  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.
