Eur. Phys. J. C (2025) 85: 502
https://doi.org/10.1140/epjc/s10052-025-14247-1

Regular Article - Theoretical Physics

Investigation of box diagrams for the peak of $Z_{\mathit{cs}}(3985)$ in $e^{+}{e}^{-}\to D_s^{-}D_{}^{\ast 0}{K}^{+}$ and $D_s^{\ast -}{D}^0{K}^{+}$

¹ College of Physics and Engineering, Qufu Normal University, 273165, Qufu, China
² School of Physical Sciences, University of Chinese Academy of Sciences, 100049, Beijing, China
³ Southern Center for Nuclear-Science Theory (SCNT), Institute of Modern Physics, Chinese Academy of Sciences, 516000, Huizhou, Guangdong, China

^a gli@qfnu.edu.cn
^b wujiajun@ucas.ac.cn

Received: 17 March 2025
Accepted: 28 April 2025
Published online: 8 May 2025

Abstract

The BESIII Collaboration recently observed a charged hidden-charm structure with strangeness in the recoil mass spectrum of $K^{+}$ in the processes $e^{+}{e}^{-}\to D_s^{-}D_{}^{\ast 0}{K}^{+}$ or $D_s^{\ast -}{D}^0{K}^{+}$, named as $Z_{\mathit{cs}}{(3985)}^{-}$. Within the energy region around the peak of $Z_{\mathit{cs}}(3985)$, 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 $e^{+}{e}^{-}\to D_s^{-}D_{}^{\ast 0}{K}^{+}$ and $D_s^{\ast -}{D}^0{K}^{+}$ 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 $Z_{\mathit{cs}}(3985)$ may be attributed to the box singularity contribution. Additionally, slight differences in the invariant mass spectra of $D_s^{-}D_{}^{\ast 0}$ and $D_s^{\ast -}{D}^0$ are identified based on the box diagrams, needing further experimental validation.