Conformal Behavior at Four Loops and Scheme (In)Dependence

Abstract

We search for infrared zeros of the beta function and evaluate the anomalous dimension of the mass at the associated fixed point for asymptotically free vector-like fermionic gauge theories with gauge group SU(N). The fixed points of the beta function are studied at the two, three and four loop level in two different explicit schemes. These are the modified regularization invariant, RI', scheme and the minimal momentum subtraction, mMOM, scheme. The search is performed in Landau gauge where the beta function of the gauge parameter vanishes. We then compare our findings to earlier identical investigations performed in the modified minimal subtraction, $\overline{\text{MS}}$, scheme. It is found that the value of the anomalous dimension of the mass is smaller at three and four loops than at two loops. This seems to be a generic pattern that is observed in all three different schemes. We then estimate the value of the anomalous dimension to be $\gamma \sim 0.225-0.375$ for twelve fundamental flavors and three colors, $\gamma \sim 0.500-0.593$ for two adjoint flavors and two colors and finally $\gamma \sim 1.12-1.70$ for two two-indexed flavors and three colors with the lower and upper bound set by the minimum and maximum value respectively over all three schemes and at three and four loops. Our analysis suggests that the former two theories lie in the conformal window while the latter belongs to the chirally broken phase.

Several changes. Matches the published version

References in corpus (23)

• Supersymmetry Inspired QCD Beta Function
• Zero of the discrete beta function in SU(3) lattice gauge theory with color sextet fermions
• The physics of eight flavours
• Nearly conformal gauge theories in finite volume
• Higher-Loop Corrections to the Infrared Evolution of a Gauge Theory with Fermions
• Conformal Windows of SU(N) Gauge Theories, Higher Dimensional Representations and The Size of The Unparticle World
• Maximum Wavelength of Confined Quarks and Gluons and Properties of Quantum Chromodynamics
• The infrared dynamics of Minimal Walking Technicolor
• Spectrum of SU(2) lattice gauge theory with two adjoint Dirac flavours
• Phase structure of SU(3) gauge theory with two flavors of symmetric-representation fermions
• Fundamental Composite Higgs Dynamics on the Lattice: SU(2) with Two Flavors
• Infrared fixed point in SU(2) gauge theory with adjoint fermions
• Beta Function and Anomalous Dimensions
• Mass anomalous dimension in SU(2) with six fundamental fermions
• An Analysis of Scheme Transformations in the Vicinity of an Infrared Fixed Point
• Scheme Transformations in the Vicinity of an Infrared Fixed Point
• Generalized Scheme Transformations for the Elimination of Higher-Loop Terms in the Beta Function of a Gauge Theory
• Comparison of Some Exact and Perturbative Results for a Supersymmetric SU($N_c$) Gauge Theory
• The bulk transition of QCD with twelve flavors and the role of improvement
• Improvement via hypercubic smearing in triplet and sextet QCD
• Orthogonal Technicolor with Isotriplet Dark Matter on the Lattice
• Exceptional and Spinorial Conformal Windows
• Renormalization-Group Flows and Fixed Points in Yukawa Theories

Cited by in corpus (13)

• Infrared Zero of $\beta$ and Value of ${\gamma }_m$ for an SU(3) Gauge Theory at the Five-Loop Level
• Scheme-Independent Series Expansions at an Infrared Zero of the Beta Function in Asymptotically Free Gauge Theories
• Scheme-Independent Calculation of ${\gamma }_{\bar{\psi }\psi ,IR}$ for an SU(3) Gauge Theory
• 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
• Physics of the Non-Abelian Coulomb Phase: Insights from Padé Approximants
• Scheme-Independent Calculations of Physical Quantities in an $\mathcal{N}=1$ Supersymmetric Gauge Theory
• Analysis of a Zero of a Beta Function Using All-Orders Summation of Diagrams
• 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
• Determination of SU(4)${}_{TC}$ Technicolor Gauge Group from Embedding in Extended Technicolor