Charmonium radiative transitions to dileptons from lattice QCD: The case of h c → η c ℓ + ℓ − and χ c 1 → 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 c 1 → 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 c 1 decays, we find Γ ( χ c 1 → J / ψ e + e − ) = 2.869 ( 90 ) <