Zsolt Szép

Existence of the critical endpoint in the vector meson extended linear sigma model

The chiral phase transition of the strongly interacting matter is investigated at nonzero temperature and baryon chemical potential (μB) within an extended (2+1) flavor Polyakov constituent quark-meson model that incorporates the effect of the vector and axial vector mesons. The effect of the fermionic vacuum and thermal fluctuations computed from the grand potential of the model is taken into account in the curvature masses of the scalar and pseudoscalar mesons. The parameters of the model are determined by comparing masses and tree-level decay widths with experimental values in a χ2-minimization procedure that selects between various possible assignments of scalar nonet states to physical particles. We examine the restoration of the chiral symmetry by monitoring the temperature evolution of condensates and the chiral partners’ masses and of the mixing angles for the pseudoscalar η-η′ and the corresponding scalar complex. We calculate the pressure and various thermodynamical observables derived from it and compare them to the continuum extrapolated lattice results of the Wuppertal-Budapest collaboration. We study the T-μB phase diagram of the model and find that a critical endpoint exists for parameters of the model, which give acceptable values of χ2.

O (N) model within the Φ -derivable expansion to order λ2: On the existence and UV/IR sensitivity of the solutions to self-consistent equations

We discuss various aspects of the O(N)-model in the vacuum and at finite temperature within the Phi-derivable expansion scheme to order lambda^2. In continuation to an earlier work, we look for a physical parametrization in the N=4 case that allows to accommodate the lightest mesons. Using zero-momentum curvature masses to approximate the physical masses, we find that, in the parameter range where a relatively large sigma mass is obtained, the scale of the Landau pole is lower compared to that obtained in the two-loop truncation. This jeopardizes the insensitivity of the observables to the ultraviolet regulator and could hinder the predictivity of the model. Both in the N=1 and N=4 cases, we also find that, when approaching the chiral limit, the (iterative) solution to the Phi-derivable equations is lost in an interval around the would-be transition temperature. In particular, it is not possible to conclude at this order of truncation on the order of the transition in the chiral limit. Because the same issue could be present in other approaches, we investigate it thoroughly by considering a localized version of the Phi-derivable equations, whose solution displays the same qualitative features, but allows for a more analytical understanding of the problem. In particular, our analysis reveals the existence of unphysical branches of solutions which can coalesce with the physical one at some temperatures, with the effect of opening up a gap in the admissible values for the condensate. Depending on its rate of growth with the temperature, this gap can eventually engulf the physical solution.

Padé approximants and analytic continuation of Euclidean Φ -derivable approximations

We investigate the Pade approximation method for the analytic continuation of numerical data and its ability to access, from the Euclidean propagator, both the spectral function and part of the physical information hidden in the second Riemann sheet. We test this method using various benchmarks at zero temperature: a simple perturbative approximation as well as the two-loop Phi-derivable approximation. The analytic continuation method is then applied to Euclidean data previously obtained in the O(4) symmetric model (within a given renormalization scheme) to assess the difference between zero-momentum and pole masses, which is in general a difficult question to answer within nonperturbative approaches such as the Phi-derivable expansion scheme.

Bose-Einstein condensation and Silver Blaze property from the two-loop

We extend our previous investigation of the two-loop

\Phi

\Phi

-derivable approximation

-derivable approximation to finite chemical potential

Critical look at the role of the bare parameters in the renormalization of σ-derivable approximations

\mu

Broken symmetry phase solution of the 4 model at two-loop level of the Φ-derivable approximation

and discuss Bose-Einstein condensation (BEC) in the case of a charged scalar field with

Thermodynamics and phase transition of the O(N) model from the two-loop Φ-derivable approximation

O(2)

Broken phase scalar effective potential and Φ-derivable approximations

symmetry. We show that the approximation is renormalizable by means of counterterms which are independent of both the temperature and the chemical potential. We point out the presence of an additional skew contribution to the propagator as compared to the