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

Abstract

Abstract We revisit the calculation of the width for the radiative decay of a $$1^{+-}$$ 1 + - heavy $$Q \bar{Q}$$ Q Q ¯ meson via the channel $$1^{+-} \rightarrow 0^{-+} +\gamma $$ 1 + - → 0 - + + γ 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 wave function structure parameter. We analyze the specific decays $$h_{\mathrm{c}}(1P) \rightarrow \eta _{\mathrm{c}}(1S) + \gamma $$ h c ( 1 P ) → η c ( 1 S ) + γ and $$h_{\mathrm{b}}(1P) \rightarrow \eta _{\mathrm{b}}(1S) + \gamma $$ h b ( 1 P ) → η b ( 1 S ) + γ . 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.