Hybrid Charmonium and the $\rho-\pi$ Puzzle

TL;DR

This paper uses QCD Sum Rules to estimate the energy of the lowest hybrid Charmonium state, suggesting the $ ho- ext{pi}$ puzzle may be explained by an admixed $car{c}$ and hybrid $car{c}g$ state.

Contribution

It proposes that the $ ho- ext{pi}$ puzzle can be explained by the $ ho- ext{pi}$ decay pattern resulting from an admixed hybrid Charmonium state.

Findings

The lowest hybrid Charmonium state is near the $ ext{Psi}'(2S)$ energy.

The $ ext{Psi}'(2S)$ is likely an admixture of $car{c}$ and hybrid $car{c}g$ states.

This admixture offers a potential explanation for the $ ho- ext{pi}$ puzzle.

Abstract

Using the method of QCD Sum Rules, we estimate the energy of the lowest hybrid Charmonium state, and find it to be at the energy of the $\Psi'(2S)$ state, about 600 Mev above the $J/\Psi(1S)$ state. Since our solution is not consistent with a pure hybrid at this energy, we conclude that the $\Psi'(2S)$ state is probably an admixed $c \bar{c}$ and hybrid $c \bar{c}g$ state. From this conjecture we find a possible explanation of the famous $\rho-\pi$ puzzle.