arXiv subjects

G. Fejos

Publications and source records attributed to G. Fejos.

At least 19 recordsLinked to original sources

arXiv2025

Range of topological fluctuations in the three-flavor linear sigma model

The topological charge density two-point function is computed in a three-flavor effective linear meson model, including contributions from topological sectors with arbitrary charge. A corresponding composite field is introduced via a Hubbard-Stratonovich transformation. In the $\eta$-$\eta$' sector, the model yields very accurate spectroscopy with negligible mixing with the composite field. The resulting topological susceptibility allows for the extraction of a surprisingly large absolute scale for the range of topological fluctuations. When compared with various QCD-based estimates, this indirectly suggests the dominance of higher topologically charged configurations in the ground state.

hep-ph↗

arXiv2025

Chiral symmetry restoration in QC_2D from effective model using the functional renormalization group

The order of the chiral phase transition in two-color and two-flavor QC$_2$D is investigated using the functional renormalization group (FRG) technique in an effective model setting. We calculate the $\beta$ function of all couplings in the dimensionally reduced Ginzburg-Landau free energy functional with Pauli-G\"ursey SU(4) symmetry. We compare results of the perturbative $\epsilon$ expansion approach with those obtained via the FRG, evaluated directly in $d=3$ dimensions. The perturbative results suggest that the fixed-point structure is more intricate than that of three-color QCD, a conclusion further supported by the FRG analysis. Both methods display an infrared stable $O(6)$ fixed point at infinite axial anomaly; however, the FRG approach also reveals the existence of $U_A(1)$ anomaly-free fixed points, which can become infrared stable if the anomaly in the underlying theory vanishes at the critical temperature. These findings imply that the phase transition can be of second order, consistent with earlier findings for three colors.

hep-ph↗

arXiv2024

Order of the SU(N_f) x SU(N_f) chiral transition via the functional renormalization group

Renormalization group flows of the $SU(N_f)\times SU(N_f)$ symmetric Ginzburg-Landau potential are calculated for a general number of flavors, $N_f$. Our approach does not rely on the $\epsilon$ expansion, but uses the functional renormalization group, formulated directly in $d=3$ spatial dimensions, with the inclusion of all possible (perturbatively) relevant and marginal operators, whose number is considerably larger than those in $d=4$. We find new, potentially infrared stable fixed points spanned throughout the entire $N_f$ range. By conjecturing that the thermal chiral transition is governed by these ``flavor continuous" fixed points, stability analyses show that for $N_f\geq 5$ the chiral transition is of second-order, while for $N_f=2,3,4$, it is of first-order. We argue that the $U_{\rm A}(1)$ anomaly controls the strength of the first-order chiral transition for $N_f=2,3,4$, and makes it almost indistinguishable from a second-order one, if it is sufficiently weak at the critical point. This could open up a new strategy to investigate the strength of the $U_{\rm A}(1)$ symmetry breaking around the critical temperature.

hep-ph↗

arXiv2023

Thermal behavior of effective U_A(1) anomaly couplings in reflection of higher topological sectors

Thermal behavior of effective, chiral condensate-dependent $U_A(1)$ anomaly couplings is investigated using the functional renormalization group approach in the $N_f = 3$ flavor meson model. We derive flow equations for anomaly couplings that arise from instantons of higher topological charge, dependent also on the chiral condensate. These flow equations are solved numerically for the $|Q|=1,2$ topological sectors at finite temperature. Assuming that the anomaly couplings at the ultraviolet scale may also exhibit explicit temperature dependence, we calculate the thermal behavior of the effective potential. In accordance with our earlier study, [G. Fejos and A. Patkos, Phys. Rev. D{\bf 105}, 096007 (2022)], we find that for increasing temperatures, the anomalous breaking of chiral symmetry tends to strengthen toward the pseudocritical temperature ($T_C$) of chiral symmetry breaking. It is revealed that below $T_C$, around $\sim$10\% of the $U_A(1)$ breaking arises from the $|Q|=2$ topological sector. Correspondingly, a detailed analysis on the thermal behavior of the mass spectrum is also presented.

hep-ph↗

arXiv2022

Backreaction of mesonic fluctuations on the axial anomaly at finite temperature

The impact of mesonic fluctuations on the restoration of the $U_A(1)$ anomaly is investigated nonperturbatively for three flavors at finite temperature in an effective model setting. Using the functional renormalization group, the dressed, fully field-dependent Kobayashi-Maskawa--'t Hooft (KMT) anomaly coupling is computed. It is found that mesonic fluctuations strengthen this signature of the $U_A(1)$ breaking as the temperature increases. On the other hand, when instanton effects are included by parametrizing the explicit temperature dependence of the bare anomaly parameter in consistency with the semiclassical result for the tunneling amplitude, a natural tendency appears diminishing the anomaly at high temperatures. As a result of the two competing effects, the dressed KMT coupling shows a well-defined intermediate strengthening behavior around the chiral (pseudo)transition temperature before the axial anomaly gets fully suppressed at high temperature. As a consequence, we conclude that below $T \sim 200 \MeV$ the $U_A(1)$ anomaly is unlikely to be effectively restored. Robustness of the conclusions against different assumptions for the temperature dependence of the bare anomaly coefficient is investigated in detail.

hep-ph↗

arXiv2022

Second order chiral phase transition in three flavor quantum chromodynamics?

We calculate the renormalization group flows of all perturbatively renormalizable interactions in the three-dimensional Ginzburg-Landau potential for the chiral phase transition of three-flavor quantum chromodynamics. On the contrary to the common belief we find a fixed point in the system that is able to describe a second-order phase transition in the infrared. This shows that long-standing assumptions on the transition order might be false. If the transition is indeed of second-order, our results may hint that the axial $U(1)$ symmetry restores at the transition temperature.

hep-ph↗

arXiv2021

Field dependence of the Yukawa coupling in the three flavor quark-meson model

We investigate the renormalization group flow of the field-dependent Yukawa coupling in the framework of the three flavor quark-meson model. In a conventional perturbative calculation, given that the field rescaling is trivial, the Yukawa coupling does not get renormalized at the one-loop level if it is coupled to an equal number of scalar and pseudoscalar fields. Its field-dependent version, however, does flow with respect to the scale. Using the functional renormalization group technique, we show that it is highly nontrivial how to extract the actual flow of the Yukawa coupling as there are several new chirally invariant operators that get generated by quantum fluctuations in the effective action, which need to be distinguished from that of the Yukawa interaction.

hep-ph↗

arXiv2021

Perturbative RG analysis of the condensate dependence of the axial anomaly in the three flavor linear sigma model

Coupling of `t Hooft's determinant term is investigated in the framework of the three flavor linear sigma model as a function of the chiral condensate. Using perturbation theory around the minimum point of the effective action, we calculate the renormalization group flow of the first field dependent correction to the coupling of the conventional U_A(1) breaking determinant term. It is found that at low temperatures mesonic fluctuations make the anomaly increase when the chiral condensate decreases. As an application, we analyze the effect at the zero temperature nuclear liquid-gas transition.

hep-ph↗

arXiv2019

Functional renormalization group approach to color superconducting phase transition

We investigate the order of the color superconducting phase transition using the functional renormalization group approach. We analyze the Ginzburg-Landau effective theory of color superconductivity and more generic scalar $SU(N_c)$ gauge theories by calculating the $β$ function of the gauge coupling in arbitrary dimension $d$ based on two different regularization schemes. We find that in $d=3$, due to gluon fluctuation effects, the $β$ function never admits an infrared fixed point solution. This indicates that, unlike the ordinary superconducting transition, color superconductivity can only show a first-order phase transition.

hep-ph↗

arXiv2019

Flows of multicomponent scalar models with U(1) gauge symmetry

We investigate the renormalization group flows of multicomponent scalar theories with $U(1)$ gauge symmetry using the functional renormalization group method. The scalar sector is built up from traces of matrix fields that belong to simple, compact Lie algebras. We find that in general these theories are non-renormalizable even at zero gauge coupling, but if we add a $U(1)$ factor to the Lie algebra structure, then they are consistent. In accordance with our earlier findings, fluctuations introduce anomalous, regulator dependent gauge contributions, which are only consistent with the flow equation for a given set of gauge fixing parameters. We establish connections between regularization procedures in the standard covariant and the $R_ξ$ gauges arguing that one is not tied by introducing regulators at the level of the functional integral, and it is allowed to switch between schemes at different levels of the calculations. We calculate $β$ functions, classify fixed points, and clarify compatibility of the flow equation and the Ward-Takahashi identity between the scalar wavefunction renormalization and the charge rescaling factor.

hep-ph↗

arXiv2018

Axial anomaly and hadronic properties in a nuclear medium

We investigate meson and nucleon dynamics at finite baryon density and temperature by coupling the nucleon field and the omega meson to the three-flavor linear sigma model and calculate hadronic properties around the nuclear liquid-gas transition. We apply the functional renormalization group method, and find that mesonic fluctuations increase the strength of the coefficient of the $U_A(1)$ breaking determinant operator as a function of the chiral condensate. As a consequence, we find that the actual value of the anomaly increases discontinuously at the first order nuclear liquid-gas transition. We calculate how mesonic masses and partial restoration of chiral symmetry are modified due to such an effect.

nucl-th↗

arXiv2017

Renormalization group flows of the N-component Abelian Higgs model

Flows of the couplings of a theory of an N-component (complex) scalar field coupled to electrodynamics is investigated using the functional renormalization group formalism in d dimensions in covariant gauges. We find charged fixed points for any number of components in d=3, in accordance with the findings of [G. Fejos and T. Hatsuda, Phys. Rev. D 93, 121701 (2016)] for N=1. It is argued that the appropriate choice of the regulator matrix is indispensible to obtain such a result. Ward-Takahashi identites are analyzed in the presence of the regulator, and their compatibility with the flow equation is investigated in detail.

hep-ph↗

arXiv2017

Mesonic and nucleon fluctuation effects at finite baryon density

Mesonic and nucleon fluctuation effects are investigated in medium. We couple the nucleon field to the $2+1$ flavor meson model and investigate the finite temperature and density behavior of the system, in particular, the axial anomaly function. Somewhat contrary to earlier expectations we find that it tends to strengthen at finite density. At lower temperatures nucleon density fluctuations can cause a relative difference in the $U_A(1)$ axial anomaly of about $20\%$. This has important consequences on the mesonic spectra, especially on the $η-η'$ system, as we observe no drop in the $η'$ mass as a function of the baryochemical potential, irrespective of the temperature. Based on the details of chiral symmetry restoration, it is argued that there has to be a competition between underlying QCD effects of the anomaly and fluctuations of the low energy hadronic degrees of freedom, and the fate of the $U_A(1)$ coefficient should be decided by taking into account both effects simultaneously.

hep-ph↗

arXiv2016

Fixed point structure of the Abelian Higgs model

The order of the superconducting phase transition is analyzed via the functional renormalization group approach. For the first time, we derive fully analytic expressions for the $β$ functions of the charge and the self-coupling in the Abelian Higgs model with one complex scalar field in $d=3$ dimensions that support the existence of two charged fixed points: an infrared (IR) stable fixed point describing a second-order phase transition and a tritical fixed point controlling the region of the parameter space that is attracted by the former one. It is found that the region separating first- and second-order transitions can be uniquely characterized by the Ginzburg-Landau parameter $κ$, and the system undergoes a second order transition, only if $κ>κ_c \approx 0.62/\sqrt2$.

cond-mat.supr-con↗

arXiv2016

Thermal properties and evolution of the $U_A(1)$ factor for 2+1 flavors

Thermal evolution of the axial anomaly is investigated in the system of the linear sigma model for $2+1$ flavors. We explore the functional form of the effective potential and the coefficient of the `t Hooft determinant term. It is found that the latter develops a non-trivial structure as a function of the chiral condensate and grows everywhere with respect to the temperature. This shows that mesonic fluctuations strengthen the axial anomaly at finite temperature and it does not get vanished at the critical point. The phenomenon has been found to have significance in the thermal properties of the mesonic spectra, especially concerning the $η-η'$ system.

hep-ph↗

arXiv2015

Functional dependence of axial anomaly via mesonic fluctuations in the three flavor linear sigma model

Temperature dependence of the $U_A(1)$ anomaly is investigated by taking into account mesonic fluctuations in the $U(3)\times U(3)$ linear sigma model. A field dependent anomaly coefficient function of the effective potential is calculated within the finite temperature functional renormalization group approach. The applied approximation scheme is a generalization of the chiral invariant expansion technique developed in [G. Fejos, Phys. Rev. D 90, 096011 (2014)]. We provide an analytic expression and also numerical evidence that depending on the relationship between the two quartic couplings, mesonic fluctuations can either strengthen of weaken the anomaly as a function of the temperature. The role of the six-point invariant of the $U(3)\times U(3)$ group, and therefore the stability of the chiral expansion is also discussed in detail.

hep-ph↗

arXiv2014

Renormalization of the 2PI-Hartree approximation in a broken phase with nonzero superflow

Nonperturbative renormalization and explicit construction of the effective potential of the Hartree approximation of the two-particle-irreducible formalism are carried out in an inhomogeneous field configuration describing a uniform superfluid. Based on the earlier article [G. Fejos et. al, Nucl. Phys. A803, 115 (2008)], we clarify certain aspects of renormalizability corresponding to the findings of [M. G. Alford et. al, Phys. Rev. D 89, 085005 (2014)]. We show that renormalizability of the approximation can be ensured by regularization schemes respecting Lorentz and translation invariance. Elimination of nonconventional superflow-dependent divergences is presented in detail, together with a discussion on the finite-temperature treatment.

hep-ph↗

arXiv2014

Fluctuation induced first order phase transition in U(n)xU(n) models using chiral invariant expansion of functional renormalization group flows

Phase transition in U(n)xU(n) models is investigated for arbitrary flavor number n. We present a nonperturbative, 3+1 dimensional finite temperature treatment of obtaining the effective potential, based on a chiral invariant expansion of the functional renormalization group flows. The obtained tower of equations is similar but not identical to that of the Dyson-Schwinger hierarchy and has to be truncated for practical purposes. We investigate the finite temperature behavior of the system in an expansive set of the parameter space for n = 2, 3, 4 and also perform a large-n analysis. Our method is capable of recovering the one-loop beta functions of the coupling constants of the epsilon expansion; furthermore, it shows direct evidence that regardless of the actual flavor number, within our approximation, the system undergoes a fluctuation induced first order phase transition.

hep-ph↗