Transvese momentum dependent parton distributions of pion at leading twist

Abstract: We calculate the leading twist pion unpolarized transverse momentum distribution $f_1(x,k_T^2)$ and the Boer-Mulders function $h_1^\perp(x,k_T^2)$, using leading Fock-state light front wave functions (LF-LFWFs) based on Dyson-Schwinger and Bethe-Salpeter equations. These DS-BSEs based LF-LFWFs provide dynamically generated s- and p-wave components, which are indispensable in producing chirally odd Boer-Mulders function that has one parton spin flipped. Employing a non-perturbative SU(3) gluon rescattering kernel to treat the gauge link of the Boer-Mulders function, we thus obtain both TMDs at hadronic scale and then evolve them to the scale of $\mu^2=4.0$ GeV$^2$. We finally calculate the generalized Boer-Mulders shift and find it to be in agreement with the lattice prediction.