Symmetries, partners and thresholds: the case of the $X_b$

TL;DR

This paper analyzes the structure of the $X_b$ state using a coupled-channels model, emphasizing the role of symmetries and channel couplings in heavy meson spectroscopy, and proposes a candidate for its partner state.

Contribution

It introduces a coupled-channels approach to study heavy meson states, highlighting how thresholds and channel couplings influence state structures beyond traditional symmetry predictions.

Findings

Identifies the importance of bare $Qar Q$ states and channel couplings in state formation.

Predicts a potential $X_b$ partner state at 10599 MeV/c^2.

Shows how symmetry considerations are affected by threshold effects.

Abstract

The discovery of the $X(3872)$ meant the revival of the heavy meson spectroscopy beyond naive $q\bar q$ structures. Once that the $SU(3)$ scheme, which was very useful in the dawn of the quark models, does not work for these states, one has to use new symmetries, like Heavy Quark Spin Symmetry (HQSS) and Heavy Flavor Symmetry (HFS), to look for new states. However, at the energy regions where these new states appear, new factors are involved and it is not straightforward to relate the predictions of the symmetries with the data. In this work, we present a critical analysis of this problem and show, in a coupled-channels model, how the relative position of the bare $Q\bar Q$ states with respect to meson-meson thresholds and the coupling with other channels modulate the strength of the interaction and, hence, modify the structure of the predicted states. We found a possible candidate to the $X(3872)$ partner at $10599$ MeV$/c^2$.