scholarly journals Asymptotically safe QED

2020 ◽  
Vol 80 (7) ◽  
Author(s):  
Holger Gies ◽  
Jobst Ziebell
Keyword(s):  
Fixed Point ◽  
Renormalization Group ◽  
Fixed Points ◽  
Quantum Electrodynamics ◽  
Planck Scale ◽  
Gauge Coupling ◽  
High Energy ◽  
Electron Mass ◽  
Landau Pole ◽  
Energy Behavior

Abstract High-energy completeness of quantum electrodynamics (QED) can be induced by an interacting ultraviolet fixed point of the renormalization flow. We provide evidence for the existence of two of such fixed points in the subspace spanned by the gauge coupling, the electron mass and the Pauli spin-field coupling. Renormalization group trajectories emanating from these fixed points correspond to asymptotically safe theories that are free from the Landau pole problem. We analyze the resulting universality classes defined by the fixed points, determine the corresponding critical exponents, study the resulting phase diagram, and quantify the stability of our results with respect to a systematic expansion scheme. We also compute high-energy complete flows towards the long-range physics. We observe the existence of a renormalization group trajectory that interconnects one of the interacting fixed points with the physical low-energy behavior of QED as measured in experiment. Within pure QED, we estimate the crossover from perturbative QED to the asymptotically safe fixed point regime to occur somewhat above the Planck scale but far below the scale of the Landau pole.

scholarly journals THE CASE OF ASYMPTOTIC SUPERSYMMETRY

2013 ◽  
Vol 28 (14) ◽  
pp. 1350053 ◽  
Author(s):  
BRUCE L. SÁNCHEZ-VEGA ◽  
ILYA L. SHAPIRO
Keyword(s):  
Fixed Point ◽  
Renormalization Group ◽  
Gauge Coupling ◽  
High Energy ◽  
Systematic Investigation ◽  
Coupling Constants ◽  
Scalar Coupling ◽  
Asymptotic State ◽  
Stable Fixed Point ◽  
Scalar Couplings

We start systematic investigation for the possibility to have supersymmetry (SUSY) as an asymptotic state of the gauge theory in the high energy (UV) limit, due to the renormalization group running of coupling constants of the theory. The answer on whether this situation takes place or not, can be resolved by dealing with the running of the ratios between Yukawa and scalar couplings to the gauge coupling. The behavior of these ratios does not depend too much on whether gauge coupling is asymptotically free (AF) or not. It can be shown that the UV stable fixed point for the Yukawa coupling is not supersymmetric. Taking this into account, one can break down SUSY only in the scalar coupling sector. We consider two simplest examples of such breaking, namely N = 1 supersymmetric QED and QCD. In one of the cases one can construct an example of SUSY being restored in the UV regime.

scholarly journals SO(10) grand unification in light of recent LHC searches and colored scalars at the TeV-scale

2016 ◽  
Vol 31 (08) ◽  
pp. 1650034 ◽  
Author(s):  
Ufuk Aydemir
Keyword(s):  
Renormalization Group ◽  
Group Analysis ◽  
Gauge Coupling ◽  
High Energy ◽  
Low Energy ◽  
Grand Unification ◽  
Renormalization Group Analysis ◽  
Low Energies ◽  
Light Color ◽  
Extended Survival

We analyze the compatibility of the recent LHC signals and the TeV-scale left–right model(s) in the minimal nonsupersymmetric SO(10) framework. We show that the models in which the Higgs content is selected based on the extended survival hypothesis do not allow the [Formula: see text] boson to be at the TeV-scale. By relaxing this conjecture, we investigate various scenarios where a number of colored-scalars, originated from various Pati–Salam multiplets, are light and whence they survive down to the low energies. Performing a detailed renormalization group analysis with various low-energy Higgs configurations and symmetry breaking chains, while keeping the high energy Higgs content unmodified; we find that, among a number of possibilities, the models which have a light color-triplet scalar, and its combination with a light color-sextet, particularly stand out. Although these models do allow a TeV-scale [Formula: see text] boson, generating the required value of the gauge coupling [Formula: see text] at this scale is nontrivial.

scholarly journals Asymptotically Safe Gravity-Fermion Systems on Curved Backgrounds

Universe ◽  
2021 ◽  
Vol 7 (8) ◽  
pp. 306
Author(s):  
Jesse Daas ◽  
Wouter Oosters ◽  
Frank Saueressig ◽  
Jian Wang
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Chiral Symmetry ◽  
Chiral Symmetry Breaking ◽  
Background Field ◽  
High Energy ◽  
Dirac Fermions ◽  
Dynamical Mechanism ◽  
Asymptotic Safety ◽  
Set Up

We set up a consistent background field formalism for studying the renormalization group (RG) flow of gravity coupled to Nf Dirac fermions on maximally symmetric backgrounds. Based on Wetterich’s equation, we perform a detailed study of the resulting fixed point structure in a projection including the Einstein–Hilbert action, the fermion anomalous dimension, and a specific coupling of the fermion bilinears to the spacetime curvature. The latter constitutes a mass-type term that breaks chiral symmetry explicitly. Our analysis identified two infinite families of interacting RG fixed points, which are viable candidates to provide a high-energy completion through the asymptotic safety mechanism. The fixed points exist for all values of Nf outside of a small window situated at low values Nf and become weakly coupled in the large Nf-limit. Symmetry-wise, they correspond to “quasi-chiral” and “non-chiral” fixed points. The former come with enhanced predictive power, fixing one of the couplings via the asymptotic safety condition. Moreover, the interplay of the fixed points allows for cross-overs from the non-chiral to the chiral fixed point, giving a dynamical mechanism for restoring the symmetry approximately at intermediate scales. Our discussion of chiral symmetry breaking effects provides strong indications that the topology of spacetime plays a crucial role when analyzing whether quantum gravity admits light chiral fermions.

Infrared Behavior in a Model for Quantum Electrodynamics

1973 ◽  
Vol 51 (24) ◽  
pp. 2511-2515
Author(s):  
Edward B. Manoukian
Keyword(s):  
Quantum Electrodynamics ◽  
Mass Shell ◽  
High Energy ◽  
Electron Propagator ◽  
Infrared Behavior ◽  
High Energy Behavior ◽  
Energy Behavior ◽  
Particular Solution ◽  
Set Up ◽  
Electron And Photon

In another paper, a particular solution of the Ward–Takahashi identity was set up as a model for quantum electrodynamics. The high energy behavior of the electron and photon propagators was investigated. The purpose of the present work is to investigate the asymptotic infrared behavior of the electron propagator near the mass shell in our model–theory. It is shown that, in general, it has a branch point, rather than just a pole at p2 = −m2, with the "singularity" being different from the known result of Abrikosov and Solov'ev, and coincides with theirs only in the gauge G = −1. The electron propagator, however, has rigorously a pole in the Yennie gauge.

Large-momentum behaviour in quantum field theory (QFT)

2021 ◽  
pp. 593-606
Author(s):  
Jean Zinn-Justin
Keyword(s):  
Field Theory ◽  
Fixed Point ◽  
Fixed Points ◽  
Quantum Electrodynamics ◽  
Particle Physics ◽  
Large Momentum ◽  
Quantum Field ◽  
Four Dimensions ◽  
Free Theory ◽  
Electron Positron Annihilation

Renormalization group (RG) equations are used to characterize the large momentum behaviour of renormalized quantum field theories (QFT), assuming implicitly that such a universal large momentum physics can be defined, something which, beyond perturbation theory is not obvious. Since the initial effective QFT is valid only up to an energy-momentum scale much smaller than some cut-off, large momentum means much larger than the renormalization scale, but still much smaller than the cut-off scale. The existence of this large momentum physics implies the existence of a crossover scale between low and large momentum physics. One theoretic reason for discussing the large momentum behaviour is the apparent connection between the existence of consistent interacting renormalized QFTs and the presence of ultraviolet (UV) fixed points. The absence of identified UV fixed points in infrared-free QFTs, like the φ4 field theory or quantum electrodynamics (QED), leads to the triviality issue. The physics reason is that in collisions it is observed that quarks, fundamental particles of the Standard Model (SM) of particle physics, behave like free particles at the shortest distances presently accessible (the property of asymptotic freedom). This property can be explained by RG arguments if the free theory is an attractive UV fixed point. Therefore, the identification of QFTs where the free theory is an UV fixed point is important, and this has led to examine the large momentum behaviour of all QFTs renormalizable in four dimensions. It is shown that only theories having a non-Abelian gauge symmetry can be asymptotically free. As an application, the total cross section of electron–positron annihilation into hadrons at large momentum is calculated.

Sign in / Sign up

Export Citation Format

Share Document