Eur. Phys. J. C (2025) 85: 616
https://doi.org/10.1140/epjc/s10052-025-14343-2

Regular Article - Theoretical Physics

Determination of the binding and DK probability of the $D_{s0}^{\ast }(2317)$ from the ${(\overline{D}\overline{K})}^{-}$ mass distributions in ${\mathrm{\Lambda }}_b\to {\mathrm{\Lambda }}_c{(\overline{D}\overline{K})}^{-}$ decays

¹ Department of Physics, Guangxi Normal University, 541004, Guilin, China
² Guangxi Key Laboratory of Nuclear Physics and Technology, Guangxi Normal University, 541004, Guilin, China
³ School of Physics, Central South University, 410083, Changsha, China
⁴ Southern Center for Nuclear-Science Theory (SCNT), Institute of Modern Physics, Chinese Academy of Sciences, 516000, Huizhou, China
⁵ Heavy Ion Science and Technology Key Laboratory, Institute of Modern Physics, Chinese Academy of Sciences, 730000, Lanzhou, China
⁶ School of Nuclear Sciences and Technology, University of Chinese Academy of Sciences, 101408, Beijing, China
⁷ Departamento de Física Teórica and IFIC, Centro Mixto Universidad de Valencia-CSIC Institutos de Investigación de Paterna, Apartado 22085, 46071, Valencia, Spain

^a liangwh@gxnu.edu.cn

Received: 13 April 2025
Accepted: 4 May 2025
Published online: 4 June 2025

Abstract

We study the ${\mathrm{\Lambda }}_b\to {\mathrm{\Lambda }}_c{\overline{D}}^0{K}^{-}$ and ${\mathrm{\Lambda }}_b\to {\mathrm{\Lambda }}_c{D}^{-}{\overline{K}}^0$ decays which proceed via a Cabibbo and $N_c$ favored process of external emission, and we determine the ${\overline{D}}^0{K}^{-}$ and $D^{-}{\overline{K}}^0$ mass distributions close to the $\overline{D}\overline{K}$ threshold. For this, we use the tree level contribution plus the rescattering of the meson-meson components, using the extension of the local hidden gauge approach to the charm sector that produces the $D_{s0}^{\ast }(2317)$ resonance. We observe a large enhancement of the mass distributions close to threshold due to the presence of this resonance below threshold. Next we undertake the inverse problem of extracting the maximum information on the interaction of the $\overline{D}\overline{K}$ channels from these distributions, and using the resampling method we find that from these data one can obtain precise values of the scattering lengths and effective ranges, the existence of an $I=0$ bound state with a precision of about $4\mathrm{M}eV$ in the mass, plus the $\overline{D}\overline{K}$ molecular probability of this state with reasonable precision. Given the fact that the ${\mathrm{\Lambda }}_b\to {\mathrm{\Lambda }}_c{\overline{D}}^0{K}^{-}$ decay is already measured by the LHCb collaboration, it is expected that in the next runs with more statistics of the decay, these mass distributions can be measured with precision and the method proposed here can be used to determine the nature of the $D_{s0}^{\ast }(2317)$, which is still an issue of debate.