Sivers and Boer-Mulders TMDs of the proton in a light-front quark-diquark model

Abstract

We obtain the leading twist T-odd quark transverse momentum-dependent parton distribution functions (TMDs) of the proton, namely, the Sivers function ${f}_{1T}^{\ensuremath{\perp}q}(x,{p}_{\ensuremath{\perp}}^{2})$ and the Boer-Mulders function ${h}_{1}^{\ensuremath{\perp}q}(x,{p}_{\ensuremath{\perp}}^{2})$, in a light-front quark-diquark model constructed with the wave functions predicted by the soft-wall AdS/QCD. The gluon rescattering is crucial to predict nonzero T-odd TMDs. We study the utility of a nonperturbative $SU(3)$ gluon rescattering kernel going beyond the usual approximation of perturbative $U(1)$ gluons. The spin asymmetries in semi-inclusive deep inelastic scattering (SIDIS) associated with these T-odd TMDs are found to be consistent with HERMES and COMPASS data. We further predict the Sivers asymmetries of pion production in the SIDIS process in the kinematical region of the Electron-Ion Collider (EIC) and the EIC in China. We also evaluate the generalized Sivers and Boer-Mulders shifts and compare them with the available lattice QCD simulations.