A new approach to quark mass determination using the gradient flow

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 $\overline{\mathrm{MS}}$ 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 ${\overline{m}}^{2}t$. We discuss the expected perturbative precision for the mass determination based on our next-to-leading order perturbative calculations, and possible non-perturbative corrections.

33 pages, 5 figures, 2 ancillary files, published version, minor modifications