Proper-time method for unequal masses

TL;DR

This paper introduces an efficient proper-time method to calculate the leading terms of the effective action series resulting from integrating out heavy particles with unequal masses, applicable across various physical theories.

Contribution

It presents a new technique based on the Schwinger proper-time method for computing the dominant terms in the effective action series for unequal mass particles.

Findings

Efficient calculation of effective action terms for unequal masses.

Explicit flavor symmetry breaking effects characterized by effective vertices.

Applicable to chiral symmetry breaking, gauge theories, and cosmology.

Abstract

The result of removing of heavy non-equal mass particles from the theory can be described, at low energy, by the effective action, which is a series in inverse-square powers of the mass. We propose a new efficient tool to calculate the leading terms of this series based on the Schwinger proper-time method. Unequal masses give rise to a large number of effective vertices describing the explicit flavour symmetry breaking effects with well-defined coupling constants. Our method is pertinent to the theory with explicit and spontaneous chiral symmetry breaking, chiral gauge theory, standard and beyond standard model effective field theory, the theory of critical phenomena, cosmology, etc.