Study of $e^{+}{e}^{-}\to \eta \phi$ via Initial State Radiation at Belle

Using $980f{b}^{-1}$ of data collected on and around the $\mathrm{{\rm Y}}(nS)(n=1,2,3,4,5)$ resonances with the Belle detector at the KEKB collider, we measure the cross section of $e^{+}{e}^{-}\to \eta \phi$ from threshold to $3.95\mathrm{G}\mathrm{e}\mathrm{V}\mathrm{/}{c}^2$ via initial-state radiation. From a multi-parameter fit assuming $\phi (2170)$ exists in the $\eta \phi$ final state according to previous measurement by BESIII, the resonant parameters of $\phi (1680)$ are determined to be $m_{\phi (1680)}=(1683\pm 7\pm 9)\mathrm{M}\mathrm{e}\mathrm{V}\mathrm{/}{c}^2$ (statistical and systematic errors, respectively), ${\mathrm{\Gamma }}_{\phi (1680)}=(149\pm 12\pm 13)\mathrm{M}\mathrm{e}\mathrm{V}$ and, depending on the possible presence of interfering resonances, ${\mathrm{\Gamma }}_{\phi (1680)}^{e^{+}{e}^{-}}\cdot \mathcal{B}[\phi (1680)\to \eta \phi ]=(122\pm 6\pm 13)\mathrm{e}\mathrm{V}$, $(219\pm 15\pm 18)\mathrm{e}\mathrm{V}$, $(163\pm 11\pm 13)\mathrm{e}\mathrm{V}$ or $(203\pm 12\pm 18)\mathrm{e}\mathrm{V}$. The branching fraction of $\phi (1680)\to \eta \phi$ decay is determined to be approximately 20%. Additionally, the branching fraction for $J\mathrm{/}\psi \to \eta \phi$ is measured to be $(7.1\pm 1.0\pm 0.5)\times {10}^{-4}$. However, there is no significant observed $\phi (2170)$ signal in the $\eta \phi$ final states in this analysis, and correspondingly the upper limit for ${\mathrm{\Gamma }}_{\phi (2170)}^{e^{+}{e}^{-}}\cdot \mathcal{B}(\phi (2170)\to \eta \phi )$ is determined to be either $0.17\mathrm{e}\mathrm{V}$ (for two fits), or $18.6\mathrm{e}\mathrm{V}$ (remaining two fits), at 90% confidence level.