Calculation of QCD Instanton Determinant with Arbitrary Mass

TL;DR

This paper presents a detailed numerical computation of the one-loop effective action in an instanton background for arbitrary quark masses, bridging the small and large mass limits with improved accuracy.

Contribution

It introduces an efficient numerical method for calculating the instanton determinant across all mass regimes, including renormalization details and comparison with approximation methods.

Findings

Numerical results match the interpolating function between mass limits.

The method effectively handles divergences through renormalization.

Results improve understanding of mass dependence in QCD instanton effects.

Abstract

The precise quark mass dependence of the one-loop effective action in an instanton background has recently been computed [arXiv:hep-th/0410190]. The result interpolates smoothly between the previously known extreme small and large mass limits. The computational method makes use of the fact that the single instanton background has radial symmetry, so that the computation can be reduced to a sum over partial waves of logarithms of radial determinants, each of which can be computed numerically in an efficient manner. The bare sum over partial waves is divergent and must be regulated and renormalized. In this paper we provide more details of this computation, including both the renormalization procedure and the numerical approach. We conclude with comparisons of our precise numerical results with a simple interpolating function that connects the small and large mass limits, and with the leading order of the derivative expansion.