Determination of the resonant parameters of excited vector strangenia with the $e^{+}e^{-}\toηϕ$ data

Abstract

We determine the resonant parameters of the vector states $ϕ(1680)$ and $ϕ(2170)$, by doing a combined fit to the $e^{+}e^{-}\to ηϕ$ cross sections from threshold to $2.85~\rm GeV$ measured by BaBar, Belle, BESIII and CMD-3 experiments. The mass $(1678^{+5}_{-3} \pm 7)~\rm MeV/c^2$ and the width $(156\pm 5 \pm 9)~\rm MeV$ are obtained for the $ϕ(1680)$, and the mass $(2169\pm 5 \pm 6)~\rm MeV/c^2$ and the width $(96^{+17}_{-14} \pm 9)~\rm MeV$ for the $ϕ(2170)$. The statistical significance of $ϕ(2170)$ is $7.2σ$. Depending on the interference between the $ϕ(1680)$, $ϕ(2170)$ and a non-resonant $ηϕ$ amplitude in the nominal fit, we obtain four solutions and $Γ^{e^{+}e^{-}}_{ϕ(1680)}\cdot \mathcal{B}[ϕ(1680)\toηϕ] = (79 \pm 4 \pm 16)$, $(127\pm 5 \pm 12)$, $(65^{+5}_{-4} \pm 13)$ or $(215 ^{+8}_{-5} \pm 11)~\rm eV$, and $Γ^{e^{+}e^{-}}_{ϕ(2170)}\cdot \mathcal{B}[ϕ(2170)\toηϕ] = (0.56^{+0.03}_{-0.02} \pm 0.07)$, $(0.36^{+0.05}_{-0.03} \pm 0.07)$, $(38 \pm 1 \pm 5)$ or $(41\pm 2 \pm 6)~\rm eV$, respectively. We also search for the production of $X(1750)\to ηϕ$ and the significance is only $2.0σ$, then we determine the upper limit of $Γ^{e^{+}e^{-}}_{X(1750)}\cdot \mathcal{B}[X(1750)\toηϕ]$ at $90\%$ confidence level.