Two- and three-loop anomalous dimensions of Weinberg's dimension-six CP-odd gluonic operator

Abstract

We apply a fully automated extension of the $R^{\ast }$-operation capable of calculating higher-loop anomalous dimensions of n-point Green's functions of arbitrary, possibly non-renormalisable, local Quantum Field Theories. We focus on the case of the CP-violating Weinberg operator of the Standard Model Effective Field Theory whose anomalous dimension is so far known only at one loop. We calculate the two-loop anomalous dimension in full QCD and the three-loop anomalous dimensions in the limit of pure Yang-Mills theory. We find sizeable two-loop and large three-loop corrections, due to the appearance of a new quartic group invariant. We discuss phenomenological implications for electric dipole moments and future applications of the method.

arXiv commentNew results included: two-loop anomalous dimension in full QCD, constraint on the Wilson coefficient with nEDM bounds. Included new section explaining the computational method

References in corpus (50)

• Dimension-Six Terms in the Standard Model Lagrangian
• 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
• Measurement of the permanent electric dipole moment of the neutron
• The three-loop QCD $\beta$-function and anomalous dimensions
• Five-Loop Running of the QCD coupling constant
• The Standard Model as an Effective Field Theory
• Weak Radiative B-Meson Decay Beyond Leading Logarithms
• The renormalization of the axial anomaly in dimensional regularization
• Electric Dipole Moments of the Atoms, Molecules, Nuclei and Particles
• 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
• Group theory factors for Feynman diagrams
• Reduced Limit on the Permanent Electric Dipole Moment of ${}^{199}$Hg
• The five-loop beta function of Yang-Mills theory with fermions
• 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
• Two-loop mixing of dimension-five flavor-changing operators
• A Monte Carlo global analysis of the Standard Model Effective Field Theory: the top quark sector
• Beta functions and anomalous dimensions up to three loops
• Anomalous Dimension Matrix for Radiative and Rare Semileptonic B Decays up to Three Loops
• Constraining the top-Higgs sector of the Standard Model Effective Field Theory
• Constraints on CP-violating Higgs couplings to the third generation
• ${\epsilon }^{\prime }/\epsilon$ at the next-to-leading order in QCD and QED
• Unraveling models of CP violation through electric dipole moments of light nuclei
• Higgs production in association with a top-antitop pair in the Standard Model Effective Field Theory at NLO in QCD
• Renormalization Group Running of Dimension-Six Sources of Parity and Time-Reversal Violation
• Three loop MSbar tensor current anomalous dimension in QCD
• QCD corrections to the electric dipole moment of the neutron in the MSSM
• Five-loop renormalisation of QCD in covariant gauges
• Hadronic EDMs, the Weinberg Operator, and Light Gluinos
• Three-Loop Mixing of Dipole Operators
• Four-Loop Anomalous Dimensions for Radiative Flavour-Changing Decays
• On Higgs decays to hadrons and the R-ratio at N^4LO
• Holomorphy without Supersymmetry in the Standard Model Effective Field Theory
• Direct and indirect constraints on CP-violating Higgs-quark and Higgs-gluon interactions
• The Nucleon Electric Dipole Form Factor From Dimension-Six Time-Reversal Violation
• LHC multijet events as a probe for anomalous dimension-six gluon interactions
• FORM version 4.2
• NLO QCD corrections to SM-EFT dilepton and electroweak Higgs boson production, matched to parton shower in POWHEG
• The Role of Lattice QCD in Searches for Violations of Fundamental Symmetries and Signals for New Physics
• The R*-operation for Feynman graphs with generic numerators
• Sum rules for CP-violating operators of Weinberg type
• Short flow-time coefficients of CP-violating operators
• Combinatorics of $\mathbf{R}$-, ${\mathbf{R}}^{-1}$-, and ${\mathbf{R}}^{\ast }$-operations and asymptotic expansions of feynman integrals in the limit of large momenta and masses
• The Hopf algebra structure of the $R^{\ast }$-operation
• Non-perturbative renormalization scheme for the CP-odd three-gluon operator
• Model independent evaluation of the Wilson coefficient of the Weinberg operator in QCD
• Present and future prospects for lattice QCD calculations of matrix elements for nEDM

Cited by in corpus (23)

• Low-energy effective field theory below the electroweak scale: matching at one loop
• Short flow-time coefficients of CP-violating operators
• Weinberg operator contribution to the nucleon electric dipole moment in the quark model
• 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
• Electric dipole moment constraints on CP-violating heavy-quark Yukawas at next-to-leading order
• Non-perturbative renormalization scheme for the CP-odd three-gluon operator
• SMEFT ATLAS of $\Delta F=2$ Transitions
• Anomalous Dimension of a General Effective Gauge Theory I: Bosonic Sector
• Renormalization-group equations of the LEFT at two loops: dimension-six baryon-number-violating operators
• Nucleon electric dipole moment from polarized deep inelastic scattering
• One-loop matching of the $CP$-odd three-gluon operator to the gradient flow
• Exploring the Flavor Symmetry Landscape
• Renormalization-group equations of the LEFT at two loops: dimension-five effects
• Bubble Trouble: a Review on Electroweak Baryogenesis
• Electric dipole moments from colour-octet scalars
• Renormalization-group equations of the LEFT at two loops: dimension-six operators
• Weinberg operator contribution to the CP-odd nuclear force in the quark model
• One-loop matching for quark dipole operators in a gradient-flow scheme
• Beautiful and charming chromodipole moments
• One-loop matching of the LEFT to the QCD gradient flow
• Renormalization of gluonic leading-twist Operators in covariant Gauges
• Contribution of the Weinberg-type Operator to atomic and nuclear electric dipole moments