X(3872) in an unquenched quark model

Abstract

In this paper, we calculate mass and probability fractions of meson-meson components of $X(3872)$ in an unquenched quark model. Different from most of other unquenched quark models, the quark pairs creation operator from $^3P_0$ is modified by considering effects of the created quark pair energy and separation between the created quark pair and the valence quark-pair. In the calculation, all the wavefunctions of mesons and the relative motion between two mesons are obtained by solving the corresponding Schr\"{o}dinger equation with the help of gaussian expansion method. The multi-channel coupling of quark-antiquark state with possible meson-meson states are performed. The results show that the $X(3872)$ can be described as a mixing state of dominant charmonium state (70\%) and meson-meson components (30\%).