Search for a scalar partner of the $X\left(3872\right)$ via $\psi \left(3770\right)$ decays into $\gamma \eta {\eta }^{\prime }$ and $\gamma {\pi }^{+}{\pi }^{-}J/\psi $

Using a data sample corresponding to an integrated luminosity of $2.93\text{}\text{}{\mathrm{fb}}^{-1}$ collected at a center-of-mass energy of 3.773 GeV with the BESIII detector at the BEPCII collider, we search for a scalar partner of the $X\left(3872\right)$, denoted as $X\left(3700\right)$, via $\psi \left(3770\right)\to \gamma \eta {\eta }^{\prime }$ and $\gamma {\pi }^{+}{\pi }^{-}J/\psi $ processes. No significant signals are observed and the upper limits of the product branching fractions $B\left(\psi \left(3770\right)\to \gamma X\left(3700\right)\right)·B\left(X\left(3700\right)\to \eta {\eta }^{\prime }\right)$ and $B\left(\psi \left(3770\right)\to \gamma X\left(3700\right)\right)·B\left(X\left(3700\right)\to {\pi }^{+}{\pi }^{-}J/\psi \right)$ are determined at the 90% confidence level, for the narrow $X\left(3700\right)$ with a mass ranging from 3710 to $3740\text{}\text{}\mathrm{MeV}/{c}^{2}$, which are from 0.9 to $1.9\left(×{10}^{-5}\right)$ and 0.9 to $3.4\left(×{10}^{-5}\right)$, respectively.