Proper-time evaluation of the effective action: unequal masses in the loop

TL;DR

This paper employs the proper-time method to derive the one-loop effective action in a chiral field theory with unequal heavy particle masses, expanding in inverse powers of these masses and calculating key coefficients.

Contribution

It introduces a systematic approach to evaluate the effective action with explicit flavor symmetry breaking due to unequal masses using the proper-time method.

Findings

Derived the effective action as a series in inverse heavy masses.

Explicitly calculated the first two Seeley-DeWitt coefficients.

Provided a framework for studying flavor symmetry breaking effects.

Abstract

The Fock-Schwinger proper-time method is used to derive the effective action in the field theory with the chiral $U(3)\times U(3)$ symmetry explicitly broken by unequal masses of heavy particles. The one-loop effective action is presented as a series in inverse powers of heavy masses. The first two Seeley-DeWitt coefficients of this expansion are explicitly calculated. This powerful technique opens a promising avenue for studying explicit flavor symmetry breaking effects in the effective field theories.