Vacuum polarization corrections to low energy quark effective couplings

TL;DR

This paper calculates vacuum polarization corrections to low energy quark effective couplings up to eighth order using a QCD-based NJL model, revealing how effective couplings vary with gluon mass and aligning with phenomenological data.

Contribution

It introduces a method to compute higher-order quark effective couplings considering vacuum polarization effects within a NJL model framework.

Findings

Effective couplings decrease with increasing gluon mass.

Results agree well with phenomenological fits.

Higher-order interactions up to eighth order are characterized.

Abstract

In this work corrections to low energy punctual effective quark couplings up to the eighth order are calculated by considering vacuum polarization effects with the scalar quark-antiquark condensate. The departing point is a QCD-based NJL model. By separating the quark field into two components, one that condenses and another one for interacting quarks, the former is integrated out with the help of usual auxiliary fields and an effective action in terms for interacting quark fields is found. The scalar auxiliary field reduces to the quark-antiquark condensate in the vacuum and the determinant is expanded in powers of the quark-antiquark bilinears generating chiral invariant effective 2N-quark interactions (N=2, 3...). The corresponding coupling constants and effective masses are estimated, and the general trend is that for increasing the effective gluon mass the values of the effective coupling constants decrease. All the values are in good agreement with phenomenological fits.