Does $X(3872)$ count?

Abstract

The question on whether or not weakly bound states should be effectively incorporated in a hadronic representation of the QCD partition function is addressed by analyzing the example of the X(3872), a resonance close to the DD * threshold which has been suggested as an example of a loosely bound molecule. This can be decided by studying the DD * scattering phase-shifts in the J PC = 1 ++ channel and their contribution to the level density in the continuum, which also gives information on its abundance in a hot medium. In this work, it is shown that, in a purely molecular picture, the bound state contribution cancels the continuum, resulting in a null occupation number density at finite temperature, which implies the X(3872) does not count below the Quark-Gluon Plasma crossover (T ∼ 150MeV). However, if a non-zero cc component is present in the X(3872) wave function such cancellation does not occur for temperatures above T 250MeV.