Non-renormalization and operator mixing via on-shell methods

Abstract

Using on-shell methods, we present a new perturbative non-renormalization theorem for operator mixing in massless four-dimensional quantum field theories. By examining how unitarity cuts of form factors encode anomalous dimensions we show that longer operators are often restricted from renormalizing shorter operators at the first order where there exist Feynman diagrams. The theorem applies quite generally and depends only on the field content of the operators involved. We apply our theorem to operators of dimension five through seven in the Standard Model Effective Field Theory, including examples of nontrivial zeros in the anomalous-dimension matrix at one through four loops. The zeros at two and higher loops go beyond those previously explained using helicity selection rules. We also include explicit sample calculations at two loops.

arXiv comment5 pages, 2 figures

References in corpus (27)

• Dimension-Six Terms in the Standard Model Lagrangian
• One-Loop n-Point Gauge Theory Amplitudes, Unitarity and Collinear Limits
• Fusing Gauge Theory Tree Amplitudes Into Loop Amplitudes
• 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
• Multi-Parton Amplitudes in Gauge Theories
• The Singular Behaviour of QCD Amplitudes at Two-loop Order
• 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
• One-Loop Amplitudes for e^+ e^- to Four Partons
• Massive Loop Amplitudes from Unitarity
• Higgs windows to new physics through d = 6 operators: Constraints and one-loop anomalous dimensions
• Renormalization Group Scaling of Higgs Operators and Γ(h -> γγ)
• Singular terms of helicity amplitudes at one-loop in QCD and the soft limit of the cross sections of multi-parton processes
• Non-renormalization Theorems without Supersymmetry
• Renormalization of dimension-six operators relevant for the Higgs decays $h\to \gamma \gamma ,\gamma Z$
• Factorization Structure of Gauge Theory Amplitudes and Application to Hard Scattering Processes at the LHC
• Holomorphy without Supersymmetry in the Standard Model Effective Field Theory
• Evanescent Effects Can Alter Ultraviolet Divergences in Quantum Gravity without Physical Consequences
• Naive Dimensional Analysis Counting of Gauge Theory Amplitudes and Anomalous Dimensions
• Renormalization group coefficients and the S-matrix
• Two-Loop Renormalization of Quantum Gravity Simplified
• The SU(2|3) dynamic two-loop form factors
• $\text{Tr}(F^3)$ supersymmetric form factors and maximal transcendentality Part I: $\mathcal{N}=4$ super Yang-Mills
• Higgs amplitudes from $\mathcal{N}=4$ super Yang-Mills theory
• $\text{Tr}(F^3)$ supersymmetric form factors and maximal transcendentality Part II: $0<\mathcal{N}<4$ super Yang-Mills

Cited by in corpus (30)

• Running in the ALPs
• Loops and trees in generic EFTs
• Enumerating higher-dimensional operators with on-shell amplitudes
• Constructing massive on-shell contact terms
• Towards the renormalisation of the Standard Model effective field theory to dimension eight: Bosonic interactions I
• Simple encoding of higher derivative gauge and gravity counterterms
• New Selection Rules from Angular Momentum Conservation
• Renormalization Group Evolution from On-shell SMEFT
• 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
• Sum Rules in the Standard Model Effective Field Theory from Helicity Amplitudes
• Building blocks of the flavourful SMEFT RG
• Charting the Higgs self-coupling boundaries
• Renormalization and non-renormalization of scalar EFTs at higher orders
• RG of GR from On-shell Amplitudes
• EFT matching from analyticity and unitarity
• 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
• Limits on ALP-neutrino couplings from loop-level processes
• 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
• Renormalising the Field-Space Geometry
• On the six-loop scaling dimensions of the $({\varphi }^2{)}^n$ operators in $d=3$
• A Note on the Analytic Structure of Celestial Amplitudes
• A Green's basis for the bosonic SMEFT to dimension 8
• Covariant derivative expansion for the renormalization of gravity