Self-consistent $O(4)$ model spectral functions from analytically continued FRG flows

Abstract

In this paper we explore practicable ways for self-consistent calculations of spectral functions from analytically continued functional renormalization group (aFRG) flow equations. As a particularly straightforward one we propose to include parametrizations of self-energies based on explicit analytic one-loop expressions. To exemplify this scheme we calculate the spectral functions of pion and sigma meson of the $O(4)$ model at vanishing temperature in the broken phase. Comparing the results with those from previous aFRG calculations, we explicitly demonstrate how self-consistency at all momenta fixes the tight relation between particle masses and decay thresholds. In addition, the two-point functions from our new semi-analytic FRG scheme have the desired domain of holomorphy built in and can readily be studied in the entire cut-complex frequency plane, on physical as well as other Riemann sheets. This is very illustrative and allows, for example, to trace the flow of the resonance pole of the sigma meson across an unphysical sheet. In order to assess the limitations due to the underlying one-loop structure, we also introduce a fully self-consistent numerical scheme based on spectral representations with scale-dependent spectral functions. The most notable improvement of this numerically involved calculation is that it describes the three-particle resonance decay of an off-shell pion, ${\pi }^{\ast }\to \sigma \pi \to 3\pi$. Apart from this further conceptual improvement, overall agreement with the results from the considerably simpler semi-analytic one-loop scheme is very encouraging, however. The latter can therefore provide a sound and practicable basis for self-consistent calculations of spectral functions in more realistic effective theories for warm and dense matter.

arXiv comment21 pages, 16 figures v2: minor changes, agrees with published version

References in corpus (52)

• Exact evolution equation for the effective potential
• Non-Perturbative Renormalization Flow in Quantum Field Theory and Statistical Physics
• Aspects of the Functional Renormalisation Group
• Optimised Renormalisation Group Flows
• The nonperturbative functional renormalization group and its applications
• Maximum Entropy Analysis of the Spectral Functions in Lattice QCD
• Introduction to Nonequilibrium Quantum Field Theory
• Introduction to the functional RG and applications to gauge theories
• QCD at finite temperature and chemical potential from Dyson-Schwinger equations
• Fermion Interactions and Universal Behavior in Strongly Interacting Theories
• Lectures on the functional renormalization group method
• The Phase Diagram of the Quark-Meson Model
• A novel Bayesian approach to spectral function reconstruction
• Nonperturbative renormalization for 2PI effective action techniques
• Renormalization Group Approach towards the QCD Phase Diagram
• Chiral phase structure and critical end point in QCD
• Quark-meson-diquark model for two-color QCD
• Spectral Functions for the Quark-Meson Model Phase Diagram from the Functional Renormalization Group
• Derivative expansion and renormalisation group flows
• Fluctuations in the quark-meson model for QCD with isospin chemical potential
• Real time correlation functions and the functional renormalisation group
• Numerical analytic continuation of Euclidean data
• In-Medium Spectral Functions of Vector- and Axial-Vector Mesons from the Functional Renormalization Group
• Real-Time Correlation Functions in the O(N) Model from the Functional Renormalization Group
• The Hot QCD White Paper: Exploring the Phases of QCD at RHIC and the LHC
• Resonance poles and threshold energies for hadron physical problems by a model-independent universal algorithm
• Analytic continuation of functional renormalization group equations
• Landau gauge Yang-Mills propagators in the complex momentum plane
• Finite temperature spectral functions in the O(N)-model
• Flow equations for spectral functions at finite external momenta
• Spectral functions in the ${\varphi }^4$-theory from the spectral DSE
• Quark spectral properties above Tc from Dyson-Schwinger equations
• Thermodynamics of QCD low-energy models and the derivative expansion of the effective action
• Dynamic critical phenomena from spectral functions on the lattice
• Bayesian analysis of quark spectral properties from the Dyson-Schwinger equation
• Spectral function at high temperature in the classical approximation
• Spectral functions and critical dynamics of the $O(4)$ model from classical-statistical lattice simulations
• Shocks and quark-meson scatterings at large density
• Spectral functions and dynamic critical behavior of relativistic $Z_2$ theories
• From quantum to classical dynamics: The relativistic $O(N)$ model in the framework of the real-time functional renormalization group
• Vector and Axial-Vector Mesons in Nuclear Matter
• Self-consistent Spectral Functions in the $O(N)$ Model from the FRG
• Spectral functions from the real-time functional renormalization group
• Meson Spectral Functions at Finite Temperature and Isospin Density with Functional Renormalization Group
• Selfconsistent calculations of spectral densities in the O(N) model: improving the Hartree-Fock approximation by including nonzero decay widths
• Fermionic spectral functions with the Functional Renormalization Group
• Tachyonic instability of the scalar mode prior to QCD critical point based on Functional renormalization-group method
• Resolving phase transitions with Discontinuous Galerkin methods
• Spectral functions and in-medium properties of hadrons
• Fermionic excitations at finite temperature and density
• Thermalization and dynamical spectral properties in the quark-meson model
• Fermion spectral function in hot strongly interacting matter from the functional renormalization group

Cited by in corpus (4)

• QCD at finite temperature and density within the fRG approach: An overview
• Real-time methods for spectral functions
• On the quark spectral function in QCD
• The QCD moat regime and its real-time properties