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

Counterterm resummation for 2PI-approximation in constant background

Explicit counterterm construction is presented in a symmetry breaking background for the 2PI effective action of the self-interacting one-component scalar field including skeleton diagrams to O(lambda(2)). The applied strategy is an extension of our treatment of the 2PI-Hartree approximation [G. Fejos, A. Patkos, Zs. Szep, Nucl. Phys. A 803 (2008) 135, arXiv: 0711.2933]. The procedure is also applied to the O(N) model

Renormalized O(N) model at next-to-leading order of the 1/N expansion: Effects of the Landau pole

Apparently convergent contributions of resummed perturbative series at the next-to-leading order of the 1/N expansion in the O(N) model are reanalyzed in terms of renormalizability. Compared to our earlier article [G. Fejős et al., Phys. Rev. D 80, 025015 (2009)], an additional subtraction is performed. We show numerically that this is indispensable for diminishing the cutoff sensitivity of some integrals below the scale of the Landau pole. Following the method of our earlier article, an improved counterterm Lagrangian is constructed in the two-particle irreducible formalism, with and without the use of an auxiliary field formulation

Renormalisability of the 2PI-Hartree approximation of multicomponent scalar models in the broken symmetry phase

Non-perturbative renormalisation of a general class of scalar field theories is performed at the Hartree level truncation of the 2PI effective action in the broken symmetry regime. Renormalised equations are explicitly constructed for the one- and two-point functions. The non-perturbative counterterms are deduced from the conditions for the cancellation of the overall and the subdivergences in the complete Hartree-Dyson-Schwinger equations, with a transparent method. The procedure proposed in the present paper is shown to be equivalent to the iterative renormalisation method of Blaizot et al. [J.-P. Blaizot, E. Iancu, U. Reinosa, Nucl. Phys. A 736 (2004) 149, hep ph/0312085]

Renormalization and resummation in finite temperature field theories

Resummation, ie. reorganization of perturbative series, can result in an inconsistent perturbation theory, unless the counterterms are reorganized in an appropriate way. In this paper two methods are presented for resummation of counterterms: one is a direct method where the necessary counterterms are constructed order by order; the other is a general one, based on renormalization group arguments. We demonstrate at one hand that, in mass independent schemes, mass resummation can be performed by gap equations renormalized prior to the substitution of the resummed mass for its argument. On the other hand it is shown that any (momentum-independent) form of mass and coupling constant resummation is compatible with renormalization, and one can explicitly construct the corresponding counterterms.Comment: 10 pages, 4 figures, revtex

The nature of the soft excitation near the end-point of the QCD

Using a large flavor number expansion and a gap equation for the pion mass the chiral quark-meson model is solved at the lowest order in the fermion contributions. In the chiral limit the tricritical point (TCP) is determined analytically. The softening of the sigma particle is verified at this point and is further investigated for a physical pion mass in the neighbourhood of the critical endpoint (CEP)

Mapping the boundary of the first order finite temperature restoration of chiral symmetry in the mpi - mK -plane with a linear sigma model

The phase diagram of the three-flavor QCD is mapped out in the low mass corner of the (m(pi)-m(K))-plane with help of the SU(L)(3)xSU(R)(3) linear sigma model (L sigma M). A novel zero temperature parametrization is proposed for the mass dependence of the couplings away from the physical point based on the three-flavor chiral perturbation theory(U(3) ChPT). One-loop thermodynamics is constructed by applying optimized perturbation theory. The unknown dependence of the scalar spectra on the pseudoscalar masses limits the accuracy of the predictions. Results are compared to lattice data and similar investigations with other variants of effective chiral models. The critical value of the pion mass is below 65 MeV for all m(K) value less than or similar to 800 MeV. Along the diagonal m(pi)=m(K), we estimate m(crit)(diag)=40 +/- 20 MeV

Classical order parameter dynamics and the decay of a metastable vacuum state

Transition of the ground state of a classical Phi^4 theory in 2+1 dimensions is studied from a metastable state into the stable equilibrium. The transition occurs in the broken Z_2 symmetry phase and is triggered by a vanishingly small amplitude homogeneous external field h. A phenomenological theory is proposed in form of an effective equation of the quantitatively accounts for the decay of the false vacuum. The large amplitude transition of the order parameter between the two minima displays characteristics reflecting dynamical aspects of the Maxwell construction

Dynamical Manifestation of the Goldstone Phenomenon at 1-loop

We have calculated the damping rate $\Gamma (|{\bf k}|)$ for classical on-shell Goldstone modes of the O(2) symmetric scalar fields propagating in a thermal medium of the broken symmetry phase taking into account the effect of the explicit symmetry breaking. The result of the one-loop analysis can be expanded around $\Gamma (0)$, which depends non-analytically on the parameter of the explicit symmetry breaking, h. $\Gamma (0)$ vanishes when $h\to 0$, demonstrating in this way the absence of the restoring force, when the equilibrium direction of the symmetry breaking is modulated homogeneously.Comment: 8 pages, Late

Non-perturbative construction of counterterms for 2PI-approximation

A concise method is presented for the non-perturbative computation of the counterterms renormalising 2PI-actions. The procedure is presented for a real scalar field up to lambda^2 order in the skeleton truncation of Gamma_2PI with respect to the self-coupling, and in a constant symmetry breaking background. The method is easily generalizable to field theories with arbitrary global symmetry.Comment: 4 pages, poster presented at Strong and Electroweak Matter (SEWM2008), Amsterdam,August 25-29 200