Transverse single-spin asymmetries of pion production in semi-inclusive DIS at subleading twist

We study the single-spin asymmetries with the $\sin\phi_S$ and $\sin(2\phi_h -\phi_S)$ angular dependences for charged and neutral pions produced in semi-inclusive deep inelastic scattering on the transversely polarized proton target. The theoretical interpretations of the two asymmetries are presented in terms of the convolution of the twist-3 quark transverse momentum dependent distributions and twist-2 fragmentation functions. Specifically, we investigate the role of the distributions $f_T$, $h_T$ and $h_T^\perp$ in the $\sin\phi_S$ asymmetry, as well as the role of the distributions $f_T^\perp$, $h_T$ and $h_T^\perp$ in the $\sin(2\phi_h -\phi_S)$ asymmetry. We calculate these distributions in a spectator-diquark model and predict the corresponding asymmetries for the first time, considering the kinematics at HERMES, JLab and COMPASS. The numerical estimates show that the asymmetries are sizable, and the dominant contribution to the $\sin\phi_S$ asymmetry comes from the T-odd distribution $f_T$, while $f_T^\perp$ gives the main contribution to the $\sin(2\phi_h -\phi_S)$ asymmetry. The future measurements on these asymmetries can shed light on the information of twist-3 transverse momentum dependent distributions.