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Precise prediction of the decay rate for ηb→γγ from lattice QCD

Brian Colquhoun1,*, Christine T. H. Davies1,†, and G. Peter Lepage2 (HPQCD Collaboration‡)

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Phys. Rev. D 112, 114513 – Published 24 December, 2025

DOI: https://doi.org/10.1103/nn49-wn7h

Abstract

We calculate the decay rate for ηb→γγ in lattice QCD for the first time, providing a precise prediction for the Belle II experiment. Our calculation includes u, d, s, and c quarks in the sea, using gluon field configurations generated by the MILC collaboration, at three values of the lattice spacing from 0.06 to 0.03 fm. All quarks are treated in the highly improved staggered quark formalism, which enables us to reach the b quark mass for our valence quarks on these fine lattices. We calculate quark-line connected correlation functions only. By working at additional heavy quark masses between those of c and b we map out the behavior of the ratio fηh/(Mηh2Fηh(0,0)), where f is the decay constant, M, the mass and F(0,0), the form factor for decay to two on-shell photons for the pseudoscalar heavyonium meson, ηh. This ratio takes the approximate value 0.5 in leading-order nonrelativistic QCD (NRQCD) but we are able to give a much more accurate analysis than this. Focusing on the b quark mass, we find a ratio of 0.467(11), giving Γ(ηb→γγ)=0.559(32)fit(1)syst  keV. Combined with a value for the branching fraction from NRQCD, our result can be used to determine the total width of the ηb with a 6% uncertainty.

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Phys. Rev. D 112, 114513– Published 24 December, 2025
  • Received 13 November 2024
  • Accepted 24 November 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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