A new approach to quark mass determination using the gradient flow

TL;DR

This paper introduces a novel method for quark mass determination using ratios of flowed quark bilinear operator VEVs, combining perturbative calculations and lattice results for improved accuracy.

Contribution

It develops a new expansion technique based on the Laplace transform and provides numerical results across a wide mass range, enhancing quark mass determination methods.

Findings

Perturbative evaluation of VEVs to next-to-leading order.

Development of a Laplace transform-based expansion technique.

Numerical results covering a broad range of quark masses.

Abstract

We propose a new method to determine quark masses using ratios of the vacuum-expectation values (VEVs) of flowed quark bilinear operators. They can be expressed as functions of the flow time $t$ and the ${\overline {\rm MS}}$ quark mass $\overline{m}$, which can then be determined by matching with the corresponding lattice results. Motivated by this, we evaluate these VEVs perturbatively through next-to-leading order in the strong coupling. We provide the results as expansions in the limits of small and large $\overline{m}^2 t$. To this end, we develop a new expansion technique based on the Laplace transform. Additionally, we present numerical results with the exact mass dependence over a wide range of $\overline{m}^2t$. We discuss the expected perturbative precision for the mass determination based on our next-to-leading order perturbative calculations, and possible non-perturbative corrections.