Hadronic loop effects on the radiative decays of the first radial excitations of η and η′

Abstract

Based on the one-state assumption of $\ensuremath{\eta}(1405)$ and $\ensuremath{\eta}(1475)$, $\ensuremath{\eta}(1295)$ and $\ensuremath{\eta}(1405/1475)$ thus being organized as the first radial excitations of $\ensuremath{\eta}$ and ${\ensuremath{\eta}}^{\ensuremath{'}}$, respectively, we investigate the productions and radiative decays of these two states in $J/\ensuremath{\psi}\ensuremath{\rightarrow}\ensuremath{\gamma}{\ensuremath{\eta}}_{X}\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\gamma}V$, where ${\ensuremath{\eta}}_{X}$ stands for $\ensuremath{\eta}(1295)$ and $\ensuremath{\eta}(1405/1475)$ and $V$ stands for vector mesons ${\ensuremath{\rho}}^{0}$, $\ensuremath{\omega}$, $\ensuremath{\phi}$. As we have learned from previous studies that the hadronic decays of these two states receive important contributions from the intermediate $\overline{K}{K}^{*}+\mathrm{c}.\mathrm{c}.$ meson loops due to the triangle singularity mechanism, we show that some measurable effects can also arise from the $\overline{K}{K}^{*}+\mathrm{c}.\mathrm{c}.$ meson loops in their radiative decays. Our calculation shows that the impact of the $\overline{K}{K}^{*}+\mathrm{c}.\mathrm{c}.$ meson loops on the $\ensuremath{\eta}(1405/1475)$ radiative decays is relatively smaller than on $\ensuremath{\eta}(1295)$ since the latter has a much larger coupling to $\overline{K}{K}^{*}+\mathrm{c}.\mathrm{c}$. However, the production of $\ensuremath{\eta}(1295)$ in the $J/\ensuremath{\psi}$ radiative decays will be strongly suppressed due to its being the radial excitation state of the $\ensuremath{\eta}$ meson. As a consequence of the $\overline{K}{K}^{*}+\mathrm{c}.\mathrm{c}.$ meson loop contributions, we find that the mixing angle extracted in the radiative decays of $\ensuremath{\eta}(1295)$ and $\ensuremath{\eta}(1405/1475)$ will be different from each other, and both are different from the one determined in other processes.