Study of the process $e^+e^-{\to}K^+K^-\eta$ with the CMD-3 detector at the VEPP-2000 collider

The process $e^+e^-{\to}K^+K^-\eta$ has been studied in the center-of-mass energy range from 1.59 to 2.007\,GeV using the data sample of 59.5 pb$^{-1}$, collected with the CMD-3 detector at the VEPP-2000 $e^+e^-$ collider in 2011, 2012 and 2017. The $K^+K^-\eta$ final state is found to be dominated by the contribution of the $\phi(1020)\eta$ intermediate state. The cross section of the process $e^+e^-{\to}\phi(1020)\eta$ has been measured with a systematic uncertainty of 5.1$\%$ on the base of 3009 $\pm$ 67 selected events. The obtained cross section has been used to calculate the contribution to the anomalous magnetic moment of the muon: $a_{\mu}^{\phi\eta}(E<1.8\, {\rm GeV})=(0.321 \pm 0.015_{\rm stat} \pm 0.016_{\rm syst}) \times 10^{-10}$, $a_{\mu}^{\phi\eta}(E<2.0\, {\rm GeV})=(0.440 \pm 0.015_{\rm stat} \pm 0.022_{\rm syst}) \times 10^{-10}$. From the cross section approximation the $\phi(1680)$ meson parameters have been determined with better statistical precision, than in previous studies.