$1^{-+}$ Hybrid in $J/\psi$ Radiative Decays from Lattice QCD

TL;DR

This paper provides the first lattice QCD prediction of the production rate of the $1^{-+}$ hybrid meson in $J/$ radiative decays, estimating a partial width and branching fraction relevant to recent experimental observations.

Contribution

It introduces a novel lattice QCD calculation of the $1^{-+}$ hybrid meson production rate in $J/$ decays, including electromagnetic form factors and decay widths.

Findings

Partial width of $J/\to \gamma \eta_1$ is 2.29(77) eV.

Estimated branching fraction for $J/\to \gamma \eta_1(1855)$ is 6.2(2.2)×10^{-5}.

Implication that $ ext{Br}(\eta_1(1855)\to \eta\eta')$ is about 4.3%.

Abstract

We present the first theoretical prediction of the production rate of $1^{-+}$ light hybrid meson $\eta_1$ in $J/\psi$ radiative decays. In the $N_f=2$ lattice QCD formalism with the pion mass $m_\pi\approx 350$ MeV, the related electromagnetic multipole form factors are extracted from the three-point functions that involve necessarily quark annihilation diagrams, which are calculated through the distillation method. The partial width of $J/\psi\to \gamma \eta_1$ is determined to be $2.29(77)~\mathrm{eV}$ at the $\eta_1$ mass $m_{\eta_1}=2.23(4)$ GeV. If $\eta_1$ corresponds to the recently observed $\eta_1(1855)$ in the process $J/\psi\to \gamma\eta_1(1855)\to \gamma \eta\eta'$ by BESIII, then the branching fraction $\mathrm{Br}(J/\psi\to \gamma\eta_1(1855))$ is estimated to be $6.2(2.2)\times 10^{-5}$, which implies $\mathrm{Br}(\eta_1(1855)\to \eta\eta')\sim 4.3\%$.