Renormalized quark masses using gradient flow

TL;DR

This paper introduces a new method using gradient flow and RG running to determine renormalized quark masses from lattice QCD simulations, achieving reliable results up to the charm quark mass.

Contribution

The authors develop a simple, non-perturbative approach combining gradient flow and short-flow-time expansion for accurate quark mass renormalization on the lattice.

Findings

Determined $m_s$ and $m_c$ in the $ar{MS}$ scheme with specified values.

Validated the method's reliability up to the charm-quark mass.

Provided a scale-independent ratio $m_c/m_s=12.1(4)$.

Abstract

We propose a new and simple method for determining the renormalized quark masses from lattice simulations. Renormalized quark masses are an important input to many phenomenological applications, including searching and modeling physics beyond the Standard Model. The non-perturbative renormalization is performed using gradient flow combined with the short-flow-time expansion that is improved by renormalization-group (RG) running to match to the $\overline{\text{MS}}$-scheme. Implementing the RG running perturbatively, we demonstrate this method works reliably at least up to the charm-quark mass and exhibits an easily-attainable ``windowing condition''. Using RBC/UKQCD's (2+1)-flavor Shamir domain-wall fermion ensembles with Iwasaki gauge action, we find $m_s^\overline{\text{MS}}(\mu=2 \text{ GeV}) = 90(3)$ MeV and $m_c^\overline{\text{MS}}(\mu=3 \text{ GeV}) = 972(16)$ MeV. These results predict the scale-independent ratio $m_c/m_s= 12.1(4)$. Generalization to other observables is possible, providing an efficient approach to determine non-perturbatively renormalized fermionic observables like form factors or bag parameters from lattice simulations.