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Renormalized quark masses using gradient flow

Matthew Black1,2, Robert V. Harlander3, Anna Hasenfratz4,*, Antonio Rago5, and Oliver Witzel2,†

  • *Contact author: anna.hasenfratz@colorado.edu
  • †Contact author: oliver.witzel@uni-siegen.de
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Phys. Rev. D 113, 094504 – Published 21 May, 2026

DOI: https://doi.org/10.1103/3nvr-pkn1

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 nonperturbative 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 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 msMS¯(μ=2  GeV)=89(3)  MeV and mcMS¯(μ=3  GeV)=972(16)  MeV. These results predict the scale-independent ratio mc/ms=12.1(4). Generalization to other observables is possible, providing an efficient approach to determine nonperturbatively renormalized fermionic observables like form factors or bag parameters from lattice simulations.

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Phys. Rev. D 113, 094504– Published 21 May, 2026
  • Received 27 June 2025
  • Accepted 31 March 2026
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