Phys. Rev. D 108, 014513 (2023) - Precise determination of decay rates for ${\ensuremath{\eta}}_{c}\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\gamma}$, $J/\ensuremath{\psi}\ensuremath{\rightarrow}\ensuremath{\gamma}{\ensuremath{\eta}}_{c}$, and $J/\ensuremath{\psi}\ensuremath{\rightarrow}{\ensuremath{\eta}}_{c}{e}^{+}{e}^{\ensuremath{-}}$ from lattice QCD

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Precise determination of decay rates for $η_{c} \to γ γ$ , $J / ψ \to γ η_{c}$ , and $J / ψ \to η_{c} e^{+} e^{-}$ from lattice QCD

Brian Colquhoun, Laurence J. Cooper, Christine T. H. Davies, and G. Peter Lepage (HPQCD Collaboration)

Phys. Rev. D 108, 014513 – Published 24 July 2023

Abstract

We calculate the decay rates for $η_{c} \to γ γ$ , $J / ψ \to γ η_{c}$ and $J / ψ \to η_{c} e^{+} e^{-}$ in lattice QCD with $u$ , $d$ , $s$ and $c$ quarks in the sea for the first time. We improve significantly on previous theory calculations to achieve accuracies of 1–2%, giving lattice QCD results that are now more accurate than the experimental values. In particular our results transform the theoretical picture for $η_{c} \to γ γ$ decays. We use gluon field configurations generated by the MILC collaboration that include $n_{f} = 2 + 1 + 1$ flavors of highly improved staggered sea quarks at four lattice spacing values from 0.15 fm to 0.06 fm and with sea u/d masses down to their physical value. We also implement the valence $c$ quarks using the highly improved staggered quark action. We find $Γ (η_{c} \to γ γ) = 6.788 (45)_{fit} (41)_{syst} keV$ , in good agreement with experimental results using $γ γ \to η_{c} \to K \bar{K} π$ but in $4 σ$ tension with the Particle Data Group global fit result [R. L. Workman (Particle Data Group), Prog. Theor. Exp. Phys. 2022, 083C01 (2022)]; we suggest this fit is revisited. We also calculate $Γ (J / ψ \to γ η_{c}) = 2.219 (17)_{fit} (18)_{syst} (24)_{expt} (4)_{QED} keV$ , in good agreement with results from CLEO, and predict the Dalitz decay rate $Γ (J / ψ \to η_{c} e^{+} e^{-}) = 0.01349 (15)_{latt} (15)_{expt} (13)_{QED} keV$ . We use our results to calibrate other theoretical approaches and to test simple relationships between the form factors and $J / ψ$ decay constant expected in the nonrelativistic limit.

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Received 16 May 2023
Accepted 23 June 2023

DOI:https://doi.org/10.1103/PhysRevD.108.014513

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.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Form factors Particle decays Quantum chromodynamics Quantum electrodynamics

Charm quark Mesons

Lattice QCD

Particles & Fields

Authors & Affiliations

Brian Colquhoun ^1,*, Laurence J. Cooper ¹, Christine T. H. Davies ^1,†, and G. Peter Lepage ² (HPQCD Collaboration^‡)

¹SUPA, School of Physics and Astronomy, University of Glasgow, Glasgow, G12 8QQ, United Kingdom
²Laboratory of Elementary Particle Physics, Cornell University, Ithaca, New York 14853, USA

^*Brian.Colquhoun@glasgow.ac.uk
^†Christine.Davies@glasgow.ac.uk
^‡http://www.physics.gla.ac.uk/HPQCD.

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Vol. 108, Iss. 1 — 1 July 2023

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Physical Review D

covering particles, fields, gravitation, and cosmology

Precise determination of decay rates for $η_{c} \to γ γ$ , $J / ψ \to γ η_{c}$ , and $J / ψ \to η_{c} e^{+} e^{-}$ from lattice QCD

Brian Colquhoun, Laurence J. Cooper, Christine T. H. Davies, and G. Peter Lepage (HPQCD Collaboration)

Phys. Rev. D 108, 014513 – Published 24 July 2023

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Physical Review D

covering particles, fields, gravitation, and cosmology

Precise determination of decay rates for ηc→γγ, J/ψ→γηc, and J/ψ→ηce+e− from lattice QCD

Brian Colquhoun, Laurence J. Cooper, Christine T. H. Davies, and G. Peter Lepage (HPQCD Collaboration)

Phys. Rev. D 108, 014513 – Published 24 July 2023

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Precise determination of decay rates for $η_{c} \to γ γ$ , $J / ψ \to γ η_{c}$ , and $J / ψ \to η_{c} e^{+} e^{-}$ from lattice QCD