Understanding $X(3862)$, $X(3872)$, and $X(3930)$ in a Friedrichs-model-like scheme

Understand

We developed a Friedrichs-model-like scheme in studying the hadron resonance phenomenology and present that the hadron resonances might be regarded as the Gamow states produced by a Hamiltonian in which the bare discrete state is described by the result of usual quark potential model and the interaction part is described by the quark pair creation model.

• In a one-parameter calculation, the $X(3862)$, $X(3872)$, and $X(3930)$ state could be simultaneously produced with a quite good accuracy by coupling the three P-wave states, $\chi_{c2}(2P)$, $\chi_{c1}(2P)$, $\chi_{c0}(2P)$ predicted in the Godfrey-Isgur model to the $D\bar D$, $D\bar D^{*}$, $D^*\bar D^*$ continuum states.
• At the same time, we predict that the $h_c(2P)$ state is at about 3902 MeV with a pole width of about 54 MeV.
• In this calculation, the $X(3872)$ state has a large compositeness.