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A. Patkos

Publications and source records attributed to A. Patkos.

53 records · Page 3Linked to original sources
arXiv2002

Finite temperature spectral function of the $σ$ meson from large N expansion

The spectral function of the scalar-isoscalar channel of the O(N) symmetric linear $σ$ model is studied in the broken symmetry phase. The investigation is based on the leading order evaluation of the self-energy in the limit of large number of Goldstone bosons. We describe its temperature dependent variation in the whole low temperature phase. This variation closely reflects the trajectory of the scalar-isoscalar quasiparticle pole. In the model with no explicit chiral symmetry breaking we have studied near the critical point also the corresponding dynamical exponent.

hep-ph↗
arXiv2002

Goldstone excitations from spinodal instability

The squared mass of a complex scalar field is turned dynamically into negative by its O(2)-invariant coupling to a real field slowly rolling down in a quadratic potential. The emergence of gapless excitations is studied in real time simulations after spinodal instability occurs. Careful tests demonstrate that the Goldstone modes appear almost instantly after the symmetry breaking is over, much before thermal equilibrium is established.

hep-ph↗
arXiv2002

Finite temperature spectral functions of the linear O(N)-model at large N applied to the $π-σ$ system

The thermal evolution of the spectral densities derivable from the two-point functions of the elementary and the quadratic composite fields of the O(N) model is studied in the isosinglet channel and in the broken symmetry phase at infinite N. The results are applied with realistic parameter values to the N=4 case. They provide a reasonable description of the $σ$ meson at T=0. Threshold enhancement is observed around $T\sim 1.07m_π$. For higher temperatures the maximum of the spectral function in the single meson channel decreases and becomes increasingly rounded.

hep-ph↗
arXiv2001

Ising-like dynamical signatures and the end-point of the QCD transition line

An increase in the size of coherent domains in the one component $Φ^4$ field theory under the influence of a uniformly changing external magnetic field near the critical end-point $T_Φ=T_c, h_Φ=0$ was proposed recently as an estimate also for the variation of the chiral correlation length of QCD near its respective hypothetical end point in the $T_{QCD}-μ_{QCD}$ plane. The present detailed numerical investigation of the effective model suggests that passing by the critical QCD end point with realistic rate of temperature change will trigger large amplitude oscillations in the temporal variation of the chiral correlation length. A simple mechanism for producing this phenomenon is suggested.

hep-ph↗
arXiv2001

Effect of the scalar condensate on the linear gauge field response in the Abelian Higgs model

The effective equations of motion for low-frequency mean gauge fields in the Abelian Higgs model are investigated in the presence of a scalar condensate, near the high temperature equilibrium. We determine the current induced by an inhomogeneous background gauge field in the linear response approximation up to order $e^4$, assuming adiabatic variation of the scalar fields. The physical degrees of freedom are found and a physical gauge choice for the numerical study of the combined Higgs+gauge evolution is proposed.

hep-ph↗
arXiv2000

Fate of the classical false vacuum

Thermalisation of configurations with initial white noise power spectrum is studied in numerical simulations of a classical one-component $Φ^4$ theory in 2+1 dimensions, coupled to a small amplitude homogenous external field. The study is performed for energy densities corresponding to the broken symmetry phase of the system in equilibrium. The effective equation of the order parameter motion is reconstructed from its trajectory which starts from an initial value near the metastable point and ends in the stable ground state. This phenomenological theory 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.

hep-th↗
arXiv1999

Coupled gap equations for the screening masses in the SU(2) Higgs model

The complete set of static screening masses is determined for the SU(2) Higgs model from one-loop coupled gap equations. Results from the version, containing scalar fields both in the fundamental and adjoint representations are compared with the model arising when the integration over the adjoint scalar field is performed. A non-perturbative and non-linear mapping between the couplings of the two models is proposed, which exhibits perfect decoupling of the heavy adjoint scalar field. Also the alternative of a gauge invariant mass resummation is investigated in the high temperature phase.

hep-ph↗
arXiv1999

Effective theory for the soft fluctuation modes in the spontaneously broken phase of the N-component scalar field theory

The effective dynamics of the low-frequency modes is derived for the O(N) symmetric scalar field theory in the broken symmetry phase. The effect of the high-frequency fluctuations is taken into account at one-loop level exactly. A new length scale is shown to govern the long-time asymptotics of the linear response function of the Goldstone modes. The large time asymptotic decay of an arbitrary fluctuation is determined in the linear regime. We propose a set of local equations for the numerical solution of the effective non-linear dynamics. The applicability of the usual gradient expansion is carefully assessed.

hep-ph↗
arXiv1999

Dynamical Manifestation of the Goldstone Phenomenon at 1-loop

We have calculated the damping rate $Γ(|{\bf k}|)$ 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 $Γ(0)$, which depends non-analytically on the parameter of the explicit symmetry breaking, h. $Γ(0)$ 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.

hep-ph↗
arXiv1999

Beyond HTL: The Classical Kinetic Theory of Landau Damping for Selfinteracting Scalar Fields in the Broken Phase

The effective theory of low frequency fluctuations of selfinteracting scalar fields is constructed in the broken symmetry phase. The theory resulting from integrating fluctuations with frequencies much above the spontanously generated mass scale $(p_0>>M)$ is found to be local. Non-local dynamics, especially Landau damping emerges under the effect of fluctuations in the $p_0 \sim M$ region. A kinetic theory of relativistic scalar gas particles interacting via their locally variable mass with the low frequency scalar field is shown to be equivalent to this effective field theory for scales below the characteristic mass, that is beyond the accuracy of the Hard Thermal Loop (HTL) approximation.

hep-ph↗
arXiv1998

QCD thermodynamics from 3d adjoint Higgs model

The screening masses of hot SU(N) gauge theory, defined as poles of the corresponding propagators are studied in 3d adjoint Higgs model, considered as an effective theory of QCD, using coupled gap equations and lattice Monte-Carlo simulations (for N=2). Using so-called lambda gauges non-perturbative evidence for gauge independence of the pole masses within this class of gauges is given. A possible application of the screening masses for the resummation of the free energy is discussed.

hep-ph↗
arXiv1998

Coupled Gap Equations for the Screening Masses in Hot SU(N) Gauge Theory

Coupled 1-loop gap equations are studied numerically for non-Abelian electric and magnetic screening in various versions of the three-dimensional effective gauge models. Corrections due to higher dimensional and non-local operators are assessed quantitatively. Comparison with numerical Monte-Carlo investigations suggests that quantitative understanding beyond the qualitative features can be achieved only by going beyond the present treatment.

hep-ph↗
arXiv1997

Screened Perturbation Theory

A new perturbative scheme is proposed for the evaluation of the free energy density of field theories at finite temperature. The screened loop expansion takes into account exactly the phenomenon of screening in thermal propagators.The approach is tested in the N-component scalar field theory at 2-loop level and also at 3-loop in the large $N$ limit. The perturbative series generated by the screened loop expansion shows much better numerical convergence than previous expansions generated in powers of the quartic coupling.

hep-ph↗
arXiv1996

Partial Path Integration of Quantum Fields: Two-Loop Analysis of the SU(2) Gauge-Higgs Model at Finite Temperature

High temperature reduction of the SU(2) Higgs model is realised by partially integrating its partition function. Various approximate forms of the effective theory resulting from the integration over nonstatic fields and the static electric potential are analysed. Also non-polynomial and non-local terms are allowed. Consistency of the perturbative solution is ensured by new types of induced counterterms. Perturbative phase transition characteristics are presented in the Higgs mass range 30-120 GeV, and compared to results of other perturbative approaches.

hep-ph↗
arXiv1995

Controlling a Non-Polynomial Reduced Finite Temperature Action in the U(1) Higgs Model

An effective theory is constructed for the scalar electrodynamics via 2-loop integration over all non-static fields and the screened electric component of the vector-potential. Non-polynomial terms of the action are preserved and included into the 2-loop calculation of the effective potential of the reduced theory. Also the inclusion of some non-local terms is shown to be important. The effect of non-polynomial operators on the symmetry restoring phase transition is quantitatively compared to results from a local, superrenormalisable approximate effective theory.

hep-ph↗
arXiv1994

Effective Scalar Field Theory for the Electroweak Phase Transition

We investigate an effective model for the finite temperature restoration phase transition of the electroweak theory. It is obtained by dimensional reduction of the $3+1$ dimensional full theory and by subsequent integration over all static gauge degrees of freedom. The resulting theory corresponds to a $3$-dimensional $O(4)$ ferromagnet containing cubic and quartic terms of the field in its potential function. Possible nonperturbative effects of a magnetic screening mass are parametrically included in the potential. We analyse the theory using mean field and numerical Monte Carlo (MC) simulation methods. At the value of the physical Higgs mass, $m_H=37~{\rm GeV}$, considered in the present investigation, we find a discontinuous symmetry restoring phase transition. We determine the critical temperature, order parameter jump, interface tension and latent heat characteristics of the transition. The Monte Carlo results indicate a somewhat weaker first order phase transition as compared to the mean field treatment, demonstrating that non-perturbative fluctuations of the Higgs field are relevant. This effect is especially important for the interface tension. Any observation of hard first order transition could result only from non-perturbative effects related to the gauge degrees of freedom.

hep-lat↗