Counting states and the Hadron Resonance Gas: Does X(3872) count?

TL;DR

This paper investigates whether the exotic state X(3872) should be included in the hadronic representation of the QCD partition function, analyzing its nature and contribution at different temperatures in heavy-ion collisions.

Contribution

It provides a detailed analysis of the conditions under which X(3872) counts as a hadronic state, highlighting the importance of its internal structure and the coupled-channels approach.

Findings

In a molecular picture, X(3872) does not contribute below the QGP crossover.

Coupled-channels approach shows X(3872) can count as an elementary particle at high temperatures.

The cancellation effect influences the production and detection of X(3872) in heavy-ion collisions.

Abstract

We analyze how the renowned X(3872), a weakly bound state right below the $D \bar D^*$ threshold, should effectively be included in a hadronic representation of the QCD partition function. This can be decided by analyzing the $D \bar D^*$ scattering phase-shifts in the $J^{PC}=1^{++}$ channel and their contribution to the level density in the continuum from which the abundance in a hot medium can be determined. We show that in a purely molecular picture the bound state contribution cancels the continuum providing a vanishing occupation number density at finite temperature and the $X(3872)$ does not count below the Quark-Gluon Plasma crossover happening at $T \sim 150$MeV. In contrast, within a coupled-channels approach, for a non vanishing $c \bar c$ content the cancellation does not occur due to the onset of the $X(3940)$ which effectively counts as an elementary particle for temperatures above $T \gtrsim 250$MeV. Thus, a direct inclusion of the $X(3872)$ in the Hadron Resonance Gas is not justified. We also estimate the role of this cancellation in X(3872) production in heavy-ion collision experiments in terms of the corresponding $p_T$ distribution due to a finite energy resolution.