<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mn>1</mml:mn><mml:mrow><mml:mo>−</mml:mo><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:math> hybrid meson in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>J</mml:mi><mml:mo stretchy="false">/</mml:mo><mml:mi>ψ</mml:mi></mml:math> radiative decays from lattice QCD

Abstract

We present the first theoretical prediction of the partial decay width of the process $J/\ensuremath{\psi}\ensuremath{\rightarrow}\ensuremath{\gamma}{\ensuremath{\eta}}_{1}$, where ${\ensuremath{\eta}}_{1}$ is the lightest flavor singlet ${1}^{\ensuremath{-}+}$ hybrid meson. Our ${N}_{f}=2$ lattice QCD calculation at ${m}_{\ensuremath{\pi}}\ensuremath{\approx}350\text{ }\text{ }\mathrm{MeV}$ results in the ${\ensuremath{\eta}}_{1}$ mass ${m}_{{\ensuremath{\eta}}_{1}}=2.23(4)\text{ }\text{ }\mathrm{GeV}$ and the related electromagnetic form factors ${M}_{1}(0)=\ensuremath{-}4.73(74)\text{ }\text{ }\mathrm{MeV}$, ${E}_{2}(0)=1.18(22)\text{ }\text{ }\mathrm{MeV}$, which give $\mathrm{\ensuremath{\Gamma}}(J/\ensuremath{\psi}\ensuremath{\rightarrow}\ensuremath{\gamma}{\ensuremath{\eta}}_{1})=2.04(61)\text{ }\text{ }\mathrm{eV}$. These form factors can be applied to the physical ${N}_{f}=3$ case, where there should be two hybrid mass eigenstates ${\ensuremath{\eta}}_{1}^{(l)}$ and ${\ensuremath{\eta}}_{1}^{(h)}$ due to the singlet-octet mixing. It is shown that the ratio of the branching fractions $\mathrm{Br}(J/\ensuremath{\psi}\ensuremath{\rightarrow}\ensuremath{\gamma}{\ensuremath{\eta}}_{1}^{(l,h)}\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\eta}{\ensuremath{\eta}}^{\ensuremath{'}})$ is inversely proportional to the ratio of the total widths of ${\ensuremath{\eta}}_{1}^{(l,h)}$. Given our results and the mixing angle derived by a previous lattice study, whether ${\ensuremath{\eta}}_{1}(1855)$ is assigned to be ${\ensuremath{\eta}}_{1}^{(1)}$ or ${\ensuremath{\eta}}_{1}^{(h)}$, the observed branching fraction $J/\ensuremath{\psi}\ensuremath{\rightarrow}{\ensuremath{\eta}}_{1}(1855)\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\eta}{\ensuremath{\eta}}^{\ensuremath{'}}$ implies a very large coupling of the octet ${\ensuremath{\eta}}_{1}$ to $\ensuremath{\eta}{\ensuremath{\eta}}^{\ensuremath{'}}$. This should be investigated in future studies.

Topics & Concepts