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

We analyze how the renowned X(3872), a weakly bound state right below the DD¯⁎ threshold, should effectively be included in a hadronic representation of the QCD partition function. This can be decided by analyzing the DD¯⁎ scattering phase-shifts in the JPC=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∼150 MeV. In contrast, within a coupled-channels approach, for a non vanishing cc¯ 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≳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 pT distribution due to a finite energy resolution.