Partial wave analysis of $\psi \left(3686\right)\to {K}^{+}{K}^{-}\eta $

Using a sample of $\left(448.1±2.9\right)×{10}^{6}$ $\psi \left(3686\right)$ events collected with the BESIII detector, we perform the first partial wave analysis of $\psi \left(3686\right)\to {K}^{+}{K}^{-}\eta $. In addition to the well established states, $\varphi \left(1020\right)$, $\varphi \left(1680\right)$, and ${K}_{3}^{*}\left(1780\right)$, contributions from $X\left(1750\right)$, $\rho \left(2150\right)$, ${\rho }_{3}\left(2250\right)$, and ${K}_{2}^{*}\left(1980\right)$ are also observed. The $X\left(1750\right)$ state is determined to be a ${1}^{--}$ resonance. The simultaneous observation of the $\varphi \left(1680\right)$ and $X\left(1750\right)$ indicates that the $X\left(1750\right)$, with previous observations in photoproduction, is distinct from the $\varphi \left(1680\right)$. The masses, widths, branching fractions of $\psi \left(3686\right)\to {K}^{+}{K}^{-}\eta $, and the intermediate resonances are also measured.