Transversity GPDs of the proton from lattice QCD

TL;DR

This paper presents the first lattice QCD calculation of the x-dependence of isovector transversity GPDs for the proton, providing new insights into its transverse spin structure.

Contribution

It introduces a novel lattice QCD approach to compute the x-dependent transversity GPDs of the proton, including non-local operators and matching to light-cone distributions.

Findings

First x-dependent transversity GPDs from lattice QCD

Renormalized GPDs in the MS-bar scheme at 2 GeV

Extracted lowest moments revealing proton's transverse spin structure

Abstract

We present the first calculation of the $x$-dependence of the isovector transversity generalized parton distributions (GPDs) for the proton within lattice QCD. We compute the matrix elements with non-local operators containing a Wilson line. The calculation implements the Breit symmetric frame. The proton momenta are chosen as $0.83,\,1.25,\,1.67$ GeV, and the values of the momentum transfer squared are $0.69,\,1.02$ GeV$^2$. These combinations include cases with zero and nonzero skewness. The calculation is performed using one ensemble of two degenerate-mass light, a strange and a charm quark of maximally twisted mass fermions with a clover term. The lattice results are renormalized non-perturbatively and finally matched to the light-cone GPDs using one-loop perturbation theory within the framework of large momentum effective theory. The final GPDs are given in the $\overline{\rm MS}$ scheme at a scale of 2 GeV. In addition to the individual GPDs, we form the combination of the transversity GPDs that is related to the transverse spin structure of the proton. Finally, we extract the lowest two moments of GPDs and draw a number of important qualitative conclusions.