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

TL;DR

This paper uses QCD sum rules with various diquark operators to analyze the mass spectrum of hidden-charm tetraquark states, providing insights into the nature of several observed exotic mesons.

Contribution

It offers a comprehensive QCD sum rule analysis of hidden-charm tetraquark states, revisiting their assignments and discussing the applicability of sum rules to molecular states.

Findings

Revised mass spectrum for various $X$, $Y$, $Z$ states.

Consistent tetraquark assignments for multiple exotic mesons.

Feasibility of QCD sum rules for tetraquark molecular states.

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 $\mathcal{O}(\alpha_s^2)$.