Monte Carlo simulation of single spin asymmetries in pion-proton collisions

We present Monte Carlo simulations of both the Sivers and the Boer-Mulders effects in the polarized Drell-Yan $\pi^\pm p^\uparrow \to \mu^+ \mu^- X$ process at the center-of-mass energy $\sqrt{s} \sim 14$ GeV reachable at COMPASS with pion beams of energy 100 GeV. For the Sivers effect, we adopt two different parametrizations for the Sivers function to explore the statistical accuracy required to extract unambiguous information on this parton density. In particular, we verify the possibility of checking its predicted sign change between Semi-Inclusive Deep-Inelastic Scattering (SIDIS) and Drell-Yan processes, a crucial test of nonperturbative QCD. For the Boer-Mulders effect, because of the lack of parametrizations we can make only guesses. The goal is to explore the possibility of extracting information on the transversity distribution, the missing piece necessary to complete the knowledge of the nucleon spin structure at leading twist, and the Boer-Mulders function, which is related to the long-standing problem of the violation of the Lam-Tung sum rule in the unpolarized Drell-Yan cross section.