A systematic phenomenological study of the cos 2 φ asymmetry in unpolarized semi--inclusive DIS

We study the $\cos 2 \phi$ azimuthal asymmetry in unpolarized semi-inclusive DIS, taking into account both the perturbative contribution (gluon emission and splitting) and the non perturbative effects arising from intrinsic transverse motion and transverse spin of quarks. In particular we explore the possibility to extract from $<\cos 2 \phi>$ some information about the Boer--Mulders function $h_1^{\perp}$, which represents a transverse--polarization asymmetry of quarks inside an unpolarized hadron. Predictions are presented for the HERMES, COMPASS and JLab kinematics, where $<\cos 2 \phi>$ is dominated by the kinematical higher--twist contribution, and turns to be of order of few percent. We show that a larger asymmetry in $\pi^-$ production, compared to $\pi^+$ production, would represent a signature of the Boer--Mulders effect.