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

Abstract

The Belle collaboration recently reported a promising candidate for the spin-2 $D^{\ast }{\bar{D}}^{\ast }$ partner of the $X(3872)$, called the $X_2$ for short, having a mass of $(4014.3\pm 4.0\pm 1.5)\mathrm{MeV}$ and a width of $(4\pm 11\pm 6)\mathrm{MeV}$. In present work, we assume the $X_2$ as a pure molecule of the $D^{\ast }{\bar{D}}^{\ast }$ under three cases, i.e., pure neutral components ($\theta =0$), isospin singlet ($\theta =\pi /4$) and neutral components dominant ($\theta =\pi /6$), 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 $\mathrm{keV}$, while the decay widths of $X_2\to PP$ are about several tens of $\mathrm{keV}$. 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.

Comments: 8 pages, 7figure, comments welcome