Structure of two-loop SMEFT anomalous dimensions via on-shell methods

Abstract

We describe on-shell methods for computing one- and two-loop anomalous dimensions in the context of effective field theories containing higher-dimension operators. We also summarize methods for computing one-loop amplitudes, which are used as inputs to the computation of two-loop anomalous dimensions, and we explain how the structure of rational terms and judicious renormalization scheme choices can lead to additional vanishing terms in the anomalous dimension matrix at two loops. We describe the two-loop implications for the Standard Model Effective Field Theory (SMEFT). As a by-product of this analysis we verify a variety of one-loop SMEFT anomalous dimensions computed by Alonso, Jenkins, Manohar and Trott.

arXiv comment58 pages, 8 figures, 6 tables

References in corpus (38)

• Dimension-Six Terms in the Standard Model Lagrangian
• Causality, Analyticity and an IR Obstruction to UV Completion
• Renormalization Group Evolution of the Standard Model Dimension Six Operators III: Gauge Coupling Dependence and Phenomenology
• Generalized Unitarity and One-Loop Amplitudes in N=4 Super-Yang-Mills
• 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 Amplituhedron
• The Standard Model as an Effective Field Theory
• Scattering Amplitudes and the Conservative Hamiltonian for Binary Systems at Third Post-Minkowskian Order
• What is the Simplest Quantum Field Theory?
• Algorithm FIRE -- Feynman Integral REduction
• Amplitudes, Observables, and Classical Scattering
• Black Hole Binary Dynamics from the Double Copy and Effective Theory
• FIRE5: a C++ implementation of Feynman Integral REduction
• Direct extraction of one-loop integral coefficients
• On-Shell Methods in Perturbative QCD
• Simplifying Multiloop Integrands and Ultraviolet Divergences of Gauge Theory and Gravity Amplitudes
• Extending the Standard Model Effective Field Theory with the Complete Set of Dimension-7 Operators
• Six-Gluon Amplitudes in Planar $\mathcal{N}=4$ Super-Yang-Mills Theory at Six and Seven Loops
• Basics of Generalized Unitarity
• Non-renormalization Theorems without Supersymmetry
• Consistency of the Standard Model Effective Field Theory
• Effective Field Theory Amplitudes the On-Shell Way: Scalar and Vector Couplings to Gluons
• Holomorphy without Supersymmetry in the Standard Model Effective Field Theory
• The electroweak effective field theory from on-shell amplitudes
• Evanescent Effects Can Alter Ultraviolet Divergences in Quantum Gravity without Physical Consequences
• Integrability of Black Hole Orbits in Maximal Supergravity
• Renormalization group coefficients and the S-matrix
• Loops and trees in generic EFTs
• Universality in string interactions
• Amplitudes, Form Factors and the Dilatation Operator in $\mathcal{N}=4$ SYM Theory
• Susy Theories and QCD: Numerical Approaches
• Renormalization of the Vector Current in QED
• The Two-Loop Four-Graviton Scattering Amplitudes
• From Scattering Amplitudes to the Dilatation Generator in N=4 SYM
• All-Multiplicity Non-Planar MHV Amplitudes in sYM at Two Loops
• On-Shell Electroweak Sector and the Higgs Mechanism
• On interference and non-interference in the SMEFT

Cited by in corpus (41)

• The Standard Model effective field theory at work
• Constructing massive on-shell contact terms
• Renormalization of the Standard Model Effective Field Theory from Geometry
• Composing Effective Prediction at Five Points
• Geometry in Scattering Amplitudes
• Amplitude bases in generic EFTs
• Anomalous Dimensions of Effective Theories from Partial Waves
• On-shell Higgsing for EFTs
• On-shell effective theory for higher-spin dark matter
• Sum Rules in the Standard Model Effective Field Theory from Helicity Amplitudes
• Building blocks of the flavourful SMEFT RG
• Effective theory tower for $\mu \to e$ conversion
• Renormalization and non-renormalization of scalar EFTs at higher orders
• Two-Loop anomalous dimensions of QCD operators up to dimension-sixteen and Higgs EFT amplitudes
• RG of GR from On-shell Amplitudes
• The EFT Bootstrap at Finite $M_{PL}$
• EFT matching from analyticity and unitarity
• Constructing on-shell operator basis for all masses and spins
• Constructing Generic Effective Field Theory for All Masses and Spins
• SMEFT ATLAS of $\Delta F=2$ Transitions
• Gearing up for the next generation of LFV experiments, via on-shell methods
• Anomalous Dimension of a General Effective Gauge Theory I: Bosonic Sector
• Two-loop running effects in Higgs physics in Standard Model Effective Field Theory
• Renormalization-group running of dimension-8 four-fermion operators in the SMEFT
• Renormalization-group equations of the LEFT at two loops: dimension-six baryon-number-violating operators
• Anomalous Dimensions via on-shell Methods: Operator Mixing and Leading Mass Effects
• Renormalization of effective field theories via on-shell methods: the case of axion-like particles
• Renormalization-group equations of the LEFT at two loops: dimension-five effects
• Renormalisation group effects in SMEFT for di-Higgs production
• Dimension-8 SMEFT contact-terms for vector-pair production via on-shell Higgsing
• Renormalization-group equations of the LEFT at two loops: dimension-six operators
• Renormalising the Field-Space Geometry
• Amplitudes and partial wave unitarity bounds
• Generalized unitarity method for unstable particles
• Complete two-loop Yukawa-induced running of the Higgs-gluon coupling in SMEFT
• A Note on the Analytic Structure of Celestial Amplitudes
• Positivity and partial wave unitarity bounds on ALP theories via amplitude methods
• One-loop matching of the LEFT to the QCD gradient flow
• A Green's basis for the bosonic SMEFT to dimension 8
• Two loops, four tops and two ${\gamma }_5$ schemes: a renormalization story
• Leading singularities in higher-derivative Yang-Mills theory and quadratic gravity