Azimuthal and spin asymmetries in $e^{+}{e}^{-}\to V\pi X$ at high energies and 3D fragmentation functions

We present the systematical decomposition results of three-dimensional (3D) fragmentation functions (FFs) from parton correlators for spin-1 hadron. We choose one of the best process $e^{+}{e}^{-}\to V\pi X$ to study the 3D and tensor polarization dependent FFs. By making a general kinematic analysis we show that the cross section is expressed by 81 independent structure functions, and get the results of the azimuthal and spin asymmetries. We also present the parton model results for this process and express the results in terms of the 3D FFs. Based on this formalism, we also give the numerical results of hadron longitudinal polarizations and predict the energy dependence.