Transversity GPDs of the proton from lattice QCD

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 nonlocal 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 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.

Hadron spin structure from lattice QCD

“…Exploratory studies of isovector GPDs are also under way, see e.g. recent studies by ETMC [40,42,43]. The way forward includes studying the continuum limit and the volume dependence and developing noise reduction techniques to reach larger boosts.…”

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

“…More recently, the first lattice QCD computation of the x-dependent transversity generalized parton distribution function (GPD) based on the LaMET approach was presented in Ref. [76]. The aim of this paper is to complement those previous studies with an independent, first computation of the leading-twist transversity PDF of the nucleon using the short-distance factorization based pseudodistribution approach.…”

Proton generalized parton distributions from lattice QCD

“…The corresponding decompositions for the helicity and transversity GPDs can be found in Refs. [21,22]. The x-dependence of the GPDs is recovered in two steps.…”

“…In this work, we follow the implementation described in Refs. [21][22][23]. Finally, given that quasi-and light-cone GPDs only differ in the ultraviolet region [25,26], one can match quasi-GPDs to light-cone GPDs via a coefficient determined in perturbation theory.…”

“…Results are presented for selected GPDs and for additional results and details we refer to Refs. [21][22][23].…”