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Charmonium radiative transitions to dileptons from lattice QCD: The case of $h_{c} \to η_{c} ℓ^{+} ℓ^{-}$ and $χ_{c 1} \to J / ψ ℓ^{+} ℓ^{-}$

Damir Bečirević ¹, Roberto Di Palma², Roberto Frezzotti ³, Giuseppe Gagliardi ⁴, Vittorio Lubicz ², Francesco Sanfilippo ⁴, and Nazario Tantalo ³

¹IJCLab, Pôle Théorie (Bâtiment 210), CNRS/IN2P3 et Université Paris-Saclay, 91405 Orsay, France, and CERN, Theory Department, 1211 Geneva 23, Switzerland
²Dipartimento di Matematica e Fisica, Università Roma Tre, and INFN, Sezione di Roma Tre, Via della Vasca Navale 84, I-00146 Rome, Italy
³Dipartimento di Fisica and INFN, Università di Roma “Tor Vergata,” Via della Ricerca Scientifica 1, I-00133 Roma, Italy
⁴Istituto Nazionale di Fisica Nucleare, Sezione di Roma Tre, Via della Vasca Navale 84, I-00146 Rome, Italy

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Phys. Rev. D 114, 054503 – Published 8 September, 2026

DOI: https://doi.org/10.1103/bkbz-5wc3

Abstract

We present a lattice QCD study of dilepton production in charmonium transitions, specifically focusing on the $1^{+ -} \to 0^{- +}$ and $1^{+ +} \to 1^{- -}$ processes: $h_{c} \to η_{c} ℓ^{+} ℓ^{-}$ and $χ_{c 1} \to J / ψ ℓ^{+} ℓ^{-}$ , where $ℓ = e$ , $μ$ . The relevant hadronic matrix elements are computed using gauge field configurations generated by the Extended Twisted Mass Collaboration with $N_{f} = 2 + 1 + 1$ dynamical Wilson-Clover twisted-mass fermions at four lattice spacings. Simulations are performed at physical dynamical $u$ , $d$ , $s$ , and $c$ quark masses, except for the coarsest lattice, where the lightest sea quark mass corresponds to a slightly heavier pion mass. A controlled continuum extrapolation is carried out. In the continuum limit for the $h_{c}$ decays, we obtain $Γ (h_{c} \to η_{c} e^{+} e^{-}) = 5.45 (19) keV$ , and $Γ (h_{c} \to η_{c} μ^{+} μ^{-}) = 0.635 (22) keV$ . For the $χ_{c 1}$ decays, we find $Γ (χ_{c 1} \to J / ψ e^{+} e^{-}) = 2.869 (90) keV$ and $Γ (χ_{c 1} \to J / ψ μ^{+} μ^{-}) = 0.1993 (72) keV$ . Our results for the $χ_{c 1}$ decays show good compatibility with experimental data. However, our prediction for the $h_{c} \to η_{c} e^{+} e^{-}$ decay rate is approximately $3 σ$ larger than the BESIII result. We also present predictions for the differential decay widths as functions of the dilepton invariant mass, $q^{2}$ , and for angular observables sensitive to longitudinal transition form factors, which are inaccessible in radiative decays with real photon emission. These results constitute the first fully dynamical lattice QCD predictions for dilepton decay rates in $h_{c}$ and $χ_{c 1}$ charmonium transitions, including their differential distributions and angular observables. They provide benchmark predictions for future experimental studies.

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Phys. Rev. D 114, 054503– Published 8 September, 2026

Vol. 114, Iss. 5 — 1 September 2026

Received 3 May 2026
Accepted 18 August 2026

DOI: https://doi.org/10.1103/bkbz-5wc3

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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Charmonium radiative transitions to dileptons from lattice QCD: The case of $h_{c} \to η_{c} ℓ^{+} ℓ^{-}$ and $χ_{c 1} \to J / ψ ℓ^{+} ℓ^{-}$

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Charmonium radiative transitions to dileptons from lattice QCD: The case of hc→ηcℓ+ℓ− and χc1→J/ψℓ+ℓ−

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Charmonium radiative transitions to dileptons from lattice QCD: The case of $h_{c} \to η_{c} ℓ^{+} ℓ^{-}$ and $χ_{c 1} \to J / ψ ℓ^{+} ℓ^{-}$