The transversity parton distribution function of the nucleon using the pseudo-distribution approach

TL;DR

This paper determines the non-singlet transversity parton distribution function of the nucleon using lattice QCD and the pseudo-distribution approach, providing insights into the nucleon's spin structure with a novel reconstruction method.

Contribution

It introduces a lattice QCD calculation of the transversity PDF using the pseudo-distribution method and Jacobi polynomial expansion to reduce model dependence.

Findings

Valence transversity PDF estimate agrees with global fits

Nucleon sea is found to be isospin symmetric in transversity

Method demonstrates feasibility of lattice-based transversity extraction

Abstract

We present a determination of the non-singlet transversity parton distribution function (PDF) of the nucleon, normalized with respect to the tensor charge at $\mu^2=2$ GeV$^2$ from lattice quantum chromodynamics. We apply the pseudo-distribution approach, using a gauge ensemble with a lattice spacing of 0.094 fm and the light quark mass tuned to a pion mass of 358 MeV. We extract the transversity PDF from the analysis of the short-distance behavior of the Ioffe-time pseudo-distribution using the leading-twist next-to-leading order (NLO) matching coefficients calculated for transversity. We reconstruct the $x$-dependence of the transversity PDF through an expansion in a basis of Jacobi polynomials in order to reduce the PDF ansatz dependence. Within the limitations imposed by a heavier-than-physical pion mass and a fixed lattice spacing, we present a comparison of our estimate for the valence transversity PDF with the recent global fit results based on single transverse spin asymmetry. We find the intrinsic nucleon sea to be isospin symmetric with respect to transversity.