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Glauber gluons in pion-induced Drell-Yan processes revisited

We reanalyze the anomalous angular distribution of lepton pairs produced in a pion-induced Drell-Yan process by taking into account the Glauber gluon effect in the $k_T$ factorization theorem. Compared to the previous study, we adopt the realistic parton distribution functions (PDFs) for a proton from the CTEQ and for a pion from the xFitter, include the QCD evolutions of the strong coupling and the PDFs, and integrate the differential cross section over the kinematic regions for the NA10, E615 and COMPASS experiments. These improvements then allow rigorous confrontations of theoretical results with the data. It is shown that the lepton angular distribution and the violation of the Lam-Tung relation measured in all the above experiments can be well accommodated with a single Glauber phase. We illustrate the Glauber effect in the geometric picture for a Drell-Yan process, and its distinction from the conventional Boer-Mulders mechanism. The observables are pointed out, which can be used to discriminate the two proposals, when data become more precise.