The glueball content of ηc

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)degrees, 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) -> gamma gamma can be understood in this c (c) over bar -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 -> gamma eta(c) cannot be alleviated by the c (c) over bar -glueball mixing picture yet, which demands future precise experimental measurements of this partial width. (c) 2022 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP(3).

Automated summary

This study presents the first lattice QCD derivation of the mixing energy and mixing angle between pseudoscalar charmonium and glueball. The results suggest a possible connection between the mixing and the large total width of the eta(c) meson. However, further experimental measurements are needed to alleviate the discrepancy between theoretical predictions and experimental results.