Scheme Transformations in the Vicinity of an Infrared Fixed Point

Abstract

We analyze the effect of scheme transformations in the vicinity of an exact or approximate infrared fixed point in an asymptotically free gauge theory with fermions. We show that there is far less freedom in carrying out such scheme transformations in this case than at an ultraviolet fixed point. We construct a transformation from the $\overline{MS}$ scheme to a scheme with a vanishing three-loop term in the $\beta$ function and use this to assess the scheme dependence of an infrared fixed point in SU($N$) theories with fermions. Implications for the anomalous dimension of the fermion bilinear operator are also discussed.

5 pages, latex

References in corpus (21)

• The four-loop beta-function in Quantum Chromodynamics
• The three-loop QCD $\beta$-function and anomalous dimensions
• The 4-loop quark mass anomalous dimension and the invariant quark mass
• Light Composite Higgs from Higher Representations versus Electroweak Precision Measurements -- Predictions for LHC
• The 2009 World Average of ${\alpha }_s$
• Minimal Walking Technicolor: Set Up for Collider Physics
• Nonperturbative QCD Coupling and its $\beta$ function from Light-Front Holography
• Eliminating the Renormalization Scale Ambiguity for Top-Pair Production Using the Principle of Maximum Conformality
• Scale Setting Using the Extended Renormalization Group and the Principle of Maximum Conformality: the QCD Coupling Constant at Four Loops
• UV and IR Zeros of Gauge Theories at The Four Loop Order and Beyond
• Higher-Loop Corrections to the Infrared Evolution of a Gauge Theory with Fermions
• Maximum Wavelength of Confined Quarks and Gluons and Properties of Quantum Chromodynamics
• Neutrino Masses in Theories with Dynamical Electroweak Symmetry Breaking
• Dynamical Symmetry Breaking of Extended Gauge Symmetries
• Phases of Chiral Gauge Theories
• An Extended Technicolor Model
• New Constraints on Chiral Gauge Theories
• Two loop QCD vertices at the symmetric point
• Instantons and the Chiral Phase Transition
• Comparison of Some Exact and Perturbative Results for a Supersymmetric SU($N_c$) Gauge Theory
• Confinement, chiral symmetry, and the lattice

Cited by in corpus (43)

• Infrared Zero of $\beta$ and Value of ${\gamma }_m$ for an SU(3) Gauge Theory at the Five-Loop Level
• Study of Possible Ultraviolet Zero of the Beta Function in Gauge Theories with Many Fermions
• Higher-Order Scheme-Independent Series Expansions of ${\gamma }_{\bar{\psi }\psi ,IR}$ and ${\beta }_{IR}^{\prime }$ in Conformal Field Theories
• Scheme-Independent Series Expansions at an Infrared Zero of the Beta Function in Asymptotically Free Gauge Theories
• Higher-Loop Structural Properties of the $\beta$ Function in Asymptotically Free Vectorial Gauge Theories
• Scheme-Independent Calculation of ${\gamma }_{\bar{\psi }\psi ,IR}$ for an SU(3) Gauge Theory
• Study of Scheme Transformations to Remove Higher-Loop Terms in the $\beta$ Function of a Gauge Theory
• Conformal Behavior at Four Loops and Scheme (In)Dependence
• 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
• Six dimensional QCD at two loops
• Generalized Scheme Transformations for the Elimination of Higher-Loop Terms in the Beta Function of a Gauge Theory
• Higher Loop Corrections to the Infrared Evolution of Fermionic Gauge Theories in the RI' Scheme
• Infrared Fixed Points in the minimal MOM Scheme
• New Scheme Transformations and Application to Study Scheme Dependence of an Infrared Zero of the Beta Function in Gauge Theories
• Banks-Zaks fixed point analysis in momentum subtraction schemes
• Infrared Fixed Point Physics in $\mathrm{SO}(N_c)$ and $\mathrm{Sp}(N_c)$ Gauge Theories
• $A_k\bar{F}$ Chiral Gauge Theories
• Physics of the Non-Abelian Coulomb Phase: Insights from Padé Approximants
• Scheme-Independent Calculations of Anomalous Dimensions of Baryon Operators in Conformal Field Theories
• Renormalization-Group Flows and Fixed Points in Yukawa Theories
• Higher-Order Scheme-Independent Calculations of Physical Quantities in the Conformal Phase of a Gauge Theory
• On the Question of an Ultraviolet Zero of the Beta Function of the $\lambda ({\vec{\varphi }}^2{)}_4^2$ Theory
• Analysis of a Zero of a Beta Function Using All-Orders Summation of Diagrams
• Renormalization Scheme Dependence in a QCD Cross Section
• Thermal order in large N conformal gauge theories
• An Integral Formalism for the Construction of Scheme Transformations in Quantum Field Theory
• Renormalization-Group Evolution of Chiral Gauge Theories
• On the Question of a Possible Infrared Zero in the Beta Function of the Finite-$N$ Gross-Neveu Model
• Study of the Renormalization-Group Evolution of $\mathcal{N}=1$ Supersymmetric Gauge Theories Using Padé Approximants
• Scheme-Independent Series for Anomalous Dimensions of Higher-Spin Operators at an Infrared Fixed Point in a Gauge Theory
• Renormalization-Group Behavior of ${\varphi }^3$ Theories in $d=6$ Dimensions
• Four-Fermion Limit of Gauge-Yukawa Theories
• Study of the Question of an Ultraviolet Zero in the Six-Loop Beta Function of the O($N$) $\lambda |\vec{\varphi }{|}^4$ Theory
• Renormalization of QCD in the interpolating momentum subtraction scheme at three loops
• Multiple Couplings and Renormalization Scheme Ambiguities
• ${\beta }_{IR}^{\prime }$ at an Infrared Fixed Point in Chiral Gauge Theories
• Effect of Scheme Transformations on a Beta Function with Vanishing One-Loop Term
• Duality in a Supersymmetric Gauge Theory From a Perturbative Viewpoint
• Anomalous Dimensions at an Infrared Fixed Point in an SU($N_c$) Gauge Theory with Fermions in the Fundamental and Antisymmetric Tensor Representations
• Search for an Ultraviolet Zero in the Seven-Loop Beta Function of the $\lambda {\varphi }_4^4$ Theory
• Large $N_f$ for multiple representations
• Study of the Ultraviolet Behavior of an O($N$) $|\vec{\varphi }{|}^6$ Theory in $d=3$ Dimensions
• A Comparative Study of Criticality Conditions for Anomalous Dimensions using Exact Results in an $\mathcal{N}=1$ Supersymmetric Gauge Theory