussed in the Run II Workshop contribution mentioned above.

As our understanding of higher order corrections improves and as new data are obtained, it is anticipated that direct photon production will continue to be a useful source of information on large transverse momentum phenomena in general and on the gluon distribution in particular. Comments on this entry can be sent to owens@hep.fsu.edu.