Combined analysis on nature of X(3960), , and

Zuo-ming Ding; Jun He

doi:10.1140/epjc/s10052-023-11977-y

EPJ

a
b
c
d
e
ap
st
h
plus
ds
pv
ti
qt
am
n

2023 Impact factor 4.2

Particles and Fields

Open Access

Eur. Phys. J. C (2023) 83: 806
https://doi.org/10.1140/epjc/s10052-023-11977-y

Regular Article - Theoretical Physics

Combined analysis on nature of X(3960), $χ_{c 0} (3930)$ $\chi _{c0}(3930)$ , and $X_{0} (4140)$

Zuo-ming Ding and Jun He^b

School of Physics and Technology, Nanjing Normal University, 210094, Nanjing, China

^b junhe@njnu.edu.cn

Received: 20 July 2023
Accepted: 27 August 2023
Published online: 11 September 2023

Abstract

In this work, a study of the $D_{s} {\bar{D}}_{s}$ $D_s{\bar{D}}_s$ interaction and its couplings to the channels $D \bar{D}$ $D{\bar{D}}$ and $J / ψ ϕ$ $J/\psi \phi$ is performed in a quasipotential Bethe–Salpeter equation approach. The $D_{s}^{+} D_{s}^{-}$ $D_s^+{D}_s^-$ and $D^{+} D^{-}$ $D^+{D}^-$ invariant mass spectra in three-body B decays are investigated in order to understand the origin of X(3960), $χ_{c 0} (3930)$ $\chi _{c0}(3930)$ , and $X_{0} (4140)$ $$X_0(4140)$$ structures reported at LHCb. With the help of effective Lagrangians, the potential kernel can be constructed with meson exchanges, from which the scattering amplitudes can be obtained. By inserting it into the three-body decay processes, the invariant mass spectra can be calculated with an additional Breit–Wigner resonance introduced. The $D_{s}^{+} D_{s}^{-}$ $D_s^+{D}_s^-$ invariant mass spectrum in the decay process $B^{+} \to D_{s}^{+} D_{s}^{-} K^{+}$ $B^+\rightarrow D^+_sD^-_sK^+$ is well reproduced, and the X(3960) structure can be explained as a molecular state from the $D_{s} {\bar{D}}_{s}$ $D_s{\bar{D}}_s$ interaction. The state also exhibits as a peak in the $D^{+} D^{-}$ $D^+{D}^-$ invariant mass spectrum in the decay $B^{+} \to D^{+} D^{-} K^{+}$ $B^+\rightarrow D^+D^-K^+$ , however, it is too narrow to reproduce the experimental structure around 3930 MeV. The dip around 4140 MeV in the $D_{s}^{+} D_{s}^{-}$ $D_s^+{D}_s^-$ invariant mass spectrum can be reproduced by the additional resonance with interference effect. However, a small bump instead of a dip is produced from the $D_{s} {\bar{D}}_{s} - J / ψ ϕ$ $D_s{\bar{D}}_s-J/\psi \phi$ coupled-channel effect, which suggests that the $X_{0} (4140)$ $$X_0(4140)$$ cannot be interpreted as the $D_{s} {\bar{D}}_{s} - J / ψ ϕ$ $D_s{\bar{D}}_s-J/\psi \phi$ coupling in the current model.

© The Author(s) 2023

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.