Coupled channel approach to the structure of the X(3872)

Abstract

We have performed a coupled channel calculation of the $1^{++}$ $c\bar{c}$ sector including $q\bar{q}$ and $D{D}^{\ast }$ molecular configurations. The calculation was done within a constituent quark model which successfully describes the meson spectrum, in particular the $c\bar{c}$ $1^{--}$ 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 $D{D}^{\ast }$ molecular component. When the mass difference between neutral and charged states is included a large $D^0{D^{\ast }}^0$ component is found which dominates for large distances and breaks isospin symmetry in the physical state. The original $c\bar{c}(2^3{P}_1)$ state acquires a sizable $D{D}^{\ast }$ component and can be identified with the X(3940). We study the $B\to K{\pi }^{+}{\pi }^{-}J/\psi$ and $B\to K{D}^0{D}^{\ast 0}$ decays finding a good agreement with Belle and BaBar experimental data.

Comments: 10 pages, 3 figures. Direct comparison with Belle and Babar data has been included.