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 $lambda$, $mu$, $ u$ and the degree of violation of the Lam-Tung relation, $1-lambda-2 u$, 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 $ u$ show a clear dependence on the dimuon mass ($Q$) while those of $mu$ have a strong rapidity ($x_F$) dependence. Furthermore, $lambda$ and $ u$ 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.