X(3872) in a hot pion bath

Right since its discovery in 2003 by the Belle collaboration, establishing the nature of the $X(3872)$ meson has been one of the main priorities in the field of quarkonium physics. Not qualifying as a conventional $c\bar{c}$ state, the multiquark structure of this exotic meson has received very different interpretations, ranging from a compact tetraquark configuration to an extended $D\bar D^*+c.c.$ molecule. In this work we explore the effect that a hot pion bath may have in the properties of the $X(3872)$, assuming this state to be a $D\bar D^*+c.c.$ molecule. We derive the finite temperature effects on the $X(3872)$ from a coupled channels unitarized amplitude, obtained including the properties of the charmed mesons under such conditions. We find that the $X(3872)$ develops a subtantial width, of the order of a few tens of MeV, in hot pionic environments at temperatures $100-150$ MeV, and its nominal mass moves above the $D D^*$ threshold. The fact that the $X(3872)$ in a hot pion gas may no longer be a narrow resonance needs to be considered in the estimation of production yields in relativistic heavy-ion collisions.