Coupled channel approach to the structure of theX(3872)

Abstract

We have performed a coupled channel calculation of the ${1}^{++}$ $c\overline{c}$ sector including $q\overline{q}$ and $D{D}^{*}$ molecular configurations. The calculation was done within a constituent quark model which successfully describes the meson spectrum, in particular, the $c\overline{c}$ ${1}^{--}$ sector. Two and four-quark configurations are coupled using the $^{3}P_{0}$ model. The elusive $X(3872)$ meson appears as a new state with a high probability for the $D{D}^{*}$ molecular component. When the mass difference between neutral and charged states is included, a large ${D}^{0}{D}^{*0}$ component is found which dominates for large distances and breaks isospin symmetry in the physical state. The original $c\overline{c}(2^{3}P_{1})$ state acquires a sizable $D{D}^{*}$ component and can be identified with the $X(3940)$. We study the $B\ensuremath{\rightarrow}K{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}J/\ensuremath{\psi}$ and $B\ensuremath{\rightarrow}K{D}^{0}{D}^{*0}$ decays, finding a good agreement with Belle and BABAR experimental data.