Evaluation of pion-nucleon sigma term in Dyson-Schwinger equation approach of QCD

TL;DR

This paper uses Dyson-Schwinger equations in QCD to calculate the pion-nucleon sigma term by analyzing the chiral condensate's variation with chemical potential, providing a new theoretical estimate.

Contribution

It introduces a method to evaluate the pion-nucleon sigma term using Dyson-Schwinger equations with different quark-gluon interaction models.

Findings

Sigma term value: 62 MeV with systematic and statistical errors

Chiral condensate variation computed at finite chemical potential

Method demonstrates consistency across different models

Abstract

We calculate the variation of the chiral condensate in medium with respect to the quark chemical potential and evaluate the pion-nucleon sigma term via the Hellmann-Feynman theorem. The variation of chiral condensate in medium are obtained by solving the truncated Dyson-Schwinger equation for quark propagator at finite chemical potential, with different models for the quark-gluon vertex and gluon propagator. We obtain the value of the sigma term $\sigma_{\pi N}$ = 62(1)(2) MeV, where the first represents the systematic error due to our different model for the quark-gluon vertex and gluon propagator and the second represents a statistical error in our linear fitting procedure.