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

TL;DR

This paper predicts decay widths of a proposed spin-2 partner of X(3872), modeled as a D*D* molecule, using an effective Lagrangian approach, and explores how its decay varies with constituent composition.

Contribution

It provides the first detailed calculation of decay widths for the spin-2 D*D* molecular candidate of X(3872) under different isospin configurations.

Findings

Decay widths for X_2 to vector mesons are a few hundred keV.

Decay widths for X_2 to pseudoscalar mesons are tens of keV.

Decay widths depend on the neutral and charged constituent proportions.

Abstract

The Belle collaboration recently reported a promising candidate for the spin-2 $D^*\bar{D}^*$ 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 $D^*\bar{D}^*$ 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.