The Glueball content of $\eta_c$

TL;DR

This study uses lattice QCD to quantify the mixing between pseudoscalar charmonium and glueball states, revealing a small mixing angle that impacts the properties of the $ ext{eta}_c$ meson and its decay widths.

Contribution

First lattice QCD calculation of the mixing energy and angle between pseudoscalar charmonium and glueball states, providing insights into their influence on meson properties.

Findings

Mixing energy is approximately 49 MeV.

Mixing angle is about 4.6 degrees.

Mixing raises the $ ext{eta}_c$ width by around 7.2 MeV.

Abstract

We carry out the first lattice QCD derivation of the mixing energy and the mixing angle of the pseudoscalar charmonium and glueball on two gauge ensembles with $N_f=2$ degenerate dynamical charm quarks. The mixing energy is determined to be $49(6)$ MeV on the near physical charm ensemble, which seems insensitive to charm quark mass. By the assumption that $X(2370)$ is predominantly a pseudoscalar glueball, the mixing angle is determined to be approximately $4.6(6)^\circ$, which results in a $+3.9(9)$ MeV mass shift of the ground state pseudoscalar charmonium. In the mean time, the mixing can raise the total width of the pseudoscalar charmonium by 7.2(8) MeV, which explains to some extent the relative large total width of the $\eta_c$ meson. As a result, the branching fraction of $\eta_c\to \gamma\gamma$ can be understood in this $c\bar{c}$-glueball mixing framework. On the other hand, the possible discrepancy of the theoretical predictions and the experimental results of the partial width of $J/\psi\to\gamma\eta_c$ cannot be alleviated by the $c\bar{c}$-glueball mixing picture yet, which demands future precise experimental measurements of this partial width.