Traces of the nuclear liquid-gas phase transition in the analytic properties of hot QCD

Abstract

The nuclear liquid-gas transition at normal nuclear densities, $n\ensuremath{\approx}{n}_{0}=0.16\phantom{\rule{4pt}{0ex}}{\mathrm{fm}}^{\ensuremath{-}3}$, and small temperatures, $T\ensuremath{\approx}20\phantom{\rule{4pt}{0ex}}\mathrm{MeV}$, has a large influence on analytic properties of the QCD grand-canonical thermodynamic potential. A classical van der Waals equation is used to determine qualitatively these unexpected features due to dense cold matter. The existence of the nuclear matter critical point results in thermodynamic branch points, which are located at complex chemical potential values, for $T>{T}_{c}\ensuremath{\simeq}20\phantom{\rule{4pt}{0ex}}\mathrm{MeV}$, and exhibit a moderate model dependence up to rather large temperatures $T\ensuremath{\lesssim}100\phantom{\rule{4pt}{0ex}}\mathrm{MeV}$. The behavior at higher temperatures is studied using the van der Waals hadron resonance gas (vdW-HRG) model. The baryon-baryon interactions have a decisive influence on the QCD thermodynamics close to ${\ensuremath{\mu}}_{B}=0$. In particular, nuclear matter singularities limit the radius of convergence ${r}_{{\ensuremath{\mu}}_{B}/T}$ of the Taylor expansion in ${\ensuremath{\mu}}_{B}/T$, with ${r}_{{\ensuremath{\mu}}_{B}/T}\ensuremath{\approx}2--3$ values at $T\ensuremath{\approx}140--170\phantom{\rule{4pt}{0ex}}\mathrm{MeV}$ obtained in the vdW-HRG model.