\begin{document}$ e^+e^- \to D^+_s \overline{D}{}^{(*)0}K^- $\end{document} and the \begin{document}$ P $\end{document} -wave charmed-strange mesons are performed based on an \begin{document}$ e^+e^- $\end{document} collision data sample corresponding to an integrated luminosity of 567 pb−1 collected with the BESIII detector at \begin{document}$ \sqrt{s}= 4.600 $\end{document} GeV. The processes of \begin{document}$ e^+e^-\to D^+_s \overline{D}{}^{*0} K^- $\end{document} and \begin{document}$ D^+_s \overline{D}{}^{0} K^- $\end{document} are observed for the first time and are found to be dominated by the modes \begin{document}$ D_s^+ D_{s1}(2536)^- $\end{document} and \begin{document}$ D_s^+ D^*_{s2}(2573)^- $\end{document} , respectively. The Born cross sections are measured to be \begin{document}$ \sigma^{B}(e^+e^-\to D^+_s \overline{D}{}^{*0} K^-) = (10.1\pm2.3\pm0.8)$\end{document} pb and \begin{document}$ \sigma^{B}(e^+e^-\to D^+_s \overline{D}{}^{0} K^-) = (19.4\pm2.3\pm1.6)$\end{document} pb, and the products of Born cross section and the decay branching fraction are measured to be \begin{document}$ \sigma^{B}(e^+e^-\to D^+_s D_{s1}(2536)^- + c.c.)\cdot$\end{document} \begin{document}$ {\cal{B}}( D_{s1}(2536)^- \to \overline{D}{}^{*0} K^-) = (7.5 \pm 1.8 \pm 0.7)$\end{document} pb and \begin{document}$\sigma^{B}(e^+e^-\to D^+_s D^*_{s2}(2573)^- + c.c.)\cdot {\cal{B}}( D^*_{s2}(2573)^- \to \overline{D}{}^{0} K^-) =$\end{document} \begin{document}$ (19.7 \pm 2.9 \pm 2.0)$\end{document} pb. For the \begin{document}$ D_{s1}(2536)^- $\end{document} and \begin{document}$ D^*_{s2}(2573)^- $\end{document} mesons, the masses and widths are measured to be \begin{document}$ M( D_{s1}(2536)^- ) = (2537.7 \pm 0.5 \pm 3.1)\; {\rm{MeV}}/c^2 $\end{document} , \begin{document}$ \Gamma( D_{s1}(2536)^- ) = (1.7\pm 1.2 \pm 0.6) $\end{document} MeV, and \begin{document}$M( D^*_{s2}(2573)^- ) = $\end{document} \begin{document}$ (2570.7\pm 2.0 \pm 1.7)\; {\rm{MeV}}/c^2, $\end{document} \begin{document}$ \Gamma( D^*_{s2}(2573)^- ) = (17.2 \pm 3.6 \pm 1.1)$\end{document} MeV. The spin-parity of the \begin{document}$ D^*_{s2}(2573)^- $\end{document} meson is determined to be \begin{document}$ J^P=2^{+} $\end{document} . In addition, the processes \begin{document}$ e^+e^-\to D^+_s \overline{D}{}^{(*)0} K^- $\end{document} are searched for using the data samples taken at four (two) center-of-mass energies between 4.416 (4.527) and 4.575 GeV, and upper limits at the 90% confidence level on the cross sections are determined."> Observation of <inline-formula> <tex-math id="M1">\begin{document}${{e^+e^- \rightarrow D_s^+} \overline{ D}^{\bf (*)0} {K^-}}$\end{document}</tex-math> <alternatives> <graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="//www.macurncorp.com/hepnp/article/app/id/34bb34cc-222e-4b8a-98f1-7ef02570c36e/CPC-2018-0444_M1.jpg"/> <graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="//www.macurncorp.com/hepnp/article/app/id/34bb34cc-222e-4b8a-98f1-7ef02570c36e/CPC-2018-0444_M1.png"/> </alternatives> </inline-formula> and study of the <i>P</i>-wave <inline-formula> <tex-math id="M3">\begin{document}${{D_s}}$\end{document}</tex-math> <alternatives> <graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="//www.macurncorp.com/hepnp/article/app/id/34bb34cc-222e-4b8a-98f1-7ef02570c36e/CPC-2018-0444_M3.jpg"/> <graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="//www.macurncorp.com/hepnp/article/app/id/34bb34cc-222e-4b8a-98f1-7ef02570c36e/CPC-2018-0444_M3.png"/> </alternatives> </inline-formula> mesons -
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