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η and η′ mesons from Nf=2+1 lattice QCD at the physical point using topological charge operators

Yue Su1,2, Nan Wang3,4,5, Long-cheng Gui1,6,7,8,*, Jun Hua3,5, Jian Liang3,5,†, and Jun Shi3,5,‡ (χQCD Collaboration)

  • 1Department of Physics, Hunan Normal University, Changsha 410081, China
  • 2Center for Joint Quantum Studies and Department of Physics, School of Science, Tianjin University, Tianjin 300350, China
  • 3State Key Laboratory of Nuclear Physics and Technology, Institute of Quantum Matter, South China Normal University, Guangzhou 510006, China
  • 4Key Laboratory of Atomic and Subatomic Structure and Quantum Control (MOE), Guangdong-Hong Kong Joint Laboratory of Quantum Matter, Guangzhou 510006, China
  • 5Guangdong Basic Research Center of Excellence for Structure and Fundamental Interactions of Matter, Guangdong Provincial Key Laboratory of Nuclear Science, Guangzhou 510006, China
  • 6Hunan Research Center of the Basic Discipline for Quantum Effects and Quantum Technologies, Hunan Normal University, Changsha 410081, China
  • 7Synergetic Innovation Center for Quantum Effects and Applications (SICQEA), Changsha 410081, China
  • 8Key Laboratory of Low-Dimensional Quantum Structures and Quantum Control of Ministry of Education, Changsha 410081, China

  • *Contact author: guilongcheng@hunnu.edu.cn
  • †Contact author: jianliang@scnu.edu.cn
  • ‡Contact author: jun.shi@scnu.edu.cn
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Phys. Rev. D 112, 114516 – Published 30 December, 2025

DOI: https://doi.org/10.1103/cmzr-h8kx

Abstract

By fitting the two-point correlation functions of topological charge density operators calculated on two 2+1-flavor gauge ensembles with physical pion mass, we determine both the η and η′ masses and also the mixing angle to be mη=0.505(72)(75)  GeV, mη′=0.952(47)(40)  GeV, and θ1=−8.9(2.1)(1.8)°, respectively, where the first error is the statistical uncertainty and the second one is the systematic uncertainty. This is the first extraction of both η/η′ masses and the mixing angle θ1 using topological charge operators. Compared with previous studies using quark bilinear operators, the error of the η mass is relatively large, but the mixing angle has comparable precision. This demonstrates that the topological charge operators are well suited to study the η and η′ mesons.

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Phys. Rev. D 112, 114516– Published 30 December, 2025
  • Received 29 May 2025
  • Accepted 17 December 2025
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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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