Renormalization and non-renormalization of scalar EFTs at higher orders

Abstract

We renormalize massless scalar effective field theories (EFTs) to higher loop orders and higher orders in the EFT expansion. To facilitate EFT calculations with the R* renormalization method, we construct suitable operator bases using Hilbert series and related ideas in commutative algebra and conformal representation theory, including their novel application to off-shell correlation functions. We obtain new results ranging from full one loop at mass dimension twelve to five loops at mass dimension six. We explore the structure of the anomalous dimension matrix with an emphasis on its zeros, and investigate the effects of conformal and orthonormal operators. For the real scalar, the zeros can be explained by a `non-renormalization' rule recently derived by Bern et al. For the complex scalar we find two new selection rules for mixing $n$- and $(n-2)$-field operators, with $n$ the maximal number of fields at a fixed mass dimension. The first appears only when the $(n-2)$-field operator is conformal primary, and is valid at one loop. The second appears in more generic bases, and is valid at three loops. Finally, we comment on how the Hilbert series we construct may be used to provide a systematic enumeration of a class of evanescent operators that appear at a particular mass dimension in the scalar EFT.

35 pages, 3 figures, 6 appendices, v3: typo corrected in appendix D

References in corpus (86)

• New Measurement of the Electron Magnetic Moment and the Fine Structure Constant
• Measurement of the fine-structure constant as a test of the Standard Model
• Renormalization Group Evolution of the Standard Model Dimension Six Operators III: Gauge Coupling Dependence and Phenomenology
• 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
• Five-Loop Running of the QCD coupling constant
• The Amplituhedron
• Weak Radiative B-Meson Decay Beyond Leading Logarithms
• Tenth-Order QED Contribution to the Electron g-2 and an Improved Value of the Fine Structure Constant
• The $\Delta S=1$ Effective Hamiltonian Including Next-to-Leading Order QCD and QED Corrections
• Delta M_K and epsilon_K in SUSY at the Next-to-Leading order
• The five-loop beta function of Yang-Mills theory with fermions
• The Uses of Conformal Symmetry in QCD
• Implications of conformal invariance in momentum space
• Two-Loop QCD Anomalous Dimensions of Flavour-Changing Four-Quark Operators Within and Beyond the Standard Model
• Effective Hamiltonian for Non-Leptonic |Delta F| = 1 Decays at NNLO in QCD
• Minimally subtracted six loop renormalization of $O(n)$-symmetric ${\varphi }^4$ theory and critical exponents
• Complete Set of Dimension-8 Operators in the Standard Model Effective Field Theory
• Two-loop mixing of dimension-five flavor-changing operators
• Beta functions and anomalous dimensions up to three loops
• Anomalous Dimension Matrix for Radiative and Rare Semileptonic B Decays up to Three Loops
• Operator bases, $S$-matrices, and their partition functions
• Four Loop Massless Propagators: an Algebraic Evaluation of All Master Integrals
• Tenth-Order Electron Anomalous Magnetic Moment --- Contribution of Diagrams without Closed Lepton Loops
• ${\epsilon }^{\prime }/\epsilon$ at the next-to-leading order in QCD and QED
• Four-Loop Non-Singlet Splitting Functions in the Planar Limit and Beyond
• A Cheap Alternative to the Lattice?
• Ultraviolet Properties of N = 8 Supergravity at Five Loops
• Numbers and Functions in Quantum Field Theory
• Hilbert series and operator bases with derivatives in effective field theories
• Six-Gluon Amplitudes in Planar $\mathcal{N}=4$ Super-Yang-Mills Theory at Six and Seven Loops
• Non-renormalization Theorems without Supersymmetry
• Master Integrals for Four-Loop Massless Propagators up to Transcendentality Weight Twelve
• Unitarity violation at the Wilson-Fisher fixed point in 4-epsilon dimensions
• Three loop MSbar tensor current anomalous dimension in QCD
• QCD corrections to the electric dipole moment of the neutron in the MSSM
• Three-Loop Mixing of Dipole Operators
• Four-Loop Anomalous Dimensions for Radiative Flavour-Changing Decays
• Effective Field Theory Amplitudes the On-Shell Way: Scalar and Vector Couplings to Gluons
• On Higgs decays to hadrons and the R-ratio at N^4LO
• Holomorphy without Supersymmetry in the Standard Model Effective Field Theory
• Complete Set of Dimension-9 Operators in the Standard Model Effective Field Theory
• The electroweak effective field theory from on-shell amplitudes
• Five loop renormalization of ${\varphi }^3$ theory with applications to the Lee-Yang edge singularity and percolation theory
• Two-loop QCD corrections to $Wb\bar{b}$ production at hadron colliders
• Four loop renormalization of the Gross-Neveu model
• Effective Field Theory of Gravity to All Orders
• Structure of two-loop SMEFT anomalous dimensions via on-shell methods
• Leading-Color Two-Loop QCD Corrections for Three-Jet Production at Hadron Colliders
• Field redefinitions in effective theories at higher orders
• Renormalization group coefficients and the S-matrix
• Loops and trees in generic EFTs
• Five-loop contributions to low-N non-singlet anomalous dimensions in QCD
• Six loop analytical calculation of the field anomalous dimension and the critical exponent $\eta$ in $O(n)$-symmetric ${\phi }^4$ model
• Constructing effective field theories via their harmonics
• The Rise of SMEFT On-shell Amplitudes
• Enumerating higher-dimensional operators with on-shell amplitudes
• Non-renormalization and operator mixing via on-shell methods
• Constructing massive on-shell contact terms
• Deligne Categories in Lattice Models and Quantum Field Theory, or Making Sense of $O(N)$ Symmetry with Non-integer $N$
• Di-photon amplitudes in three-loop Quantum Chromodynamics
• On critical exponents without Feynman diagrams
• 2, 12, 117, 1959, 45171, 1170086, ...: A Hilbert series for the QCD chiral Lagrangian
• New Selection Rules from Angular Momentum Conservation
• Hilbert Series and Operator Basis for NRQED and NRQCD/HQET
• Two-loop leading-colour QCD helicity amplitudes for two-photon plus jet production at the LHC
• The R*-operation for Feynman graphs with generic numerators
• Four Loop Massless Propagators: a Numerical Evaluation of All Master Integrals
• Two- and three-loop anomalous dimensions of Weinberg's dimension-six CP-odd gluonic operator
• The spectrum of critical exponents in $({\vec{\varphi }}^2{)}^2$-theory in $d=4-\eps$ dimensions -- Resolution of degeneracies and hierarchical structures
• The Constructive Standard Model: Part I
• The structure of the spectrum of anomalous dimensions in the N-vector model in 4-epsilon dimensions
• Top quark decay at next-to-leading order in the Standard Model Effective Field Theory
• Classification and one loop renormalization of dimension six and eight operators in quantum gluodynamics
• Anomalous Dimensions of Effective Theories from Partial Waves
• Four loop MSbar mass anomalous dimension in the Gross-Neveu model
• EFT Asymptotics: the Growth of Operator Degeneracy
• A Feynman-graph generator for any order of coupling constants
• 2-, 3- and 4-Body Decays in the Constructive Standard Model
• Two-Loop anomalous dimensions of QCD operators up to dimension-sixteen and Higgs EFT amplitudes
• Covariantizing Phase Space
• The Hopf algebra structure of the $R^{\ast }$-operation
• Reparameterization Invariant Operator Basis for NRQED and HQET
• Independently Parameterised Momenta Variables and Monte Carlo IR Subtraction
• Perturbation theory of transformed quantum fields
• The method of global R* and its applications

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• Building blocks of the flavourful SMEFT RG
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• Gluonic evanescent operators: classification and one-loop renormalization
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