Search for $C$-even states decaying to $D_s^{\pm }{D}_s^{\ast \mp }$ with masses between $4.08$ and $4.32\mathrm{G}\mathrm{e}\mathrm{V}\mathrm{/}{c}^2$

Six $C$-even states, denoted as $X$, with quantum numbers $J^{PC}=0^{-+}$, $1^{\pm +}$, or $2^{\pm +}$, are searched for via the $e^{+}{e}^{-}\to \gamma D_s^{\pm }{D}_s^{\ast \mp }$ process using $(1667.39\pm 8.84){\mathrm{p}\mathrm{b}}^{-1}$ of $e^{+}{e}^{-}$ collision data collected with the BESIII detector operating at the BEPCII storage ring at center-of-mass energy of $\sqrt{s}=(4681.92\pm 0.30)\mathrm{M}\mathrm{e}\mathrm{V}$. No statistically significant signal is observed in the mass range from $4.08$ to $4.32\mathrm{G}\mathrm{e}\mathrm{V}\mathrm{/}{c}^2$. The upper limits of $\sigma [e^{+}{e}^{-}\to \gamma X]\cdot \mathcal{B}[X\to D_s^{\pm }{D}_s^{\ast \mp }]$ at a $90\mathrm{\%}$ confidence level are determined.