Flavor separation of the Boer-Mulders function from unpolarized $\pi^- p$ and $\pi^- D$ Drell-Yan processes

We show that measuring the $\cos 2\phi$ angular dependence in unpolarized Drell-Yan processes with $\pi^-$ beams colliding on proton and deuteron targets can determine the ratio of the Boer-Mulders functions for $d$ and $u$ quarks inside the proton $h_1^{\perp,d}/h_1^{\perp,u}$, which is still lack of theoretical constraint. The comparison of the $\cos 2 \phi$ asymmetries measured in unpolarized $\pi^- p$ and $\pi^- D$ Drell-Yan processes, which are accessible at CERN by the COMPASS collaboration, can help to discriminate whether $h_1^\perp$ effects or QCD vacuum effects are preferred by data.