A phenomenological study on the $\cos\phi_h$ azimuthal asymmetry in double longitudinally Polarized SIDIS

We study the $\cos{\phi_h}$ azimuthal asymmetry in double polarized semi-inclusive pion production by considering dynamical twist-3 effects. In particular, we evaluate the role of the transverse momentum dependent distributions $e_L(x, k_T^2)$ and $g_L^\perp(x, k_T^2)$ on the asymmetry. Using two different sets of spectator model results for these distributions, we predict the $\cos{\phi_h}$ asymmetry of $\pi^+$, $\pi^-$, and $\pi^0$ at the kinematic configuration available at CLAS, HERMES and COMPASS. Our estimates show that the asymmetries are positive for all the pions and could be accessed by CLAS and HERMES. We also find that $g_L^\perp$ gives the dominant contribution to the $\cos\phi_h$ asymmetry, while the contribution of $e_L$ is almost negligible.