Hadronic electroweak current and $\pi - a_1$ mixing

TL;DR

This paper investigates how electroweak interactions modify the meson mixing and current dominance in the effective meson Lagrangian, revealing deviations from traditional vector and axial-vector dominance models.

Contribution

It introduces a gauge covariant diagonalization approach for axial-vector and pseudoscalar mixing, analyzing its effects within the extended Nambu-Jona-Lasinio model using the Schwinger-DeWitt method.

Findings

Deviation from vector and axial-vector dominance in hadronic electroweak current

Modification of meson mixing due to electroweak interactions

Application of Schwinger-DeWitt method to effective action analysis

Abstract

It is found that in presence of electroweak interactions the gauge covariant diagonalization of the axial-vector -- pseudoscalar mixing in the effective meson Lagrangian leads to a deviation from the vector meson and the axial-vector meson dominance of the entire hadronic electroweak current. The essential features of such a modification of the theory are investigated in the framework of the extended Nambu-Jona-Lasinio model with explicit breaking of chiral $U(2) \times U(2)$ symmetry. The Schwinger-DeWitt method is used as a major tool in our study of the real part of the relevant effective action. Some straightforward applications are considered.