Analysis of the hidden-charm tetraquark mass spectrum with the QCD sum rules

Abstract

In this article, we take the pseudoscalar, scalar, axialvector, vector, tensor (anti)diquark operators as the basic constituents, and construct the scalar, axialvector and tensor tetraquark currents to study the mass spectrum of the ground state hidden-charm tetraquark states with the QCD sum rules in a comprehensive way. We revisit the assignments of the $X$, $Y$, $Z$ states, such as the $X(3860)$, $X(3872)$, $X(3915)$, $X(3940)$, $X(4160)$, $Z_c(3900)$, $Z_c(4020)$, $Z_c(4050)$, $Z_c(4055)$, $Z_c(4100)$, $Z_c(4200)$, $Z_c(4250)$, $Z_c(4430)$, $Z_c(4600)$, etc in the scenario of tetraquark states in a consistent way based on the QCD sum rules. Furthermore, we discuss the feasibility of applying the QCD sum rules to study the tetraquark states and tetraquark molecular states (more precisely, the color-singlet-color-singlet type tetraquark states), which begin to receive contributions at the order $\mathcal{O}(\alpha_s^0)$, not at the order $\mathcal{O}(\alpha_s^2)$.