We propose an effective field theory incorporating light SU(3)-flavor and heavy quark spin symmetry to describe charmed meson-antimeson bound states. At lowest order the effective field theory entails a remarkable simplification: it only involves contact range interactions among the heavy meson and antimeson fields. We show that the isospin violating decays of the $X(3872)$ can be used to constrain the interaction between the $D$ and a ${\overline{D}}^{*}$ mesons in the isovector channel. As a consequence, we can rule out the existence of an isovector partner of the $X(3872)$. If we additionally assume that the $X(3915)$ and $Y(4140)$ are $D^{*}{\overline{D}}^{*}$ and $D_s^{*}{\overline{D}}_s^{*}$ molecular states, we can determine the full spectrum of molecular states with isospin $I=0$, $\frac{1}{2}$ and 1.

• Received 19 October 2012

DOI:https://doi.org/10.1103/PhysRevD.87.076006