$X(3872)$ in an unquenched quark model

In this paper we calculate the mass and probability fractions of the meson-meson components of $X(3872)$ in an unquenched quark model. Different from most other unquenched quark models, the quark-pair creation operator from ${}^3{P}_0$ is modified by considering the effects of the created quark pair’s energy and the separation between the created quark pair and the valence quark pair. In the calculation all of the wave functions of the mesons and the relative motion between two mesons are obtained by solving the corresponding Schrödinger equation with the help of the Gaussian expansion method. The multichannel couplings of the quark-antiquark state with possible meson-meson states are calculated. The results show that $X(3872)$ can be described as a mixing state of the dominant charmonium state (70%) and meson-meson components (30%).