Mass spectrum of the hidden-charm hybrid states via the QCD sum rules

TL;DR

This paper calculates the mass spectrum of various hidden-charm hybrid states using QCD sum rules, incorporating higher-order condensates and exploring the energy scale dependence for the first time.

Contribution

It introduces a comprehensive QCD sum rule analysis for multiple quantum numbers of hidden-charm hybrids, including energy scale dependence and higher-order condensates.

Findings

Mass predictions for various hybrid states.

First exploration of energy scale dependence in this context.

Inclusion of vacuum condensates up to dimension-6.

Abstract

In this work, we study the mass spectrum of the hidden-charm hybrid states with the $J^{PC}=0^{-+}$, $0^{++}$, $0^{--}$, $1^{++}$, $1^{+-}$, $1^{-+}$, $1^{--}$, $2^{-+}$ and $2^{++}$ via the QCD sum rules in a consistent way. We calculate the vacuum condensates up to dimensions-6 by taking account of both the leading order and next-to-leading order contributions, and take the energy scale formula $\mu=\sqrt{M^2_{X/Y/Z}-(2{\mathbb{M}}_c)^2}$ to choose the suitable energy scales of the QCD spectral densities, it is the first time to explore the energy scale dependence of the QCD sum rules for the hidden-charm hybrid states.