Decay widths of the spin-2 partners of the X(3872)

TL;DR

This paper predicts the decay widths of the spin-2 partner of X(3872), modeled as a D*D* molecule, including its bottom counterpart, and explores radiative decay modes sensitive to their internal structure.

Contribution

It provides the first calculation of decay widths for the $2^{++}$ partner of X(3872) and its bottom analog, incorporating heavy quark symmetry and analyzing radiative decay channels.

Findings

Partial widths are of the order of a few MeV.

Radiative decays are sensitive to the internal structure and final state interactions.

Predictions for both charm and bottom sector partners.

Abstract

We consider the $X(3872)$ resonance as a $J^{PC}=1^{++}$ $D\bar D^*$ hadronic molecule. According to heavy quark spin symmetry, there will exist a partner with quantum numbers $2^{++}$, $X_{2}$, which would be a $D^*\bar D^*$ loosely bound state. The $X_{2}$ is expected to decay dominantly into $D\bar D$, $D\bar D^*$ and $\bar D D^*$ in $d$-wave. In this work, we calculate the decay widths of the $X_{2}$ resonance into the above channels, as well as those of its bottom partner, $X_{b2}$, the mass of which comes from assuming heavy flavor symmetry for the contact terms. We find partial widths of the $X_{2}$ and $X_{b2}$ of the order of a few MeV. Finally, we also study the radiative $X_2\to D\bar D^{*}\gamma$ and $X_{b2} \to \bar B B^{*}\gamma$ decays. These decay modes are more sensitive to the long-distance structure of the resonances and to the $D\bar D^{*}$ or $B\bar B^{*}$ final state interaction.