Low-energy effective field theory below the electroweak scale: one-loop renormalization in the 't Hooft-Veltman scheme

Abstract

The low-energy effective field theory below the electroweak scale (LEFT) describes the effects at low energies of both the weak interaction and physics beyond the Standard Model. We study the one-loop renormalization of the LEFT in the 't Hooft-Veltman scheme, which offers an algebraically consistent definition of the Levi-Civita symbol and ${\gamma }_5$ in dimensional regularization. However, in connection with minimal subtraction this scheme leads to a spurious breaking of chiral symmetry in intermediate steps of the calculation. Based on the 't Hooft-Veltman prescription, we define a renormalization scheme that restores chiral symmetry by including appropriate finite counterterms. To this end, we extend the physical LEFT operator basis by a complete set of off-shell and one-loop-evanescent operators and we perform the renormalization at one loop. We determine the finite counterterms to the physical parameters that compensate both the insertions of evanescent operators, as well as the chiral-symmetry-breaking terms from the renormalizable part of the Lagrangian in $D$ dimensions. Our results can be applied in next-to-leading-log calculations in the 't Hooft-Veltman scheme: using our renormalization scheme instead of pure minimal subtraction separates the physical sector from the unphysical evanescent sector and leads to results that are manifestly free of spurious chiral-symmetry-breaking terms.

arXiv comment38 pages, 11 tables

References in corpus (59)

• Weak Decays Beyond Leading Logarithms
• Dimension-Six Terms in the Standard Model Lagrangian
• Asymptotic expansion of Feynman integrals near threshold
• New Developments in FeynCalc 9.0
• 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
• FeynCalc 9.3: New features and improvements
• Measurement of the permanent electric dipole moment of the neutron
• Package-X: A Mathematica package for the analytic calculation of one-loop integrals
• Standard Model CP-violation and Baryon asymmetry
• Electroweak Baryogenesis and Standard Model CP Violation
• The $\Delta S=1$ Effective Hamiltonian Including Next-to-Leading Order QCD and QED Corrections
• Standard Model CP-violation and Baryon asymmetry Part II: Finite Temperature
• Low-Energy Effective Field Theory below the Electroweak Scale: Operators and Matching
• Two-Loop QCD Anomalous Dimensions of Flavour-Changing Four-Quark Operators Within and Beyond the Standard Model
• Package-X 2.0: A Mathematica package for the analytic calculation of one-loop integrals
• Low-Energy Effective Field Theory below the Electroweak Scale: Anomalous Dimensions
• The Two-Loop Anomalous Dimension Matrix for $\Delta S=1$ Weak Non-Leptonic Decays I: $\mathcal{O}({\alpha }_s^2)$
• Two-loop mixing of dimension-five flavor-changing operators
• Next-to-Leading Order QCD Corrections to $\Delta F=2$ effective Hamiltonians
• Beta functions and anomalous dimensions up to three loops
• Revisiting Lepton Flavour Universality in B Decays
• Renormalization-group evolution of new physics contributions to (semi)leptonic meson decays
• Matching of gauge invariant dimension 6 operators for $b\to s$ and $b\to c$ transitions
• Compilation of low-energy constraints on 4-fermion operators in the SMEFT
• Low-energy effective field theory below the electroweak scale: matching at one loop
• Evanescent Operators, Scheme Dependences and Double Insertions
• Facts of life with gamma(5)
• Renormalisation-group improved analysis of $\mu \to e$ processes in a systematic effective-field-theory approach
• B physics Beyond the Standard Model at One Loop: Complete Renormalization Group Evolution below the Electroweak Scale
• Non-standard Charged Current Interactions: beta decays versus the LHC
• Standard Model CP-violation and Baryon asymmetry Part I: Zero Temperature
• Three-loop matching of the dipole operators for b -> s gamma and b -> s g
• Renormalization Group Running of Dimension-Six Sources of Parity and Time-Reversal Violation
• FeynHelpers: Connecting FeynCalc to FIRE and Package-X
• EFT approach to the electron Electric Dipole Moment at the two-loop level
• Four-Loop Anomalous Dimensions for Radiative Flavour-Changing Decays
• Practical Algebraic Renormalization
• Algebraic Structure of Lepton and Quark Flavor Invariants and CP Violation
• Spin-dependent $\mu \to e$ conversion
• DsixTools 2.0: The Effective Field Theory Toolkit
• The $\mu \to e\gamma$ decay in a systematic effective field theory approach with dimension 6 operators
• Semi-leptonic $B$-physics anomalies: a general EFT analysis within $U(2{)}^n$ flavor symmetry
• Neutrinoless Quadruple Beta Decay
• One-loop matching in the SMEFT extended with a sterile neutrino
• Low Energy Effective Field Theory Operator Basis at $d\le 9$
• General neutrino interactions with sterile neutrinos in light of coherent neutrino-nucleus scattering and meson invisible decays
• Evanescent Operators in One-Loop Matching Computations
• Action principles, restoration of BRS symmetry and the renormalization group equation for chiral non-Abelian gauge theories in dimensional renormalization with a non-anticommuting ${\gamma }_5$
• Dimensional Regularization and Breitenlohner-Maison / 't Hooft-Veltman Scheme for ${\gamma }_5$ applied to Chiral YM Theories: Full One-Loop Counterterm and RGE Structure
• Mu to e gamma and matching at mW
• Low-Energy Effective Field Theory below the Electroweak Scale: Dimension-8 Operators
• Two-loop application of the Breitenlohner-Maison/'t Hooft-Veltman scheme with non-anticommuting ${\gamma }_5$: Full renormalization and symmetry-restoring counterterms in an abelian chiral gauge theory
• Gauge Invariance and Finite Counterterms in Chiral Gauge Theories
• Two-Loop Rational Terms in Yang-Mills Theories
• Non-perturbative renormalization scheme for the CP-odd three-gluon operator
• One-loop matching of $CP$-odd four-quark operators to the gradient-flow scheme
• One-loop matching of the $CP$-odd three-gluon operator to the gradient flow

Cited by in corpus (9)

• Low-Energy Effective Field Theory below the Electroweak Scale: Anomalous Dimensions
• Renormalization-group equations of the LEFT at two loops: dimension-six baryon-number-violating operators
• On sum rules for semi-leptonic $b\to c$ and $b\to u$ decays
• Renormalization-group equations of the LEFT at two loops: dimension-five effects
• Baryon Number Violation: From Nuclear Matrix Elements to BSM Physics
• Renormalization-group equations of the LEFT at two loops: dimension-six operators
• Symmetry Restoration in the SMEFT: Finite Counterterms for a Non-Anticommuting ${\gamma }_5$
• Two loops, four tops and two ${\gamma }_5$ schemes: a renormalization story
• One-loop matching of the LEFT to the QCD gradient flow