On mass dependences of the one-loop effective action in simple backgrounds

TL;DR

This paper discusses a systematic large mass expansion method for the one-loop effective action in quantum field theory, enabling interpolation between small and large mass limits and estimating QCD vacuum tunneling contributions.

Contribution

It introduces a method to relate small and large mass limits of the effective action, allowing for arbitrary mass estimates in background fields.

Findings

Large mass expansion using Seeley-DeWitt coefficients provides reliable approximations.

The method allows inference of effective actions at arbitrary masses from known limits.

Application to QCD vacuum tunneling amplitude estimates for quarks of any mass.

Abstract

If background fields are soft on the scale set by mass of the particle involved, a reliable approximation to the field-theoretic one-loop effective action is obtained by a systematic large mass expansion involving higher-order Seeley-DeWitt coefficients. Moreover, if the small mass limit of the effective action in a particular background has been found by some other means, the two informations may be used to infer the corresponding result for {\em arbitrary} mass values. This method is used to estimate the one-loop contribution to the QCD vacuum tunneling amplitude by quarks of arbitrary mass.