Eta-nucleon coupling constant in QCD with SU(3) symmetry breaking

TL;DR

This paper estimates the eta-nucleon coupling constant using QCD sum rules, accounting for SU(3) symmetry breaking effects, and finds significant deviations from SU(3) symmetric predictions.

Contribution

It introduces a method to calculate the eta-nucleon coupling constant considering SU(3) symmetry breaking within the QCD sum rules framework, providing more accurate estimates.

Findings

SU(3) breaking effects are as large as 50%.

Three sum rules yield consistent results.

The eta-nucleon coupling constant is significantly affected by SU(3) symmetry breaking.

Abstract

We study the $\eta$NN coupling constant using the method of QCD sum rules starting from the vacuum-to-eta correlation function of the interpolating fields of two nucleons. The matrix element of this correlation has been taken with respect to nucleon spinors to avoid unwanted pole contribution. The SU(3)-flavor symmetry breaking effects have been accounted for via the $\eta$-mass, s-quark mass and eta decay constant to leading order. Out of the four sum rules obtained by taking the ratios of the two sum rules in conjunction with the two sum rules in nucleon mass, three are found to give mutually consistent results. We find the SU(3) breaking effects significant, as large as 50% of the SU(3) symmetric part.