The Bethe–Heitler Process in Polarized Photon–Nucleon Interactions

We calculate the Bethe–Heitler cross section for the production of lepton pairs in the field of a longitudinally polarized nucleon, taking into account the lepton masses and the target mass. This process is a dominant background to the detection of open charm from semi-leptonic decay modes, which is a potential probe of the polarized gluon distribution in the nucleon. The knowledge on the spin structure of the nucleon has improved considerably over the past few years. More precise measurements of the spin asymmetry A1(x,Q ) ' g1(x,Q )/F1(x,Q ) in longitudinally polarized deep-inelastic scattering (DIS) of leptons off proton, deuterium and neutron targets [1] yielded valuable information on spin sum rules and on the polarized valence quark distributions. On the theoretical side, it has become possible to perform a consistent analysis of polarized DIS in next-to-leading order (NLO), since the required spin-dependent two-loop splitting functions have been calculated recently [2]. Nevertheless, all NLO analyses [3, 4] have demonstrated, that the available data sets are still not sufficient for an accurate extraction of the spin-dependent sea quark and gluon densities of the nucleon. This is true in particular for the detailed xshape of the spin-dependent gluon distribution, even though a tendency towards a sizeable positive total gluon polarization was found [3, 4]. The spin-dependent gluon distribution enters the polarized structure functions at leading order (LO) only indirectly via the Qdependence of g1 which could not be studied accurately up to now due to the rather limited kinematical coverage in (x,Q) of the present fixed target experiments [1]. Moreover, a direct extraction of the gluon distribution from scaling violations of the polarized structure functions is more involved than in the unpolarized case, as a complicated interplay of quark and gluon contributions to the scaling violations [5] is taking place even at low values of x. Clearly, the determination of the polarized gluon distribution is one of the most interesting challenges for future spin physics experiments. Recently much effort was devoted to examine the feasibility of such measurements at future polarized pp (RHIC, [6]) and ep colliders, one conceivable option for a future HERA upgrade which is currently under discussion [7]. An alternative measurement could be possible at the recently approved COMPASS experiment [8] at CERN or at the proposed E156 experiment [9] at SLAC. The key process studied in these latter fixed target experiments is the production of charmed particles, as the cross section asymmetry for open charm photoproduction ∆σ/σ provides a clear tool to access the spin-