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

Abstract

We analyze how the renowned X(3872), a weakly bound state right below the $D{\bar{D}}^{\ast }$ threshold, should effectively be included in a hadronic representation of the QCD partition function. This can be decided by analyzing the $D{\bar{D}}^{\ast }$ 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.

7 pages, 6 figures and 1 table. Version accepted for publication in Phys. Lett. B

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Cited by in corpus (9)

• X(3872): propagating in a dense medium
• $X(3872)$ as virtual companion pole of the charm-anticharm state ${\chi }_{c1}(2P)$
• X(3872) in a hot pion bath
• Thermal contribution of unstable states
• Thermodynamics of the Glueball Resonance Gas
• Density of States of a Coupled-Channel System
• Is the X(3872) a bound state ?
• QFT treatment of a bound state in a thermal gas
• On the precise measurement of the $X(3872)$ mass and its counting rate