Fully charmed P-wave tetraquark resonant states in the quark model

Abstract

We conduct the first comprehensive P-wave four-body dynamical calculations of the fully charmed tetraquark systems within the quark potential model. We apply the Gaussian expansion method to solve the four-body Schrödinger equation, incorporating both dimeson and diquark-antidiquark spatial configurations. The matrix elements of P-wave states are calculated analytically using the infinitesimally-shifted Gaussian basis functions. With the complex scaling method, we obtain several fully charmed P-wave resonant states with compact tetraquark configuration in the mass region of $(7.0,7.2)$ GeV, including states with exotic quantum numbers $J^{PC}=0^{--},1^{-+}$. However, we find no resonant states with the mass $M<7$ GeV and width $\Gamma <200$ MeV. Combining the present investigation with our previous results on S-wave fully charmed tetraquark systems, we find no candidates for the experimental states $X(6400)$ and $X(6600)$ in the quark model.

Comments: version accepted by PRD