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 D¯D∗threshold, should effectively be included in a hadronic representation of the QCD partition function. This can be decided by analyzing the D¯D∗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∼150MeV. In contrast, within a coupled-channels approach, for a non vanishing c¯ccontent the cancellation does not occur due to the onset of the X (3940) which effectively counts as an elementary particle for temperatures above T _250MeV. 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.This work has been partially funded by the Span-ish Ministerio de Economia y Competitividad and European ERDF funds (Grant No. FIS2014-59386-P, FPA2016-77177-C2-2-P and FIS2017-85053-C2-1-P ), the Agencia de Innovacion y Desarrollo de Andalucia (Grant No. FQM225), and by Junta de Castilla y León and European Regional Development Funds (ERDF) under Contract no. SA041U16