Lepton Angular Distributions of Fixed-target Drell-Yan Experiments in Perturbative QCD and a Geometric Approach

The lepton angular distributions of the Drell-Yan process in fixed-target experiments are investigated by NLO and NNLO perturbative QCD. We present the calculated angular parameters $\lambda$, $\mu$, $\nu$ and the degree of violation of the Lam-Tung relation, $1-\lambda-2\nu$, for the NA10, E615 and E866 experiments. Predictions for the ongoing COMPASS and SeaQuest experiments are also presented. The transverse momentum ($q_T$) distributions of $\lambda$ and $\nu$ show a clear dependence on the dimuon mass ($Q$) while those of $\mu$ have a strong rapidity ($x_F$) dependence. Furthermore, $\lambda$ and $\nu$ are found to scale with $q_T/Q$. These salient features could be qualitatively understood by a geometric approach where the lepton angular distribution parameters are expressed in terms of the polar and azimuthal angles of the "natural axis" in the dilepton rest frame.