Particle number fluctuations in nuclear collisions within excluded volume hadron gas model

The multiplicity fluctuations are studied in the van der Waals excluded volume hadron-resonance gas model. The calculations are done in the grand canonical ensemble within the Boltzmann statistics approximation. The scaled variances for positive, negative and all charged hadrons are calculated along the chemical freeze-out line of nucleus-nucleus collisions at different collision energies. The multiplicity fluctuations are found to be suppressed in the van der Waals gas. The numerical calculations are presented for two values of hard-core hadron radius, $r=0.3$ fm and 0.5 fm, as well as for the upper limit of the excluded volume suppression effects.Comment: 19 pages, 4 figure

Evolution of fluctuations near QCD critical point

We propose to describe the time evolution of quasi-stationary fluctuations near QCD critical point by a system of stochastic Boltzmann-Langevin-Vlasov-type equations. We derive the equations and study the system analytically in the linearized regime. Known results for equilibrium stationary fluctuations as well as the critical scaling of diffusion coefficient are reproduced. We apply the approach to the long-standing question of the fate of the critical point fluctuations during the hadronic rescattering stage of the heavy-ion collision after chemical freezeout. We find that if conserved particle number fluctuations survive the rescattering, so do, under a certain additional condition, the fluctuations of non-conserved quantities, such as mean transverse momentum. We derive a simple analytical formula for the magnitude of this "memory" effect.Comment: 13 pages, as published, typos corrected, some definitions made more explici

The three-flavor chiral phase structure in hot and dense QCD matter

Chiral symmetry restoration at nonzero temperature and quark densities are investigated in the framework of a linear sigma model with N_f=3 light quark flavors. After the derivation of the grand potential in mean-field approximation, the nonstrange and strange condensates, the in-medium masses of the scalar and pseudoscalar nonets are analyzed in hot and dense medium. The influence of the axial anomaly on the nonet masses and the isoscalar mixings on the pseudoscalar \eta-\eta' and scalar \sigma(600)-f_0(1370) complex are examined. The sensitivity of the chiral phase transition as well as the existence and location of a critical end point in the phase diagram on the value of the sigma mass is explored. The chiral critical surface with and without the influence of the axial U(1)_A anomaly is elaborated as a function of the pion and kaon masses for several values of the sigma mass.Comment: 19 pages, 12 figures, 2 tables, RevTex4; revised version, accepted for publication in PR

Fluctuations as probe of the QCD phase transition and freeze-out in heavy ion collisions at LHC and RHIC

We discuss the relevance of higher order moments of net baryon number fluctuations for the analysis of freeze-out and critical conditions in heavy ion collisions at LHC and RHIC. Using properties of O(4) scaling functions, we discuss the generic structure of these higher moments at vanishing baryon chemical potential and apply chiral model calculations to explore their properties at non-zero baryon chemical potential. We show that the ratios of the sixth to second and eighth to second order moments of the net baryon number fluctuations change rapidly in the transition region of the QCD phase diagram. Already at vanishing baryon chemical potential they deviate considerably from the predictions of the hadron resonance gas model which reproduce the second to fourth order moments of the net proton number fluctuations at RHIC. We point out that the sixth order moments of baryon number and electric charge fluctuations remain negative at the chiral transition temperature. Thus, they offer the possibility to probe the proximity of the thermal freeze-out to the crossover line.Comment: 24 pages, 12 EPS files, revised version, to appear in EPJ

A Random Matrix Study of the QCD Sign Problem

We investigate the severity of the sign problem in a random matrix model for QCD at finite temperature T and baryon chemical potential mu. We obtain analytic expression for the average phase factor -- the measure of the severity of the sign problem at arbitrary T and mu. We observe that the sign problem becomes less severe as the temperature is increased. We also find the domain where the sign problem is maximal -- the average phase factor is zero, which is related to the pion condensation phase in the QCD with finite isospin chemical potential. We find that, in the matrix model we studied, the critical point is located inside the domain of the maximal sign problem, making the point inaccessible to conventional reweighting techniques. We observe and describe the scaling behavior of the size and shape of the pion condensation near the chiral limit.Comment: 16 pages, 3 figure

Impact of resonance decays on critical point signals in net-proton fluctuations

The non-monotonic beam energy dependence of the higher cumulants of net-proton fluctuations is a widely studied signature of the conjectured presence of a critical point in the QCD phase diagram. In this work we study the effect of resonance decays on critical fluctuations. We show that resonance effects reduce the signatures of critical fluctuations, but that for reasonable parameter choices critical effects in the net-proton cumulants survive. The relative role of resonance decays has a weak dependence on the order of the cumulants studied with a slightly stronger suppression of critical effects for higher-order cumulants

Multiplicity Fluctuations in Hadron-Resonance Gas

The charged hadron multiplicity fluctuations are considered in the canonical ensemble. The microscopic correlator method is extended to include three conserved charges: baryon number, electric charge and strangeness. The analytical formulae are presented that allow to include resonance decay contributions to correlations and fluctuations. We make the predictions for the scaled variances of negative, positive and all charged hadrons in the most central Pb+Pb (Au+Au) collisions for different collision energies from SIS and AGS to SPS and RHIC.Comment: 19 pages, 4 figure

Lepton asymmetry and the cosmic QCD transition

We study the influence of lepton asymmetry on the evolution of the early Universe. The lepton asymmetry $l$ is poorly constrained by observations and might be orders of magnitude larger than the baryon asymmetry $b$, $|l|/b \leq 2\times 10^8$. We find that lepton asymmetries that are large compared to the tiny baryon asymmetry, can influence the dynamics of the QCD phase transition significantly. The cosmic trajectory in the $\mu_B-T$ phase diagram of strongly interacting matter becomes a function of lepton (flavour) asymmetry. Large lepton asymmetry could lead to a cosmic QCD phase transition of first order.Comment: 23 pages, 14 figures; matches published version, including Erratum. Conclusions, pictures, numerics remained unchange

Chemical potential response of meson masses at finite temperature

We study the response of meson masses to the chemical potential ($\partial{m}/\partial{\mu}$) at high temperature and at zero chemical potential on $N_f=2$ lattice with staggered fermions. Preliminary results for the meson composed of different quarks show that $\partial{m}/\partial{\mu}|_{\mu=0}$ is negative in the confinement phase and positive in the deconfinement phase.Comment: Lattice 2000 (Finite Density), 4 pages, 2 figure

Scalar density fluctuation at critical end point in NJL model

Soft mode near the critical end point in the phase diagram of two-flavor Nambu--Jona-Lasinio (NJL) model is investigated within the leading 1/N_c approximation with N_c being the number of the colors. It is explicitly shown by studying the spectral function of the scalar channel that the relevant soft mode is the scalar density fluctuation, which is coupled with the quark number density, while the sigma meson mode stays massive.Comment: 9 pages, 4 figure