Revisiting radiative decays of $1^{+-}$ heavy quarkonia in the covariant light-front approach

Abstract

We revisit the calculation of the width for the radiative decay of a $1^{+-}$ heavy $Q\bar{Q}$ meson via the channel $1^{+-}\to 0^{-+}+\gamma$ in the covariant light-front quark model. We carry out the reduction of the light-front amplitude in the non-relativistic limit, explicitly computing the leading and next-to-leading order relativistic corrections. This shows the consistency of the light-front approach with the non-relativistic formula for this electric dipole transition. Furthermore, the theoretical uncertainty in the predicted width is studied as a function of the inputs for the heavy quark mass and wavefunction structure parameter. We analyze the specific decays $h_c(1P)\to {\eta }_c(1S)+\gamma$ and $h_b(1P)\to {\eta }_b(1S)+\gamma$. We compare our results with experimental data and with other theoretical predictions from calculations based on non-relativistic models and their extensions to include relativistic effects, finding reasonable agreement.