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.
Highlights
The thermodynamic properties of QCD at finite temperatures and densities are important issues of modern highenergy nuclear physics
Nuclear matter singularities limit the radius of convergence rμB/T of the Taylor expansion in μB/T, with rμB/T ≈ 2–3 values at T ≈ 140–170 MeV obtained in the van der Waals hadron resonance gas (vdW-hadron resonance gas (HRG)) model
Mechanisms other than the nuclear liquid-gas transition are present in full QCD, which affect the analytic properties of the thermodynamic potential and which are not covered within the van der Waals (vdW)-HRG model
Summary
The thermodynamic properties of QCD at finite temperatures and densities are important issues of modern highenergy nuclear physics. I.e., at μB = 0, this transition is a crossover, according to lattice QCD simulations [1]. The experimental search for the hypothetical QCD chiral critical point (CP) [2] is performed at nonzero intermediate baryon densities using measurements of fluctuations in heavy-ion collisions [3,4,5,6] as well as indirect lattice gauge theory methods, such as a Taylor expansion around μB = 0 [7,8] or analytic continuation from imaginary μB [9,10]. An extrapolation to higher temperatures is achieved in the framework of the vdW-HRG model, with a focus on the influence of the nuclear matter LGPT singularities on convergence properties of the Taylor expansion in μB/T around μB = 0 (Sec. IV).
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