Study of Possible Ultraviolet Zero of the Beta Function in Gauge Theories with Many Fermions

Abstract

We study the possibility of an ultraviolet (UV) zero in the $n$-loop beta function of U(1) and non-Abelian gauge theories with $N_f$ fermions for large $N_f$. The effect of scheme transformations on the coefficients of different powers of $N_f$ in the $n$-loop term in the beta function is calculated. A general scheme-independent criterion is given for determining whether or not the $n$-loop beta function has a UV zero for large $N_f$. We compare the results with exact integral representations of the leading terms in the beta functions for the respective Abelian and non-Abelian theories in the limit $N_f\to \infty$ limit with $N_f\alpha$ finite. As part of this study, new analytic and numerical results are presented for certain coefficients, denoted $b_{n,n-1}$, that control the large-$N_f$ behavior at $n$-loop order in the beta function. We also investigate various test functions incorporating a power-law and essential UV zero in the beta function and determine their manifestations in series expansions in powers of coupling and in powers of $1/N_f$.

26 pages

References in corpus (10)

• Higher-Loop Corrections to the Infrared Evolution of a Gauge Theory with Fermions
• Large N flavor beta-functions: a recap
• An Analysis of Scheme Transformations in the Vicinity of an Infrared Fixed Point
• Scheme Transformations in the Vicinity of an Infrared Fixed Point
• Study of Scheme Transformations to Remove Higher-Loop Terms in the $\beta$ Function of a Gauge Theory
• Higher-Loop Calculations of the Ultraviolet to Infrared Evolution of a Vectorial Gauge Theory in the Limit $N_c\to \infty$, $N_f\to \infty$ with $N_f/N_c$ Fixed
• The relation between the QED charge renormalized in MSbar and on-shell schemes at four loops, the QED on-shell beta-function at five loops and asymptotic contributions to the muon anomaly at five and six loops
• Comparison of Some Exact and Perturbative Results for a Supersymmetric SU($N_c$) Gauge Theory
• Higher Loop Corrections to the Infrared Evolution of Fermionic Gauge Theories in the RI' Scheme
• Renormalization group functions of QCD in the minimal MOM scheme

Cited by in corpus (45)

• Asymptotically Safe Standard Model via Vector-Like Fermions
• Asymptotically Safe Standard Model Extensions?
• Conformal Window 2.0: The Large $N_f$ Safe Story
• UV conformal window for asymptotic safety
• Conformal Behavior at Four Loops and Scheme (In)Dependence
• Gauge-Yukawa theories: Beta functions at large $N_f$
• Six dimensional QCD at two loops
• Generalized Scheme Transformations for the Elimination of Higher-Loop Terms in the Beta Function of a Gauge Theory
• Fourth-order QCD renormalization group quantities in the {\rm{V}}-scheme and the relation of the $\beta$-function to the Gell-Mann--Low function in QED
• Safe Pati-Salam
• New Scheme Transformations and Application to Study Scheme Dependence of an Infrared Zero of the Beta Function in Gauge Theories
• Quantum Critical Behaviour of Semi-Simple Gauge Theories
• Continuous renormalization group $\beta$ function from lattice simulations
• Banks-Zaks fixed point analysis in momentum subtraction schemes
• Asymptotically Safe QED
• Gradient flow step-scaling function for SU(3) with ten fundamental flavors
• Safe Trinification
• Renormalization-Group Flows and Fixed Points in Yukawa Theories
• On the Question of an Ultraviolet Zero of the Beta Function of the $\lambda ({\vec{\varphi }}^2{)}_4^2$ Theory
• Safety versus triviality on the lattice
• Towards the QED beta function and renormalons at $1/N_f^2$ and $1/N_f^3$
• Analysis of a Zero of a Beta Function Using All-Orders Summation of Diagrams
• The $\beta$-function for Yukawa theory at large $N_f$
• The abelian gauge-Yukawa $\beta$-functions at large $N_f$
• Analytic Coupling Structure of Large $N_f$ (Super) QED and QCD
• An Integral Formalism for the Construction of Scheme Transformations in Quantum Field Theory
• Renormalization-Group Evolution of Chiral Gauge Theories
• Safe Glueballs and Baryons
• Technicolor models with coupled systems of Schwinger-Dyson equations
• Five loop minimal MOM scheme field and quark mass anomalous dimensions in QCD
• Perturbative corrections to technicolor
• The accidental Higgs
• Conformal Phase Diagram of Complete Asymptotically Free Theories
• $a$-theorem at large $N_f$
• Effect of Scheme Transformations on a Beta Function with Vanishing One-Loop Term
• Dynamical Symmetry Breaking in Chiral Gauge Theories with Direct-Product Gauge Groups
• Safe and free instantons
• Bubble-resummation and critical-point methods for $\beta$-functions at large $N$
• Fermion mass splitting in the technicolor coupled scenario
• Renormalization Flow of Nonlinear Electrodynamics
• Large $N_f$ for multiple representations
• Vacuum Alignment with more Flavors
• Composite scalar boson mass dependence on the constituent mass anomalous dimension
• IR-conformal gauge theories and composite Higgs
• Conformal Windows beyond Asymptotic Freedom