Search for charmonium(like) states $X$ in $e^{+}e^{-}\rightarrowγX\rightarrowγD^{*0}\bar{D}^{*0}$ at BESIII
A search is performed for a state $X$ decaying into $D^{*0}\bar{D}^{*0}$ produced in the process $e^{+}e^{-}\rightarrowγX$ using a data sample corresponding to an integrated luminosity of 1667.4 $\rm pb^{-1}$ collected at $\sqrt{s} = 4.682$ GeV with the BESIII detector at the BEPCII. The state $X$ could be one of the $C$-even states $X(4013)$, $η_{c}(3S)$, $χ_{c0}(3P)$, $χ_{c1}(3P)$, or $χ_{c2}(3P)$. No significant signal is observed in the corresponding signal region. Upper limits of $σ_{e^{+}e^{-}\rightarrowγX}\cdot {\rm Br}_{X\rightarrow D^{*0}\bar{D}^{*0}}$ at 90% confidence level are provided, where $σ_{e^{+}e^{-}\rightarrowγX}$ represents the cross section of the $e^{+}e^{-}\rightarrowγX$ process, and ${\rm Br}_{X\rightarrow D^{*0}\bar{D}^{*0}}$ is the branching fraction of the $X\rightarrow D^{*0}\bar{D}^{*0}$ process.