Renormalized quark masses using gradient flow

Physical review. D/Physical review. D., vol. 113

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 m s MS ¯ ( μ = 2 GeV ) = 89 ( 3 ) MeV and m c MS ¯ ( μ = 3 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 nonperturbatively renormalized fermionic observables like form factors or bag parameters from lattice simulations.

Authors 5

1. Matthew Black

   University of Siegen · University of Edinburgh

   Affiliation as printed

   University of Edinburgh

   Universität Siegen

2. Robert V. Harlander Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University

3. Anna Hasenfratz A

   University of Colorado Boulder

   Affiliation as printed

   University of Colorado, Boulder

4. Antonio Rago

   University of Southern Denmark

   Affiliation as printed

   University of Southern Denmark

5. Oliver Witzel

   University of Siegen

   Affiliation as printed

   Universität Siegen