Radiative decay $Y(4260)\to X(3872)+\gamma$ involving hadronic molecular and charmonium components

We apply a phenomenological Lagrangian approach to the radiative decay $Y(4260)\to X(3872)+\gamma$. The $Y(4260)$ and $X(3872)$ resonances are considered as composite states containing both molecular hadronic and charmonium components. Having a leading molecular component in the $X(3872)$ and a sole molecular configuration for the $Y(4260)$ results in a prediction compatible with present data.

Figure 1

Hadronic molecular component contributions to the mass operators of $X(3872)$ and $Y(4260)$.

Figure 2

Charmonium component contribution to the mass operators of $H=X(3872),Y(4260)$.

Figure 3

Diagram describing the hadronic molecular component contribution to the radiative decay $Y(4260)\to X(3872)+\gamma$.

Figure 4

Diagrams describing the charmonium component contribution to the radiative decay $Y(4260)\to X(3872)+\gamma$.

Figure 5

Decay width $\mathrm{\Gamma }(Y(4260)\to X(3872)+\gamma )$ as a function of the mixing angle ${\theta }_Y$ for three different scenarios of molecular-charmonium mixing in the $X(3872)$ state: I (${\theta }_X=68.9^0$), II (${\theta }_X=-12.6^0$) and III (${\theta }_X=-20.2^0$).