X(3872)as a hadronic molecule and its decays to charmonium states and pions

Abstract

The $X(3872)$ with quantum numbers ${J}^{PC}={1}^{++}$ is considered as a composite hadronic state comprised of the dominant molecular ${D}^{0}{D}^{*0}$ component and other hadronic pairs---${D}^{\ifmmode\pm\else\textpm\fi{}}{D}^{*\ensuremath{\mp}}$, $J/\ensuremath{\psi}\ensuremath{\omega}$, and $J/\ensuremath{\psi}\ensuremath{\rho}$. Applying the compositeness condition we constrain the couplings of the $X(3872)$ to its constituents. We calculate two- and three-body hadronic decays of the $X(3872)$ to charmonium states ${\ensuremath{\chi}}_{cJ}$ and pions using a phenomenological Lagrangian approach. Next using the estimated $XJ/\ensuremath{\psi}\ensuremath{\omega}$ and $XJ/\ensuremath{\psi}\ensuremath{\rho}$ couplings we calculate the widths of $X(3872)\ensuremath{\rightarrow}J/\ensuremath{\psi}+h$ transitions, where $h={\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$, ${\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\pi}}^{0}$, ${\ensuremath{\pi}}^{0}\ensuremath{\gamma}$, and $\ensuremath{\gamma}$. The obtained results for the decay pattern of the $X(3872)$ in a molecular interpretation could be useful for running and planned experiments.