Charmonium radiative transitions to dileptons from lattice QCD: The case of $h_c \to \eta_c \ell^+\ell^-$ and $\chi_{c1} \to J/\psi\,\ell^+\ell^-$

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: $h_c \to \eta_c \ell^+ \ell^-$ and $\chi_{c1} \to J/\psi \ell^+ \ell^-$, where $\ell = e, \mu$. 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 $\Gamma(h_c \to \eta_c e^+ e^-) = 5.45(19)~\mathrm{keV}$, and $\Gamma(h_c \to \eta_c \mu^+ \mu^-) = 0.635(22)~\mathrm{keV}$. For the $\chi_{c1}$ decays, we find: $\Gamma(\chi_{c1} \to J/\psi e^+ e^-)= 2.869(90)~\mathrm{keV}$, and $\Gamma(\chi_{c1} \to J/\psi \mu^+ \mu^-) = 0.1993(72)~\mathrm{keV}$. Our results for the $\chi_{c1}$ decays show good compatibility with experimental data. However, our prediction for the $h_c \to \eta_c e^+ e^- $ decay rate is approximately $3\sigma$ 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 $\chi_{c1}$ charmonium transitions, including their differential distributions and angular observables. They provide benchmark predictions for future experimental studies.