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A. Patkós

Publications and source records attributed to A. Patkós.

12 recordsLinked to original sources
arXiv2020

Bound-state spectra of field theories through separation of external and internal dynamics

A general strategy is formulated for computing bound state spectra in the framework of functional renormalisation group (FRG). Dynamical "coordinates" characterising bound states are introduced as coupling parameters in the $n$-point functions of effective fields representing the bound states in an extended effective action functional. Their scale dependence is computed with functional renormalisation group equations. In the infrared an interaction potential among the constituting fields is extracted as smooth function of the coupling parameters. Eventually quantised bound state solutions are found by solving the Schrödinger eigenvalue problem formulated for the coupling parameters transmuted into coordinates. The proposed strategy is exemplified through the analysis of a recently published FRG study of the one-flavor chiral Nambu--Jona-Lasinio model.

hep-th↗
arXiv2017

Pseudo-Goldstone excitations in chiral Yukawa-theories with quadratic explicit symmetry breaking

The symmetry breakdown pattern is studied in models containing one fermion flavor multiplet and a multicomponent scalar field, supplemented with a chiral Yukawa-interaction, and in presence of an explicit symmetry breaking source quadratic in the scalar field. In a detailed investigation of the model with $U_L(1) \times U_R(1)$ chiral symmetry it is shown that by diminishing the strength of quadratic explicit symmetry breaking one can still keep stable the mass ratio of the fermionic and the pseudo-Goldstone excitation. At the same time the mass ratio of the two bosonic excitations appears to approach a limiting value depending only on the infrared value of the first ratio, but not on the microscopic (ultraviolet) coupling values. The observations receive a general interpretation by the existence of an ultraviolet fixed point located in the symmetric phase. Understanding the general conditions for its existence allows the construction of a similar theory with $U_L(2) \times U_R(2)$ chiral symmetry. All results of the present investigation were obtained with nonperturbative functional renormalisation group technique making use of the first two approximations to the gradient expansion of the effective action.

hep-ph↗
arXiv2012

Invariant formulation of the Functional Renormalisation Group method for $U(n)\times U(n)$ symmetric matrix models

The Local Potential Approximation (LPA) to the Wetterich-equation is formulated explicitly in terms of operators, which are invariant under the $U(n)\times U(n)$ symmetry group. Complete formulas are presented for the two-flavor ($U(2)\times U(2)$) case. The same approach leads to a unique natural truncation of the functional driving the renormalisation flow of the potential of the three-flavor case ($U(3)\times U(3)$). The procedure applied to the $SU(3)\times SU(3)$ symmetric theory, results in an equation, which potentially allows an RG-investigation of the effect of the 't Hooft term representing the $U_A(1)$ anomaly, disentangled from the other operators.

hep-ph↗
arXiv1996

Critical Higgs Mass and Temperature Dependence of Gauge Boson Masses in the SU(2) Gauge-Higgs Model

We study the effective 3-D SU(2) Gauge-Higgs model at finite temperature for Higgs-masses in the range from $60$ GeV up to $100$ GeV. The first order electroweak phase transition weakens with increasing Higgs-mass and terminates at a critical end-point. For Higgs-mass values larger than about $m_{H,c}=75.4(6)$ GeV the thermodynamic signature of the transition is described by a crossover. Close to this Higgs-mass value we investigate the vector boson propagator in Landau gauge. The calculated W-boson screening masses are compared with predictions based on gap equations.

hep-lat↗
arXiv1996

The ${\cal O}(g^6)$ coefficient in the thermodynamic potential of hot SU(N) Gauge Theories and MQCD

The non-perturbative input necessary for the determination of the ${\cal O}(g^6)$ part of the weak coupling expansion of the free energy density for SU(2) and SU(3) gauge theories is estimated. Although the perturbative information completing the contribution to this order is missing, we give arguments that the magnetic fluctuations are dominated by screened elementary magnetic gluons.

hep-lat↗
arXiv1996

Gauge Boson Masses in the 3-d, SU(2) Gauge-Higgs Model

We study gauge boson propagators in the symmetric and symmetry broken phases of the 3-d, $SU(2)$ gauge-Higgs model. Correlation functions for the gauge fields are calculated in Landau gauge. They are found to decay exponentially at large distances leading to a non-vanishing mass for the gauge bosons. We find that the W-boson screening mass drops in the symmetry broken phase when approaching the critical temperature. In the symmetric phase the screening mass stays small and is independent of the scalar--gauge coupling (the hopping parameter). Numerical results coincide with corresponding calculations performed for the pure gauge theory. We find $m_w = 0.35(1)g^2T $ in this phase which is consistent with analytic calculations based on gap equations. This is, however, significantly smaller than masses extracted from gauge invariant vector boson correlation functions. As internal consistency check we also have calculated correlation functions for gauge invariant operators leading to scalar and vector boson masses. Finite lattice size effects have been systematically analyzed on lattices of size $L^2\times L_z$ with $L=4-24$ and $L_z = 16 - 128$.

hep-lat↗
arXiv1995

Effective Models of the Electroweak Phase Transition

The consecutive integration over the distinct mass scales ${\cal O}(T),{\cal O}(gT)$ leads to a hierarchy of effective models for the electroweak phase transition. Different techniques for the realisation of such strategy are reviewed. Advantages and difficulties resulting from the use of reduced models are discussed.

hep-ph↗
arXiv1995

RENORMALISATION GROUP AIDED FINITE TEMPERATURE REDUCTION OF QUANTUM FIELD THEORIES

Dimensional reduction of finite temperature quantum field theories can be improved with help of continous renormalisation group steps. The method is applied to the integration of the lowest non-static ($n=\pm 1$) modes of the finite temperature $Φ^4$-theory. A second, physically important application is the integration of the Debye-screened ${\bf A_0}(x)$ static scalar potential in the gauged SU(2) Higgs model.

hep-ph↗
arXiv1994

Finite Temperature Reduction of the SU(2) Higgs-Model with Complete Static Background

Direct evaluation of the 1-loop fluctuation determinant of non-static degrees of freedom in a complete static background is advocated to be more efficient for the determination of the effective three-dimensional model of the electroweak phase transition than the one-by-one evaluation of Feynman diagrams. The relation of the couplings and fields of the effective model to those of the four-dimensional finite temperature system is determined in the general 't Hooft gauge with full implementation of renormalisation effects. Only field renormalisation constants display dependence on the gauge fixing parameter. Characteristics of the electroweak transition are computed from the effective theory in Lorentz-gauge. The dependence of various physical observables on the three-dimensional gauge fixing parameter is investigated.

hep-ph↗
arXiv1993

A Hierarchy of Effective Field Theories of Hot Electroweak Matter

Abst\-ract: A hierarchy of effective three-dimensional theories of finite temperature electroweak matter is studied. First an integration over non-static modes leads to an effective theory containing a gauge field $A_{i}^{a}$, an adjoint Higgs field $A_{0}^a$ and the fundamental Higgs field $ϕ_α$. We carry out the integration in the 1-loop approximation, study renormalisation effects and estimate quantitatively those terms of the effective action which are suppressed by inverse powers of the temperature. Secondly, because of the existence of well-separated thermal mass scales, $A_{0}^a$ can be integrated over, and finally also $ϕ_α$, leaving an effective theory of the $A_{i}^{a}$.In the analysis of the subsequent models particular attention is paid to the screening of the magnetic fluctuations due to the integrated-out degrees of freedom. Files of 2 Tables and 4 Figures are available in (la)tex-format upon request

hep-ph↗
arXiv1993

Weak Coupling Phase Structureof the Abelian Higgs Model at Finite Temperature

Using the 1-loop reduced 3D action of the Abelian Higgs-model we discuss the order of its finite temperature phase transition. A two-variable saddle point approximation is proposed for the evaluation of the effective potential. The strength of the first order case scales like \sim e^{3-6}. Analytic asymptotic weak coupling and numerical small coupling solutions are compared with special emphasis on the cancellation of divergences. (Figures are not included, can be sent upon request from jako@hercules.elte.hu .)

hep-ph↗