Contact-interaction Faddeev equation and, inter alia, proton tensor charges

TL;DR

This paper develops a Dyson-Schwinger equation approach with a contact interaction to solve Faddeev equations for nucleons, enabling the calculation of properties like tensor charges and parton distribution functions with momentum dependence.

Contribution

It introduces a momentum-dependent Faddeev amplitude formulation using a symmetry-preserving contact interaction, improving upon static approximations and connecting to QCD-like models.

Findings

Computed proton tensor charges and sigma-term.

Analyzed large Bjorken-x ratios of valence quark distributions.

Assessed effects of dressed-quark EDMs on nucleon EDMs.

Abstract

A confining, symmetry-preserving, Dyson-Schwinger equation treatment of a vector-vector contact interaction is used to formulate Faddeev equations for the nucleon and Delta-baryon in which the kernel involves dynamical dressed-quark exchange and whose solutions therefore provide momentum-dependent Faddeev amplitudes. These solutions are compared with those obtained in the static approximation and with a QCD-kindred formulation of the Faddeev kernel. They are also used to compute a range of nucleon properties, amongst them: the proton's sigma-term; the large Bjorken-x values of separate ratios of unpolarised and longitudinally-polarised valence u- and d-quark parton distribution functions; and the proton's tensor charges, which enable one to directly determine the effect of dressed-quark electric dipole moments (EDMs) on neutron and proton EDMs.