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We present a lattice QCD calculation of the transversity isovector- andisoscalar-quark parton distribution functions (PDFs) of the proton utilizing aperturbative matching at next-to-leading-order (NLO) accuracy. Additionally, wedetermine the isovector and isoscalar tensor charges for the proton. In bothcalculations, the disconnected contributions to the isoscalar matrix elementshave been ignored. The calculations are performed using a single ensemble of$N_f = 2 +1$ highly-improved staggered quarks simulated with physical-massquarks and a lattice spacing of $a = 0.076$ fm. The Wilson-clover action, withphysical quark masses and smeared gauge links obtained from one iteration ofhypercubic (HYP) smearing, is used in the valence sector. Using the NLOoperator product expansion, we extract the lowest four to six Mellin momentsand the PDFs from the matrix elements via a neural network. In addition, wecalculate the $x$-dependence of the PDFs with hybrid-scheme renormalization andthe recently developed leading-renormalon resummation technique, at NLO withthe resummation of leading small-$x$ logarithms.

Transversity PDFs of the proton from lattice QCD with physical quark masses