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

TL;DR

This paper presents a lattice QCD study of the proton's transversity PDFs and tensor charges using physical quark masses, employing NLO perturbative matching, neural networks, and novel renormalization techniques.

Contribution

It introduces a comprehensive lattice QCD calculation of transversity PDFs and tensor charges with NLO accuracy, utilizing multiple approaches and advanced renormalization methods.

Findings

Calculated transversity PDFs and tensor charges for the proton.

Extracted Mellin moments and PDFs using pseudo- and quasi-PDF approaches.

Applied NLO perturbative matching and renormalon resummation techniques.

Abstract

We present a lattice QCD calculation of the transversity isovector- and isoscalar-quark parton distribution functions (PDFs) of the proton utilizing a perturbative matching at next-to-leading-order (NLO) accuracy. Additionally, we determine the isovector and isoscalar tensor charges for the proton. In both calculations, the disconnected contributions to the isoscalar matrix elements have been ignored. The calculations are performed using a single ensemble of $N_f = 2 +1$ highly-improved staggered quarks simulated with physical-mass quarks and a lattice spacing of $a = 0.076$ fm. The Wilson-clover action, with physical quark masses and smeared gauge links obtained from one iteration of hypercubic smearing, is used in the valence sector. Using the NLO operator product expansion, we extract the lowest four to six Mellin moments and the PDFs via a neural network from the matrix elements in the pseudo-PDF approach. In addition, we calculate the PDFs in the quasi-PDF approach with hybrid-scheme renormalization and the recently developed leading-renormalon resummation technique, at NLO with the resummation of leading small-$x$ logarithms.