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

TL;DR

This paper recalculates the radiative decay widths of certain heavy quarkonia states using the covariant light-front approach, including relativistic corrections, and compares results with experimental data and other models.

Contribution

It provides a detailed analysis of relativistic effects in heavy quarkonium radiative decays within the covariant light-front framework, confirming consistency with non-relativistic formulas.

Findings

Relativistic corrections are explicitly computed and shown to be consistent with non-relativistic results.

Predicted decay widths agree reasonably with experimental data.

Theoretical uncertainties are analyzed based on quark mass and wavefunction parameters.

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.