Precise Quark Mass Dependence of Instanton Determinant

TL;DR

This paper presents an exact numerical method to determine the quark mass dependence of the fermion determinant in an instanton background, bridging the gap between small and large mass analytical limits.

Contribution

It introduces a novel numerical approach that accurately computes the fermion determinant for any quark mass, improving upon previous limited analytical approximations.

Findings

Exact determinant calculation for arbitrary quark mass.

Smooth interpolation between small and large mass limits.

Enhanced understanding of instanton effects across mass regimes.

Abstract

The fermion determinant in an instanton background for a quark field of arbitrary mass is determined exactly using an efficient numerical method to evaluate the determinant of a partial wave radial differential operator. The bare sum over partial waves is divergent but can be renormalized in the minimal subtraction scheme using the result of WKB analysis of the large partial wave contribution. Previously, only a few leading terms in the extreme small and large mass limits were known for the corresponding effective action. Our approach works for any quark mass and interpolates smoothly between the analytically known small and large mass expansions.