Radiative decays of $0^{\mathbf{++}}$ and $1^{\mathbf{+}\mathbf{-}}$ heavy mesons

The radiative decay is believed to be an ideal lab to study the hadronic structure of newly observed resonances because the reactions are governed by only the electromagnetic interaction (tree level). However, to obtain correct theoretical values, one has to properly deal with the nonperturbative QCD effects in the wave function and hadronization. In this work, we derive the formulas for the radiative decays of $0^{++}$ and $1^{-+}$ heavy mesons in the light-front quark model. Because $\mathcal{B}({\chi }_{c0}\to J/\psi \gamma )$ is well-measured, the theoretical evaluation of the transition rate can be used to test our approach. Within this theoretical framework, the width of ${\chi }_{b0}\to {\rm Y}(1S)\gamma$ is evaluated. The formulas can be applied to identify the inner structures of new resonances, for example the isospin of $h_{c(b)}$ and the structure of $D_s(2317)$, via processes $h_c\to {\eta }_c\gamma$, $h_b\to {\eta }_b\gamma$ and $D_s(2317)\to D_s^{*}+\gamma$.

Figure 1

Feynman diagrams for radiative decay.