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High-precision scale setting with the $Ω$ -baryon mass and gradient flow

Alexei Bazavov^1,*, Claude W. Bernard², David A. Clarke³, Carleton DeTar³, Aida X. El-Khadra^4,5, Elvira Gámiz⁶, Steven Gottlieb⁷, Anthony V. Grebe ^8,9,†, Urs M. Heller¹⁰ et al. (Fermilab Lattice and MILC Collaborations)

Urs M. Heller¹⁰, Leon Hostetler⁷, William I. Jay¹¹, Hwancheol Jeong⁷, Andreas S. Kronfeld^8,‡, Yin Lin (林胤)¹², Shaun Lahert³, Jack Laiho¹³, Michael Lynch^4,5, Andrew T. Lytle^4,5, Aaron S. Meyer¹⁴, Ethan T. Neil¹⁵, Curtis T. Peterson¹, James N. Simone⁸, Jacob W. Sitison¹⁵, Ruth S. Van de Water⁸, Alejandro Vaquero^3,16,17, and Michael L. Wagman⁸ (Fermilab Lattice and MILC Collaborations)

¹Department of Computational Mathematics, Science and Engineering, and Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824, USA
²Department of Physics, Washington University, St. Louis, Missouri 63130, USA
³Department of Physics and Astronomy, University of Utah, Salt Lake City, Utah 84112, USA
⁴Department of Physics, University of Illinois Urbana-Champaign, Urbana, Illinois 61801, USA
⁵Illinois Center for Advanced Studies of the Universe, University of Illinois Urbana-Champaign, Urbana, Illinois 61801, USA
⁶CAFPE and Departamento de Física Teórica y del Cosmos, Universidad de Granada, 18071 Granada, Spain
⁷Department of Physics, Indiana University, Bloomington, Indiana 47405, USA
⁸Theory Division, Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA
⁹Maryland Center for Fundamental Physics and Department of Physics, University of Maryland, College Park, Maryland 20742, USA
¹⁰American Physical Society, Hauppauge, New York 11788, USA
¹¹Department of Physics, Colorado State University, Fort Collins, Colorado 80523, USA
¹²Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
¹³Department of Physics, Syracuse University, Syracuse, New York 13244, USA
¹⁴Nuclear and Chemical Sciences Division, Lawrence Livermore National Laboratory, Livermore, California 94550, USA
¹⁵Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
¹⁶Departmento de Física Teórica, Universidad de Zaragoza, 50009 Zaragoza, Spain
¹⁷Centro de Astropartículas y Física de Altas Energías, Universidad de Zaragoza, 50009 Zaragoza, Spain

^*Contact author: bazavov@msu.edu
^†Contact author: agrebe@umd.edu
^‡Contact author: ask@fnal.gov

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Phys. Rev. D 113, 054501 – Published 3 March, 2026

DOI: https://doi.org/10.1103/t18c-bpqy

Abstract

The gradient-flow scale $w_{0}$ in lattice QCD is determined using the mass of the $Ω^{-}$ baryon to set the physical scale. Nine ensembles using the highly improved staggered quark (HISQ) action with lattice spacings of 0.15 fm down to 0.04 fm are used, seven of which have nearly physical light-quark masses. Electromagnetic corrections to the $Ω^{-}$ mass are defined in order to compute a pure-QCD $Ω$ mass. The final result is $w_{0} = 0.17187 (68) fm$ , corresponding to a relative uncertainty of 0.40% and a central value in good agreement with previous calculations in the literature.

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Phys. Rev. D 113, 054501– Published 3 March, 2026

Vol. 113, Iss. 5 — 1 March 2026

Received 8 October 2025
Accepted 28 January 2026

DOI: https://doi.org/10.1103/t18c-bpqy

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

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High-precision scale setting with the $Ω$ -baryon mass and gradient flow

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High-precision scale setting with the Ω-baryon mass and gradient flow

Abstract

Physics Subject Headings (PhySH)

Article Text

References (84)

High-precision scale setting with the $Ω$ -baryon mass and gradient flow