Transversity GPDs of the proton from lattice QCD

Constantia Alexandrou,Krzysztof Cichy,Karl Jansen,Kyriakos Hadjiyiannakou,Martha Constantinou,Aurora Scapellato,Fernanda Steffens

doi:10.1103/physrevd.105.034501

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.

Highlights

The current picture of the nucleon structure stems from decades of increasingly precise measurements of form factors (FFs) and parton distribution functions (PDFs), which, in turn, are special cases of more general functions, the generalized parton distributions (GPDs)
At a given hard scale Q2, GPDs depend on three variables: the longitudinal momentum fraction of the parent nucleon carried by a given parton, x; the square of the fourmomentum transferred to the target in a given reaction, t; and the skewness, ξ, which represents the change in the longitudinal momentum fraction induced by the momentum transfer
We remind the reader that h1TðΓ2Þ is directly related to the leading HT GPD; see Eq (6). h2TðΓ0Þ has a smaller signal than the above matrix elements, but it is clearly non-negligible

Summary

Introduction

The current picture of the nucleon structure stems from decades of increasingly precise measurements of form factors (FFs) and parton distribution functions (PDFs), which, in turn, are special cases of more general functions, the generalized parton distributions (GPDs). At a given hard scale Q2, GPDs depend on three variables: the longitudinal momentum fraction of the parent nucleon carried by a given parton, x; the square of the fourmomentum transferred to the target in a given reaction, t; and the skewness, ξ, which represents the change in the longitudinal momentum fraction induced by the momentum transfer. GPDs can be seen as correlations between the longitudinal momentum of partons, with a given spin, and their position in the transverse spatial plane of the parent hadron.

Objectives

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Results

Conclusion