Charmonium radiative transitions to dileptons from lattice QCD: The case of h_c → η_c ℓ⁺ℓ⁻ and χ_c1 → J/ψ ℓ⁺ℓ⁻

We present a lattice QCD study of dilepton production in charmonium transitions, specifically focusing on the 1⁺⁻ → 0⁻⁺ and 1⁺⁺ → 1⁻⁻ processes: h_c → η_c ℓ⁺ℓ⁻ and χ_c1 → 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 → η_c e⁺e⁻) = 5.45(19) keV, and Γ(h_c → η_c μ⁺μ⁻) = 0.635(22) keV. For the χ_c1 decays, we find: Γ(χ_c1 → J/ψ e⁺e⁻) = 2.869(90) keV, and Γ(χ_c1 → J/ψ μ⁺μ⁻) = 0.1993(72) keV. Our results for the χ_c1 decays show good compatibility with experimental data. However, our prediction for the h_c → η_c e⁺e⁻ decay rate is approximately 3σ larger than the BESIII result. We also present predictions for the differential decay widths as functions of the dilepton invariant mass, q², 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_c1 charmonium transitions, including their differential distributions and angular observables. They provide benchmark predictions for future experimental studies.