Observation of the $Y\left(4230\right)$ and evidence for a new vector charmoniumlike state $Y\left(4710\right)$ in ${e}^{+}{e}^{-}\to {K}_{S}^{0}{K}_{S}^{0}J/\psi $

Cross sections for the process ${e}^{+}{e}^{-}\to {K}_{S}^{0}{K}_{S}^{0}J/\psi $ at center-of-mass energies from 4.128 to 4.950 GeV are measured using data samples with a total integrated luminosity of $21.2\text{}\text{}{\mathrm{fb}}^{-1}$ collected by the BESIII detector operating at the BEPCII storage ring. The $Y\left(4230\right)$ state is observed in the energy dependence of the ${e}^{+}{e}^{-}\to {K}_{S}^{0}{K}_{S}^{0}J/\psi $ cross section for the first time with a statistical significance of $26.0\sigma $. In addition, an enhancement around 4.710 GeV, labeled as the $Y\left(4710\right)$, is seen with a statistical significance of $4.2\sigma $. There is no clear structure around 4.484 GeV. Using a fit with a coherent sum of three Breit-Wigner functions, we determine the mass and width of the $Y\left(4230\right)$ state to be $4226.9±6.6±22.0\text{}\text{}\mathrm{MeV}/{c}^{2}$ and $71.7±16.2±32.8\text{}\text{}\mathrm{MeV}$, respectively, and the mass and width of the $Y\left(4710\right)$ state to be $4704.0±52.3±69.5\text{}\text{}\mathrm{MeV}/{c}^{2}$ and $183.2±114.0±96.1\text{}\text{}\mathrm{MeV}$, respectively, where the first uncertainties are statistical and the second are systematic. In addition, the average Born cross section ratio $\frac{{\sigma }^{\text{Born}}\left({e}^{+}{e}^{-}\to {K}_{S}^{0}{K}_{S}^{0}J/\psi \right)}{{\sigma }^{\text{Born}}\left({e}^{+}{e}^{-}\to {K}^{+}{K}^{-}J/\psi \right)}$ is measured to be ${0.388}_{-0.028}^{+0.035}±0.016$, or ${0.426}_{-0.031}^{+0.038}±0.018$ if three-body phase space is considered.