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We analyze how the renowned X(3872), a weakly bound state right below the $D\bar D^*$ threshold, should effectively be included in a hadronicrepresentation of the QCD partition function. This can be decided by analyzingthe $D \bar D^*$ scattering phase-shifts in the $J^{PC}=1^{++}$ channel andtheir contribution to the level density in the continuum from which theabundance in a hot medium can be determined. We show that in a purely molecularpicture the bound state contribution cancels the continuum providing avanishing occupation number density at finite temperature and the $X(3872)$does not count below the Quark-Gluon Plasma crossover happening at $T \sim150$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 temperaturesabove $T \gtrsim 250$MeV. Thus, a direct inclusion of the $X(3872)$ in theHadron Resonance Gas is not justified. We also estimate the role of thiscancellation in X(3872) production in heavy-ion collision experiments in termsof the corresponding $p_T$ distribution due to a finite energy resolution.

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