Cluster expansion model for QCD baryon number fluctuations: No phase transition at μB/T<π

Abstract

A cluster expansion model (CEM), representing a relativistic extension of Mayer's cluster expansion, is constructed to study baryon number fluctuations in QCD. The temperature dependent first two coefficients, corresponding to the partial pressures in the baryon number B ¼ 1 and B ¼ 2 sectors, are the only model input, which we fix by recent lattice data at imaginary baryochemical potential. All other coefficients are constructed in terms of the first two and required to match the Stefan-Boltzmann limit of noninteracting quarks and gluons at T → ∞. The CEM allows calculations of the baryon number susceptibilities χ B k to arbitrary order. We obtain excellent agreement with all available lattice data for the baryon number fluctuation measures χ The grand canonical thermodynamic potential of QCD is an even function of the real baryon chemical potential μ B because of the CP-symmetry. Taking the quantization of the baryon charge into account, the QCD pressure has a fugacity expansionThis relation can formally be viewed as a relativistic extension of Mayer's cluster expansion in fugacities [1]. A similar formalism is also employed in the canonical approach [2][3][4][5], where the fugacity expansion is applied to the partition function Z itself (see Refs. [6,7] for recent developments).The net baryon density readswhere b k ðTÞ ≡ kp k ðTÞ. Analytic continuation to an imaginary chemical potential yields a purely imaginary ρ B =T 3 , with b k ðTÞ becoming its Fourier expansion coefficients. The analytic continuation to/from imaginary μ is one of the methods used to study QCD at finite net baryon density [8][9][10][11][12][13][14][15][16]. The leading four Fourier coefficients b k were studied in Refs. [17,18] using lattice simulations with physical quark masses at imaginary μ B , as well as phenomenological models.At low temperatures, below the crossover transition, a behavior similar to an uncorrelated gas of hadrons, i.e., jb k ðTÞ=b 1 ðTÞj ≪ 1 for k ≥ 2, is seen in lattice QCD (LQCD) [17,18]. Lattice simulations at T > 135 MeV yield negative b 2 ðTÞ values, which could be interpreted in terms of repulsive baryonic interactions. The first four LQCD Fourier coefficients, up to T ≃ 185 MeV, can indeed be described rather well by a hadron resonance gas (HRG) model with excluded-volume (EV) interactions between the (anti)

Critical point signatures in the cluster expansion in fugacities

“…4 the predictions of the cluster expansion model (CEM) of Ref. [20]. The CEM describes the available lattice data on b k within errors, the asymptotic behavior of the Fourier coefficients in this model matches the general form given in Eq.…”

“…This behavior is determined by the asymptotic properties of Hermite polynomials, which are known. Extra care should be taken here, as both the index and the argument of the Hermite polynomials in (20) tend to large values as k → ∞. In such a case the asymptotic behavior depends on the relative increase rate of the Hermite polynomial index and its argument.…”

QCD equation of state at finite baryon density with fugacity expansion

“…Here we construct a model for the QCD equation of state at finite baryon density which incorporates all of the above-mentioned constraints. Our considerations are based on the recently developed cluster expansion model (CEM) formalism [15,16]. It uses the cluster expansion in baryonic fugacity,…”

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

“…This is a consequence of the fact that limiting singularity lies in the complex plane, with a non-zero imaginary part µ I br /T = 0. In such a case the ratio estimator does not converge [13,47].…”

“…The experimental search for the hypothetical QCD chiral critical point (CP) [2] is performed at non-zero 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 µ B = 0 [7,8] or analytic continuation from imaginary µ B [9,10]. Current high quality lattice QCD data at physical quark masses show no evidence or signatures of a chiral CP and disfavor the existence of a phase transition of first or second order at moderate baryon densities µ B /T π [11][12][13][14]. The location or even the existence of that CP is not settled to date.…”