Mixing of X and Y states from QCD Sum Rules analysis

TL;DR

This paper uses QCD sum rules to analyze the mixing of different quark configurations in exotic states, providing predictions for their masses and couplings, and suggesting complex internal structures for certain mesons.

Contribution

It introduces a method to estimate the mixing of $ar{Q}Qar{q}q$ and $ar{Q}qQar{q}$ states using two-point correlation functions in QCD sum rules, offering new insights into their internal structure.

Findings

$1^{++}$ states likely result from mixing of $ar{Q}Qar{q}q$ and $ar{Q}qQar{q}$ components.

Less mixing observed for $1^{--}$ and $1^{-+}$ states.

$Y$ states may have more complex internal configurations.

Abstract

We study $\bar{Q}Q\bar{q}q$ and $\bar{Q}qQ\bar{q}$ states as mixed states in QCD sum rules. By calculating the two-point correlation functions of pure states of their corresponding currents, we review the mass and coupling constant predictions of $J^{PC}=1^{++}$, $1^{--}$, $1^{-+}$ states. By calculating the two-point mixed correlation functions of $\bar{Q}Q\bar{q}q$ and $\bar{Q}qQ\bar{q}$ currents, and we estimate the mass and coupling constants of the corresponding `"physical state" that couples to both $\bar{Q}Q\bar{q}q$ and $\bar{Q}qQ\bar{q}$ currents. Our results suggest that $1^{++}$ states are more likely mixing from $\bar{Q}Q\bar{q}q$ and $\bar{Q}qQ\bar{q}$ components, while for $1^{--}$ and $1^{-+}$ states, there is less mixing between $\bar{Q}Q\bar{q}q$ and $\bar{Q}qQ\bar{q}$. Our results suggest the $Y$ series of states have more complicated components.