Pretzelosity $h_{1T}^{\perp}$ and quark orbital angular momentum

We calculate the pretzelosity distribution ($h_{1T}^{\perp}$), which is one of the eight leading twist transverse momentum dependent parton distributions (TMDs), in the light-cone formalism. We find that this quantity has a simple relation with the quark orbital angular momentum distribution, thus it may provide a new possibility to access the quark orbital angular momentum inside the nucleon. The pretzelosity distribution can manifest itself through the $\sin(3\phi_h-\phi_S)$ asymmetry in semi-inclusive deep inelastic scattering process. We calculate the $\sin(3\phi_h-\phi_S)$ asymmetry at HERMES, COMPASS and JLab kinematics, and present our prediction on different targets including the proton, deuteron and neutron targets. Inclusion of transverse momentum cut in data analysis could significantly enhance the $\sin(3\phi_h-\phi_S)$ asymmetry for future measurements.