Anomalous Dimension of a General Effective Gauge Theory I: Bosonic Sector

Abstract

We classify the physical operators of the most general bosonic effective gauge theory up to dimension six using on-shell methods. Based on this classification, we compute the complete one-loop anomalous dimension employing both on-shell unitarity-based and geometric techniques. Our analysis fully accounts for the mixing of operators with different dimensions. The results broadly apply to any Effective Field Theory with arbitrary gauge symmetry and bosonic degrees of freedom. To illustrate their utility, we perform a complete cross-check of results on the renormalization of the Standard Model Effective Field Theory (SMEFT), $O(n)$ scalar theory, and the SMEFT extended with an axion-like particle. Additionally, we present new results for axion-like particles with CP-violating interactions.

arXiv comment47 pages + appendices

References in corpus (61)

• Dimension-Six Terms in the Standard Model Lagrangian
• Perturbative Gauge Theory As A String Theory In Twistor Space
• Renormalization Group Evolution of the Standard Model Dimension Six Operators III: Gauge Coupling Dependence and Phenomenology
• Two-Loop Renormalization Group Equations for Soft Supersymmetry-Breaking Couplings
• Renormalization Group Evolution of the Standard Model Dimension Six Operators II: Yukawa Dependence
• Renormalization Group Evolution of the Standard Model Dimension Six Operators I: Formalism and lambda Dependence
• The Standard Model as an Effective Field Theory
• Infrared singularities of scattering amplitudes in perturbative QCD
• Renormalization of the Neutrino Mass Operator
• Multi-loop Amplitudes and Resummation
• Renormalization Group Equations for Seesaw Neutrino Masses
• Beyond the Minimal Composite Higgs Model
• Low-Energy Effective Field Theory below the Electroweak Scale: Anomalous Dimensions
• Neutrino Mass Operator Renormalization Revisited
• Flaxion: a minimal extension to solve puzzles in the standard model
• The Axiflavon
• Renormalization group evolution of dimension-six baryon number violating operators
• Two-loop Renormalization Group Equations in General Gauge Field Theories
• A Periodic Table of Effective Field Theories
• Non-renormalization Theorems without Supersymmetry
• Renormalization of vacuum expectation values in spontaneously broken gauge theories
• The Standard Model effective field theory at work
• Factorization Structure of Gauge Theory Amplitudes and Application to Hard Scattering Processes at the LHC
• S@M, a Mathematica Implementation of the Spinor-Helicity Formalism
• EFT approach to the electron Electric Dipole Moment at the two-loop level
• Renormalization constants and beta functions for the gauge couplings of the Standard Model to three-loop order
• Effective Field Theory Amplitudes the On-Shell Way: Scalar and Vector Couplings to Gluons
• The electroweak effective field theory from on-shell amplitudes
• Renormalization of vacuum expectation values in spontaneously broken gauge theories: Two-loop results
• Double-Cut of Scattering Amplitudes and Stokes' Theorem
• Structure of two-loop SMEFT anomalous dimensions via on-shell methods
• Renormalization group coefficients and the S-matrix
• Revisiting RGEs for general gauge theories
• GroupMath: A Mathematica package for group theory calculations
• Enumerating higher-dimensional operators with on-shell amplitudes
• Non-renormalization and operator mixing via on-shell methods
• Minimally extended SILH
• Towards the renormalisation of the Standard Model effective field theory to dimension eight: Bosonic interactions I
• Constraints on 3- and 4-loop $\beta$-functions in a general four-dimensional Quantum Field Theory
• Renormalization of the Standard Model Effective Field Theory from Geometry
• Renormalization Group Evolution from On-shell SMEFT
• Renormalization Group Evolution of Dimension-seven Operators in Standard Model Effective Field Theory and Relevant Phenomenology
• Weyl Consistency Conditions and ${\gamma }_5$
• Six-loop beta functions in general scalar theory
• Two- and three-loop anomalous dimensions of Weinberg's dimension-six CP-odd gluonic operator
• Four-Loop Gauge and Three-Loop Yukawa Beta-Functions in a General Renormalizable Theory
• Hunting for CP-violating axionlike particle interactions
• Majorana Neutrino Masses in the RGEs for Lepton Flavour Violation
• On the Structure of Anomalous Composite Higgs Models
• The Chiral Lagrangian of CP-Violating Axion-Like Particles
• Renormalization and non-renormalization of scalar EFTs at higher orders
• NLO QCD Renormalization Group Evolution for Non-Leptonic $\Delta F=2$ Transitions in the SMEFT
• RG of GR from On-shell Amplitudes
• Towards general scalar-Yukawa renormalisation group equations at three-loop order
• Renormalisation of SMEFT bosonic interactions up to dimension eight by LNV operators
• Collider and astrophysical signatures of light scalars with enhanced $\tau$ couplings
• Anomalous Dimensions via on-shell Methods: Operator Mixing and Leading Mass Effects
• Renormalization-group running of dimension-8 four-fermion operators in the SMEFT
• A Guide to Functional Methods Beyond One-Loop Order
• Learning the Simplicity of Scattering Amplitudes
• Extra-dimensional axion patterns

Cited by in corpus (5)

• The Art of Counting: a reappraisal of the HEFT expansion
• Amplitudes and partial wave unitarity bounds
• Multi-Higgs Amplitudes Bootstrapped: Dissecting SMEFT and HEFT
• Positivity and partial wave unitarity bounds on ALP theories via amplitude methods
• Symmetry Restoration in the SMEFT: Finite Counterterms for a Non-Anticommuting ${\gamma }_5$