Scheme dependence of asymptotically free solutions

Abstract

Recent studies have provided evidence for the existence of new asymptotically free trajectories in non-Abelian particle models without asymptotic symmetry in the high-energy limit. We extend these results to a general $\mathrm{SU}(N_{\mathrm{L}})\times \mathrm{SU}(N_{\mathrm{c}})$ Higgs-Yukawa model that includes the non-Abelian sector of the standard model, finding further confirmation for such scenarios for a wide class of regularizations that account for threshold behavior persisting to highest energies. We construct these asymptotically free trajectories within conventional $\overline{\text{MS}}$ schemes and systematic weak coupling expansions. The existence of these solutions is argued to be a scheme-independent phenomenon, as demonstrated for mass-dependent schemes based on general momentum-space infrared regularizations. A change of scheme induces a map of the theory's coupling space onto itself, which in the present case also translates into a reparametrization of the space of asymptotically free solutions.

arXiv comment30 pages, 4 figures

References in corpus (82)

• Exact evolution equation for the effective potential
• Non-Perturbative Renormalization Flow in Quantum Field Theory and Statistical Physics
• The Exact Renormalisation Group and Approximate Solutions
• Investigating the near-criticality of the Higgs boson
• Aspects of the Functional Renormalisation Group
• Optimised Renormalisation Group Flows
• Optimisation of the exact renormalisation group
• Parton Distribution Functions, ${\alpha }_s$ and Heavy-Quark Masses for LHC Run II
• An Introduction to the Nonperturbative Renormalization Group
• Fermion Interactions and Universal Behavior in Strongly Interacting Theories
• The Standard Model Effective Potential at Two Loops
• Stability of the Electroweak Vacuum: Gauge Independence and Advanced Precision
• Two-loop effective potential for a general renormalizable theory and softly broken supersymmetry
• Asymptotic safety guaranteed
• Gauge bosons at zero and finite temperature
• Nonperturbative renormalization group approach to the Ising model: a derivative expansion at order ${\partial }^4$
• Perturbative renormalization and infrared finiteness in the Wilson renormalization group: the massless scalar case
• Scale Invariant Instantons and the Complete Lifetime of the Standard Model
• Ising exponents from the functional renormalisation group
• Lectures on renormalization and asymptotic safety
• Vacuum stability of asymptotically safe gauge-Yukawa theories
• Higher order quark-mesonic scattering processes and the phase structure of QCD
• Non-perturbative renormalization group preserving full-momentum dependence: implementation and quantitative evaluation
• The Renormalization Group and Two Dimensional Multicritical Effective Scalar Field Theory
• Directions for model building from asymptotic safety
• The Higgs Mass and the Scale of New Physics
• Softened Gravity and the Extension of the Standard Model up to Infinite Energy
• Brout-Englert-Higgs physics: From foundations to phenomenology
• Asymptotically Safe Standard Model via Vector-Like Fermions
• Decay Rate of Electroweak Vacuum in the Standard Model and Beyond
• Asymptotically Safe Standard Model Extensions?
• Higgs Mass Bounds from Renormalization Flow for a Higgs-top-bottom model
• Multi-meson Yukawa interactions at criticality
• On the Fixed-Point Structure of Scalar Fields
• Higgs Mass Bounds from Renormalization Flow for a simple Yukawa model
• Asymptotically Safe Grand Unification
• An asymptotic safety scenario for gauged chiral Higgs-Yukawa models
• Asymptotically Free Natural SUSY Twin Higgs
• Epsilon Expansion for Multicritical Fixed Points and Exact Renormalisation Group Equations
• The Planck scale, the Higgs mass and scalar dark matter
• Global flow of the Higgs potential in a Yukawa model
• More asymptotic safety guaranteed
• Stable Asymptotically Free Extensions (SAFEs) of the Standard Model
• Accessing directly the properties of fundamental scalars in the confinement and Higgs phase
• Functional perturbative RG and CFT data in the $\epsilon$-expansion
• Impact of generalized Yukawa interactions on the lower Higgs mass bound
• On the observable spectrum of theories with a Brout-Englert-Higgs effect
• Safe Pati-Salam
• Non-Abelian Supercurrents and de Sitter Ground State in Electroweak Theory
• Symmetry breaking, conformal geometry and gauge invariance
• (Non-)Aligned gauges and global gauge symmetry breaking
• Phase Diagram and Fixed-Point Structure of two dimensional N=1 Wess-Zumino Models
• Scaling and superscaling solutions from the functional renormalization group
• Low-energy phenomenology of trinification: an effective left-right-symmetric model
• Semiclassical analysis of the phases of 4d SU(2) Higgs gauge systems with cutoff at the Gribov horizon
• Quantum Critical Behaviour of Semi-Simple Gauge Theories
• Phase structure of complete asymptotically free SU($N_c$) theories with quarks and scalar quarks
• Gauge contribution to the $1/N_F$ expansion of the Yukawa coupling beta function
• A functional perspective on emergent supersymmetry
• Predicting the singlet vector channel in a partially Higgsed gauge theory
• Conformal Gauge-Yukawa Theories away From Four Dimensions
• Asymptotically free scaling solutions in nonabelian Higgs models
• The (IR-)relevance of the Gribov ambiguity in SU(2) x U(1) gauge theories with fundamental Higgs matter
• The spectrum of an SU(3) gauge theory with a fundamental Higgs field
• Nonabelian Higgs models: paving the way for asymptotic freedom
• The fate of non-polynomial interactions in scalar field theory
• In search of a UV completion of the Standard Model - 378.000 models that don't work
• A complete asymptotically safe embedding of the Standard Model
• Asymptotically safe and free chiral theories with and without scalars
• Gauge invariance and the physical spectrum in the two-Higgs-doublet model
• Higgs stability-bound and fermionic dark matter
• Nonperturbative renormalization-group approach preserving the momentum dependence of correlation functions
• Asymptotic freedom in $Z_2$-Yukawa-QCD models
• Scalar mass stability bound in a simple Yukawa-theory from renormalisation group equations
• Vacuum Stability and Perturbativity of SU(3) Scalars
• High scale boundary conditions with an additional complex singlet
• Asymptotic freedom in certain $SO(N)$ and $SU(N)$ models
• SU(2) x U(1) Yang-Mills theories in 3d with Higgs field and Gribov ambiguity
• Critical Wess-Zumino models with four supercharges from the functional renormalization group
• Conformal Phase Diagram of Complete Asymptotically Free Theories
• Conformal Data of Fundamental Gauge-Yukawa Theories
• Pseudo-Goldstone excitations in chiral Yukawa-theories with quadratic explicit symmetry breaking

Cited by in corpus (8)

• The nonperturbative functional renormalization group and its applications
• The Asymptotically Safe Standard Model: From quantum gravity to dynamical chiral symmetry breaking
• Asymptotically Safe QED
• Functional Renormalization and $\overline{\text{MS}}$
• An asymptotically safe SU(5) GUT
• Radiative corrections to the $R$ and $R^2$ invariants from torsion fluctuations on maximally symmetric spaces
• The quantum criticality of the Standard Model and the hierarchy problem
• Renormalization Flow of Nonlinear Electrodynamics