Eur. Phys. J. C (2024) 84: 1019
https://doi.org/10.1140/epjc/s10052-024-13424-y

Regular Article

Charmless decays of the spin-2 partner of X(3872)

¹ College of Physics and Engineering, Qufu Normal University, 273165, Qufu, China
² Institute of Modern Physics, Chinese Academy of Sciences, 730000, Lanzhou, China
³ CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, 100190, Beijing, China
⁴ School of Nuclear Science and Technology, University of Chinese Academy of Sciences, 101408, Beijing, China
⁵ Southern Center for Nuclear-Science Theory (SCNT), Institute of Modern Physics, Chinese Academy of Sciences, 516000, Huizhou, Guangdong, China

^c gli@qfnu.edu.cn

Received: 8 July 2024
Accepted: 25 September 2024
Published online: 8 October 2024

Abstract

The Belle collaboration recently reported a pro-mising candidate for the spin-2 $D^{\ast }{\overline{D}}^{\ast }$ partner of the X(3872), called the $X_2$ for short, having a mass of $(4014.3\pm 4.0\pm 1.5)\text{MeV}$ and a width of $(4\pm 11\pm 6)\text{MeV}$. In present work, we assume the $X_2$ as a pure molecule of the $D^{\ast }{\overline{D}}^{\ast }$ under four cases, i.e., pure neutral components ($\theta =0$), isospin singlet ($\theta =\pi /4$), neutral components dominant ($\theta =\pi /6$), and purely charged components ($\theta =\pi /2$), where $\theta$ is a phase angle describing the proportion of neutral and charged constituents. Using an effective Lagrangian approach, we calculated the partial widths of $X_2\to VV$ and $X_2\to PP$ (V and P stand for light vector and pseudoscalar mesons, respectively). The predicted decay widths of $X_2\to VV$ can reach a few hundreds of $\text{keV}$, while the decay widths of $X_2\to PP$ are about several tens of $\text{keV}$. In addition, the effects from the proportion of neutral and charged constituent on the decay widths of $X_2\to VV$ and PP are also investigated. We hope that the present calculations will be checked experimentally in the future.