The $\sin2\phi_h$ azimuthal asymmetry of pion production in SIDIS within TMD factorization

We study the $\sin2\phi_h$ azimuthal asymmetry of charged and neutral pion productions off the longitudinally polarized nucleon targets in semi-inclusive deeply inelastic scattering (SIDIS) process within the transverse momentum dependent~(TMD) factorization. The asymmetry is contributed by the convolution of the TMD distribution $h_{1L}^{\perp}$ and the Collins fragmentation function $H_{1}^\perp$. We adopt the Wandzura-Wilczek-type~(WW-type) approximation for $h_{1L}^{\perp}$ and two different parametrizations on the nonperturbative part of TMD evolution for $h_{1L}^{\perp}$ and $H_{1}^\perp$. We numerically estimate the asymmetry in the kinematical configurations available at HERMES, CLAS and CLAS12. It is shown that our theoretical calculation can describe the HERMES and CLAS data, except the asymmetry of the $\pi^-$ production off proton target at HERMES and CLAS. We also find that different choices of the nonperturbative part of TMD evolution lead qualitatively similar results.