D ¯ s ( * ) D ( * ) molecular state with J P = 1 +

In this paper, we construct ${\overline{D}}_{s}^{(*)}{D}^{(*)}$-molecule-type interpolating currents ${J}_{(\ifmmode\pm\else\textpm\fi{})\ensuremath{\mu}}(x)$ with ${J}^{P}={1}^{+}$, calculate the corresponding mass and magnetic moment using the QCD sum rule method and its extension in the weak electromagnetic field, and study the processes of ${Z}_{(\ifmmode\pm\else\textpm\fi{})cs}$ to ${\ensuremath{\eta}}_{c}{K}^{*}$, $J/\ensuremath{\psi}K$, $\overline{D}{D}_{s}^{*}$, and ${\overline{D}}^{*}{D}_{s}$ via three-point sum rules. The numerical values are ${m}_{{Z}_{(\ifmmode\pm\else\textpm\fi{})cs}}=3.9{9}_{\ensuremath{-}0.14}^{+0.17}\text{ }\text{ }\mathrm{GeV}$, ${\ensuremath{\lambda}}_{{Z}_{(\ifmmode\pm\else\textpm\fi{})cs}}=2.0{7}_{\ensuremath{-}0.16}^{+0.28}\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}2}\text{ }\text{ }{\mathrm{GeV}}^{5}$, and ${\ensuremath{\mu}}_{{Z}_{(\ifmmode\pm\else\textpm\fi{})cs}}=0.1{8}_{\ensuremath{-}0.09}^{+0.16}\text{ }\text{ }{\ensuremath{\mu}}_{N}$ with ${\ensuremath{\mu}}_{N}$ the nucleon magneton, ${\mathrm{\ensuremath{\Gamma}}}_{{Z}_{(+)cs}}=17.4{7}_{\ensuremath{-}8.08}^{+12.70}$, and ${\mathrm{\ensuremath{\Gamma}}}_{{Z}_{(\ensuremath{-})cs}}=13.8{6}_{\ensuremath{-}6.51}^{+10.37}$. The masses are in agreement with the recently measured value of ${Z}_{cs}(3985)$ by the BESIII Collaboration, ${m}_{{Z}_{cs}}^{\mathrm{exp}}=({3982.5}_{\ensuremath{-}2.6}^{+1.8}\ifmmode\pm\else\textpm\fi{}2.1)\text{ }\text{ }\mathrm{MeV}$. The widths are compatible with the experimental value ${\mathrm{\ensuremath{\Gamma}}}_{{Z}_{cs}}^{\mathrm{exp}}=\phantom{\rule{0ex}{0ex}}({12.8}_{\ensuremath{-}4.4}^{+5.3}\ifmmode\pm\else\textpm\fi{}3.0)\text{ }\text{ }\mathrm{MeV}$. The magnetic moment and the various decay modes can help us to determine the inner structure of ${Z}_{cs}(3985)$ when being confronted with experimental data in the future.