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We investigate the theoretical framework of the $\cos 2\phi$ azimuthalasymmetry contributed by the coupling of two Boer-Mulders functions in thedilepton production unpolarized $\pi p$ Drell-Yan process by applying thetransverse momentum dependent factorization at leading order. We adopt themodel calculation results of the unpolarized distribution function $f_1$ andBoer-Mulders function $h_1^\perp$ of pion meson from the light-cone wavefunctions. We take into account the transverse momentum evolution effects forboth the distribution functions of pion and proton by adopting the existedextraction of the nonperturbative Sudakov form factor for the pion and protondistribution functions. An approximate kernel is included to deal with theenergy dependence of the Boer-Mulders function related twist-3 correlationfunction $T_{q,F}^{(\sigma)}(x,x)$ needed in the calculation. We numericallyestimate the Boer-Mulders asymmetry $\nu_{BM}$ as the functions of $x_p$,$x_\pi$, $x_F$ and $q_T$ considering the kinematics at COMPASS Collaboration.

Boer-Mulders effect in the unpolarized pion induced Drell-Yan process at COMPASS within TMD factorization