Subtraction of power counting breaking terms in chiral perturbation theory: spinless matter fields

TL;DR

This paper systematically derives and absorbs power counting breaking terms in chiral perturbation theory with spinless matter fields at one-loop order, ensuring consistent effective field theory calculations.

Contribution

It introduces a method to calculate and absorb power counting breaking terms for matter fields in chiral perturbation theory at next-to-next-to-leading order.

Findings

Derived explicit form of breaking terms at one-loop order

Demonstrated absorption into counterterms in the Lagrangian

Method applicable to other matter fields

Abstract

When matter fields are included in chiral perturbation theory, the nonvanishing mass in the chiral limit introduces a new energy scale so that the loop diagrams including such matter field propagators spoil the usual power counting. However, the power counting breaking terms can be absorbed into counterterms in the chiral Lagrangian. In this paper, we systematically derive these terms to leading one-loop order (next-to-next-to leading order in the chiral expansion) at once by calculating the generating functional using the path integral. They are then absorbed by counterterms in the next-to-leading order Lagrangian. The method can be extended to calculating power counting breaking terms for other matter fields.