Light Flavour and Heavy Quark Spin Symmetry in Heavy Meson Molecules

Abstract

We propose an effective field theory incorporating light SU(3)-flavour 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 constraint the interaction between the $D$ and a $\bar{D}^*$ mesons in the isovector channel. As a consequence, we can rule out the existence of a isovector partner of the X(3872). If we additionally assume that the X(3915) and Y(4140) are $D^*\bar{D}^*$ and $D_s^*\bar{D}_s^*$ molecular states, we can determine the full spectrum of molecular states with isospin I=0, 1/2 and 1.