One flavor mass reweighting in lattice QCD

TL;DR

This paper introduces a new stochastic method for one flavor mass reweighting in lattice QCD, enabling precise quark mass tuning even with complex phase determinants, improving accuracy and applicability.

Contribution

The paper presents an unbiased stochastic estimation technique for the one flavor determinant, applicable to complex phases, with error control via determinant factorizations.

Findings

Method successfully tunes up-down quark mass difference.

Unbiased stochastic estimation handles complex phase determinants.

Error controlled through mass interpolation and Schur decomposition.

Abstract

One flavor mass reweighting can be used in lattice QCD computations to fine tune the quark masses to their physical values. We present a new method that utilizes an unbiased stochastic estimation of the one flavor determinant. The stochastic estimation is based on the integral representation of the determinant of a complex matrix, which we prove. In contrast to other methods it can also be applied in situations where the determinant has a complex phase. The stochastic error is controlled by determinant factorizations based on mass interpolation and Schur decomposition. As an example of an application we demonstrate how the method can be used to tune the up-down quark mass difference.