Evaluation of pion-nucleon sigma term in Dyson–Schwinger equations approach of QCD with three-constituent quark approximation

Abstract

In this paper, we study the pion-nucleon sigma term in Dyson–Schwinger equations approach of QCD with a three-constituent-quark approximation. The constituent quark mass is defined by the quark mass function obtained from the quark gap equation with various quark-gluon vertex and effective interaction models. We investigate the parameter dependence of the numerical results with fixed values of chiral condensate. We found that in all cases the numerical results of the pion-nucleon sigma term decrease with increasing constituent quark mass. Quantitatively, the dependence is insensitive to different interaction models, but is quite different with different quark-gluon vertices. Concerning the experimental results, we give the proper model and parameter range with which the theoretical value of pion-nucleon sigma term is consistent with the experiments.