586 research outputs found
The O(N)-model within the Phi-derivable expansion to order lambda^2: on the existence, UV and 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.Comment: 26 pages, 15 figures, uses RevTeX4-1, published versio
Chiral phase transition in an extended linear sigma model: initial results
We investigate the scalar meson mass dependence on the chiral phase
transition in the framework of an SU(3), (axial)vector meson extended linear
sigma model with additional constituent quarks and Polyakov loops. We determine
the parameters of the Lagrangian at zero temperature in a hybrid approach,
where we treat the mesons at tree-level, while the constituent quarks at 1-loop
level. We assume two nonzero scalar condensates and together with the
Polyakov-loop variables we determine their temperature dependence according to
the 1-loop level field equations.Comment: Presented at the Workshop on Unquenched Hadron Spectroscopy:
Non-Perturbative Models and Methods of QCD vs. Experiment, At the occasion of
Eef van Beveren's 70th birthda
Loss of solution in the symmetry improved Phi-derivable expansion scheme
We consider the two-loop Phi-derivable approximation for the O(2)-symmetric
scalar model, augmented by the symmetry improvement introduced in [A. Pilaftsis
and D. Teresi, Nucl. Phys. B874, 594 (2013)], which enforces Goldstone's
theorem in the broken phase. Although the corresponding equations admit a
solution in the presence of a large enough infrared (IR) regulating scale, we
argue that, for smooth ultraviolet (UV) regulators, the solution is lost when
the IR scale becomes small enough. Infrared regular solutions exist for certain
non-analytic UV regulators, but we argue that these solutions are artifacts
which should disappear when the sensitivity to the UV regulator is removed by a
renormalization procedure. The loss of solution is observed both at zero and at
finite temperature, although it is simpler to identify in the latter case. We
also comment on possible ways to cure this problem.Comment: 20 pages, 7 figures, uses elsarticle, published versio
Thermodynamics and phase transition of the O(N) model from the two-loop Phi-derivable approximation
We discuss the thermodynamics of the O(N) model across the corresponding
phase transition using the two-loop Phi-derivable approximation of the
effective potential and compare our results to those obtained in the literature
within the Hartree-Fock approximation. In particular, we find that in the
chiral limit the transition is of the second order, whereas it was found to be
of the first order in the Hartree-Fock case. These features are manifest at the
level of the thermodynamical observables. We also compute the thermal sigma and
pion masses from the curvature of the effective potential. In the chiral limit,
this guarantees that the Goldstone's theorem is obeyed in the broken phase. A
realistic parametrization of the model in the N=4 case, based on the vacuum
values of the curvature masses, shows that a sigma mass of around 450 MeV can
be obtained. The equations are renormalized after extending our previous
results for the N=1 case by means of the general procedure described in [J.
Berges et al., Annals Phys. 320, 344-398 (2005)]. When restricted to the
Hartree-Fock approximation, our approach reveals that certain problems raised
in the literature concerning the renormalization are completely lifted.
Finally, we introduce a new type of Phi-derivable approximation in which the
gap equation is not solved at the same level of accuracy as the accuracy at
which the potential is computed. We discuss the consistency and applicability
of these types of "hybrid" approximations and illustrate them in the two-loop
case by showing that the corresponding effective potential is renormalizable
and that the transition remains of the second order.Comment: 26 pages, 9 figures, uses RevTeX4-1, published versio
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 mu_B within
an extended (2+1) flavor Polyakov constituent quark-meson model which
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
chi^2-minimization procedure which 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 eta-eta'
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-mu_B phase diagram of the model and find that a critical end point exists
for parameters of the model, which give acceptable values of chi^2.Comment: 21 pages, 8 color eps figures, published versio
Pad\'e approximants and analytic continuation of Euclidean Phi-derivable approximations
We investigate the Pad\'e 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.Comment: 20 pages, 8 figures, uses RevTeX 4-
Chiral phase transition in the vector meson extended linear sigma model
In the framework of an SU(3) (axial)vector meson extended linear sigma model
with additional constituent quarks and Polyakov loops, we investigate the
effects of (axial)vector mesons on the chiral phase transition. The parameters
of the Lagrangian are set at zero temperature and we use a hybrid approach
where in the effective potential the constituent quarks are treated at one-loop
level and all the mesons at tree-level. We have four order parameters, two
scalar condensates and two Polyakov loop variables and their temperature and
baryochemical potential dependence are determined from the corresponding field
equations. We also investigate the changes of the tree-level scalar meson
masses in the hot and dense medium.Comment: 5 pages, 6 figure
The granger causality analysis of energy consumption and economic growth
After the first oil crisis the world’s countries had to face recession caused by the high oil prices, and the role of energy consumption became a core element of economics. Many studies examined (and examine today) connection between energy consumption, economic growth and energy efficiency. The purpose of the paper is to contribute to this topic with an analysis of Granger causality between energy consumption and economic growth in East-Central Europe
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