Mixing of X and Y states from QCD Sum Rules analysis

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.