arXiv subjects

Zs. Szep

Publications and source records attributed to Zs. Szep.

At least 19 recordsLinked to original sources

arXiv2014

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. Fejos 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.

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arXiv2011

Broken symmetry phase solution of the phi^4 model at two-loop level of the Phi-derivable approximation

The set of coupled equations for the self-consistent propagator and the field expectation value is solved numerically with high accuracy in Euclidean space at zero temperature and in the broken symmetry phase of the phi^4 model. Explicitly finite equations are derived with the adaptation of the renormalization method of van Hees and Knoll [H. van Hees, J. Knoll, Phys. Rev. D65, 025010 (2001)] to the case of non-vanishing field expectation value. The set of renormalization conditions used in this method leads to the same set of counterterms obtained recently in A. Patkos, Zs. Szep, Nucl. Phys. A811, 329-352 (2008). This makes possible the direct comparison of the accurate solution of explicitly finite equations with the solution of renormalized equations containing counterterms. The numerically efficient way of solving iteratively these latter equations is obtained by deriving at each order of the iteration new counterterms which evolve during the iteration process towards the counterterms determined based on the asymptotic behavior of the converged propagator. As shown at different values of the coupling, the use of these evolving counterterms accelerates the convergence of the solution of the equations.

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arXiv2010

The effect of the Polyakov loop on the chiral phase transition

The Polyakov loop is included in the SU(2)_L x SU(2)_R chiral quark-meson model by considering the propagation of the constituent quarks, coupled to the (sigma,pi) meson multiplet, on the homogeneous background of a temporal gauge field, diagonal in color space. The model is solved at finite temperature and quark baryon chemical potential both in the chiral limit and for the physical value of the pion mass by using an expansion in the number of flavors N_f. Keeping the fermion propagator at its tree-level, a resummation on the pion propagator is constructed which resums infinitely many orders in 1/N_f, where O(1/N_f) represents the order at which the fermions start to contribute in the pion propagator. The influence of the Polyakov loop on the tricritical or the critical point in the mu_q-T phase diagram is studied for various forms of the Polyakov loop potential.

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arXiv2010

Influence of the Polyakov loop on the chiral phase transition in the two flavor chiral quark model

The SU(2)_L x SU(2)_R chiral quark model consisting of the (sigma,pi) meson multiplet and the constituent quarks propagating on the homogeneous background of a temporal gauge field is solved at finite temperature and quark baryon chemical potential mu_q using an expansion in the number of flavors N_f, both in the chiral limit and for the physical value of the pion mass. Keeping the fermion propagator at its tree-level, several approximations to the pion propagator are investigated. These approximations correspond to different partial resummations of the perturbative series. Comparing their solution with a diagrammatically formulated resummation relying on a strict large-N_f expansion of the perturbative series one concludes that only when the local part of the approximated pion propagator resums infinitely many orders in 1/N_f of fermionic contributions a sufficiently rapid crossover transition at mu_q=0 is achieved allowing for the existence of a tricritical point or a critical end point in the mu_q-T phase diagram. The renormalization and the possibility of determining the counterterms in the resummation provided by a strict large-N_f expansion are investigated.

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arXiv2010

Strange mass dependence of the tricritical point in the U(3)_L x U(3)_R chiral sigma model

We study the strange quark mass dependence of the tricritical point of the U(3)_L x U(3)_R linear sigma model in the chiral limit. Assuming that the tricritical point is at a large strange mass value, the strange sector as well as the η-a_0 sector decouples from the light degrees of freedom which determines the thermodynamics. By tracing this decoupling we arrive from the original U(3)_L x U(3)_R symmetric model, going through the U(2)_L x U(2)_R symmetric one, at the SU(2)_L x SU(2)_R linear sigma model. One-loop level beta functions for the running of the parameters in each of these models and tree-level matching of the coupling of these models performed at intermediate scales are used to determine the influence of the heavy sector on the parameters of the SU(2)_L x SU(2)_R linear sigma model. By investigating the thermodynamics of this latter model we identified the tricritical surface of the U(3)_L x U(3)_R linear sigma model in the chiral limit. To apply the results for QCD we used different scenarios for the m_s and μ_q dependence of the effective model parameters, then the μ_q^TCP(m_s) function can be determined. Depending on the details, a curve bending upwards or downwards near μ_q=0 can be obtained, while with explicit chemical potential dependence of the parameters the direction of the curve can change with m_s, too.

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arXiv2009

Renormalized effective actions for the O(N) model at next-to-leading order of the 1/N expansion

A fully explicit renormalized quantum action functional is constructed for the O(N)-model in the auxiliary field formulation at next-to-leading order (NLO) of the 1/N expansion. Counterterms are consistently and explicitly derived for arbitrary constant vacuum expectation value of the scalar and auxiliary fields. The renormalized NLO pion propagator is exact at this order and satisfies Goldstone's theorem. Elimination of the auxiliary field sector at the level of the functional provides with order N^0 accuracy the renormalized effective action of the model in terms of the original variables. Alternative elimination of the pion and sigma propagators provides the renormalized NLO effective potential for the expectation values of the N-vector and of the auxiliary field with the same accuracy.

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arXiv2008

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(λ^2). The applied strategy is an extension of our treatment of the 2PI-Hartree approximation [G. Fejos, A. Patkos and Zs. Szep, Nucl. Phys. A803 (2008) 135]. The procedure is also applied to the O(N) model.

hep-ph↗

arXiv2008

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.

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arXiv2008

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., Nucl. Phys. A736 (2004) 149.

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arXiv2008

Influence of the isospin and hypercharge chemical potentials on the location of the CEP in the mu_B-T phase diagram of the SU(3)_L x SU(3)_R chiral quark model

We investigate the influence of the asymmetric quark matter (rho_u\ne rho_d\ne rho_s) on the mass of the quasiparticles and the phase diagram of the chiral quark model parametrized at one-loop level of the renormalized theory, using the optimized perturbation theory for the resummation of the perturbative series. The effect of various chemical potentials introduced in the grand canonical ensemble is investigated with the method of relativistic many-body theory. The temperature dependence of the topological susceptibility is estimated with the help of the Witten-Veneziano mass formula.

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arXiv2007

Phase structure and phase transitions of the SU(2) x O(N) symmetric scalar field theory

Radiatively induced SU(2) symmetry breaking is shown to be a genuine feature of SU(2) x O(N) globally symmetric renormalisable field theories in the large N limit, describing interaction of a complex SU(2) doublet, O(N)-singlet field with an SU(2) singlet, O(N) vector. Symmetry breaking solutions are found even when all fields have positive renormalised squared mass. The emerging novel mechanism of symmetry breaking can reproduce with a choice of N~300 the standard range of the electroweak condensate and the Higgs mass occurring in the extended Higgs dynamics of an SU(2) symmetric Gauge+Higgs model.

hep-th↗

arXiv2006

The critical surface of the SU(3)_L x SU(3)_R chiral quark model at non-zero baryon density

The boundary of the first order chiral phase transition region is studied in the m_pi-m_K-mu_B space using the one-loop optimized perturbation theory for the resummation of the perturbative series. Chiral perturbation theory for mesons and baryons is used for the T=0 parametrization of the model. The surface of second order transition points bends with increasing mu_B towards the physical point of the m_pi-m_K mass plane allowing for the existence of the critical end point in the mu_B-T plane at the physical point. The location and scaling region of the CEP is explored.

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arXiv2006

Phantom field fluctuation induced Higgs effect

Symmetry breaking solutions are investigated in the $N\to \infty$ limit for the ground state of a system consisting of a Lorentz-scalar, N component ``phantom'' field and an O(N) singlet. The most general form of O(N) x Z_2 invariant quartic interaction is considered. The non-perturbatively renormalised solution demonstrates the possibility for Z_2 symmetry breaking induced by phantom fluctuations. It becomes also evident that the strength of the ``internal'' dynamics of the N-component field tunes away the ratio of the Higgs condensate and the Higgs mass from its perturbative (nearly tree-level) expression.

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arXiv2006

The boundary of the first order chiral phase transition in the m_pi-m_K--plane with a linear sigma model

Tree-level and complete one-loop parametrisation of the linear sigma model (LSM) is performed and the phase boundary between first order and crossover transition regions of the m_pi-m_K-plane is determined using the optimised perturbation theory (OPT) as a resummation tool of perturbative series. Away from the physical point the parameters of the model were determined by making use of chiral perturbation theory (ChPT). The location of the phase boundary for m_pi=m_K and of the tricritical point (TCP) on the m_pi=0 were estimated.

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arXiv2006

Resummed one-loop determination of the phase boundary of the SU(3)_R x SU(3)_L linear sigma model in the m_pi-m_K-plane

Complete one-loop parametrization of the linear sigma model is performed and the phase boundary between first order and crossover transition regions of the m_pi-m_K-plane is determined using the optimized perturbation theory as a resummation tool of perturbative series. Away from the physical point the parameters of the model were determined by making use of chiral perturbation theory. Along the diagonal m_pi=m_K of the mass--plane we estimate m_pi^c=110 +- 20 MeV. The location of the tricritical point on the m_pi=0 axis is estimated in the interval m_K^TCP in (1700,1850) MeV.

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arXiv2005

Chiral phase transition in effective models of QCD

Incorporating its most relevant global symmetry, chiral effective models are aimed at investigating, in a simplified framework, important aspects of the yet unsolved QCD. We review some recent results obtained in these models on the restoration of chiral and axial symmetries, on the boundary of the first order phase transition region in the m_pi-m_K-plane at vanishing baryonic chemical potential mu_B,and on the mu_B-T phase diagram.

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arXiv2005

Sensitivity of the chiral phase transition of QCD to the scalar meson sector

Gribov's theory of light quark confinement implies the existence of two kinds of scalar bound states. The phase diagram of the three-flavor QCD is mapped out in the (m_pi-m_K)-plane with help of the SU_L(3)xSU_R(3) linear sigma model supplemented with the assumption that the masses of the so-called superbound scalars do not change under the variation of the pion and kaon mass. The phase boundary along the m_pi=m_K line is found in the interval 15 MeV<m_crit<25 MeV, irrespective which f_0-sigma linear combination is identified with the pure superbound state.

hep-ph↗

arXiv2005

Mapping the boundary of the first order finite temperature restoration of chiral symmetry in the m_pi-m_K--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) x SU_R(3) linear sigma model (LSM). A novel zero temperature parametrization is proposed for the mass dependence of the couplings away from the physical point based on the 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 limitates 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 values <= 800 MeV. Along the diagonal m_pi=m_K, we estimate m_crit(diag)=40+-20 MeV.

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