Study of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mi>e</mml:mi><mml:mo>+</mml:mo></mml:msup><mml:msup><mml:mi>e</mml:mi><mml:mo>−</mml:mo></mml:msup><mml:mo stretchy="false">→</mml:mo><mml:mi>η</mml:mi><mml:mi>ϕ</mml:mi></mml:math> via initial state radiation at Belle

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