Investigation of box diagrams for the peak of \(Z_{cs}(3985)\) in \(e^+e^- \rightarrow D^-_s D^{*0} K^+\) and \( D^{*-}_s D^0 K^+\)

Abstract

The BESIII Collaboration recently observed a charged hidden-charm structure with strangeness in the recoil mass spectrum of \(K^+\) in the processes \(e^+e^- \rightarrow D^-_s D^{*0} K^+\) or \(D^{*-}_s D^0 K^+\), named as \(Z_{cs}(3985)^-\). Within the energy region around the peak of \(Z_{cs}(3985)\), various box diagrams are present. A systematic study of these box diagrams reveals the existence of a box singularity. Dalitz plots and invariant mass distributions of two charmed mesons from the box diagram for the processes \(e^+e^- \rightarrow D^-_s D^{*0} K^+\) and \(D^{*-}_s D^0 K^+\) are presented at five energy points \(\sqrt{s} = 4.628,\,4.641,\,4.661,\,4.681\), and 4.698 GeV. It is found that these box diagrams can generate peaks similar to those observed in experiments, suggesting that the peak of \(Z_{cs}(3985)\) may be attributed to the box singularity contribution. Additionally, slight differences in the invariant mass spectra of \(D^-_s D^{*0}\) and \(D^{*-}_s D^0 \) are identified based on the box diagrams, needing further experimental validation.