Transversity distribution of the proton from lattice QCD

The transversity distribution is considerably less constrained from experiments due to their chiral-odd nature. Complementary information from lattice QCD is essential. In this talk, we present a lattice QCD calculation of the transversity parton distribution functions (PDFs) of the proton under the framework of large-momentum effective theory. The $x$-dependent PDFs are extracted from the boosted quasi-PDF matrix elements with improved matching, including the next-to-leading order perturbative corrections, and leading renormalon and renormalization group resummations. In addition, we report a calculation of the rapidity anomalous dimension of quark transverse-momentum-dependent distributions, i.e., the Collins-Soper (CS) kernel, up to transverse separations of about 1 fm. They are non-perturbaive QCD input for the global analysis of the transverse-momentum-dependent transversity distributions. The CS kernel is extracted from the ratios of pion quasi-transverse-momentum-dependent wave functions (quasi-TMDWFs) at next-to-leading logarithmic perturbative accuracy. The calculations are performed using ensembles of $N_f$=2+1 quarks simulated with physical-mass quarks with lattice spacings $a$ around 0.08 fm.