Hadronic loop effects on the radiative decays of the first radial excitations of $\hat{I}\cdot$ and $\hat{I}{\cdot }^{\prime }$

Abstract

Based on the one state assumption of $\hat{I}\cdot (1405)$ and $\hat{I}\cdot (1475)$, thus, $\hat{I}\cdot (1295)$ and $\hat{I}\cdot (1405/1475)$ are organized as the first radial excitations of $\hat{I}\cdot$ and $\hat{I}{\cdot }^{\prime }$, respectively, we investigate the productions and radiative decays of these two states in $J/\ddot{I}ˆ\to {\hat{I}}^3\hat{I}{\cdot }_X\to {\hat{I}}^3{\hat{I}}^{3}V$, where $\hat{I}{\cdot }_X$ stands for $\hat{I}\cdot (1295)$ and $\hat{I}\cdot (1405/1475)$ and $V$ for vector mesons $\ddot{I}{}^0,\ddot{I}‰,\ddot{I}•$. As we have learned from previous studies that the hadronic decays of these two states receive important contributions from the intermediate $\bar{K}{K}^{\ast }+c.c.$ meson loops due to the triangle singularity mechanism, we show that some measurable effects can also arise from the $\bar{K}{K}^{\ast }+c.c.$ meson loops in their radiative decays. Our calculation shows that the impact of the $\bar{K}{K}^{\ast }+c.c.$ meson loops on the $\hat{I}\cdot (1405/1475)$ radiative decays is relatively smaller than on $\hat{I}\cdot (1295)$ since the latter has a much larger coupling to $\bar{K}{K}^{\ast }+c.c.$ However, the production of $\hat{I}\cdot (1295)$ in the $J/\ddot{I}ˆ$ radiative decays will be strongly suppressed. As a consequence of the $\bar{K}{K}^{\ast }+c.c.$ meson loop contributions, we find that the mixing angle extracted in the radiative decays of $\hat{I}\cdot (1295)$ and $\hat{I}\cdot (1405/1475)$ will be different from each other, and both are different from the one determined in other processes.

Revtex, 6 eps figures, 21 pages