Evanescent Operators, Scheme Dependences and Double Insertions

Abstract

The anomalous dimension matrix of dimensionally regularized four-quark operators is known to be affected by evanescent operators, which vanish in $D=4$ dimensions. Their definition, however, is not unique, as one can always redefine them by adding a term proportional to $(D-4)$ times a physical operator. In the present paper we compare different definitions used in the literature and find that they correspond to different renormalization schemes in the physical operator basis. The scheme transformation formulae for the Wilson coefficients and the anomalous dimension matrix are derived in the next-to-leading order. We further investigate the proper treatment of evanescent operators in processes appearing at second order in the effective four-fermion interaction such as particle-antiparticle mixing, rare hadron decays or inclusive decays.

23 pages, LaTeX 2.09, uses packages epsf, rotate, a4. 3 figures included as PostScript files in a seperate uuencoded compressed tar file. A complete PostScript file may be obtained from ftp://feynman.t30.physik.tu-muenchen.de/pub/preprints/tum-66-94.ps.gz This submission includes the changes made during the refereeing process. To appear in Nucl.Phys.B

References in corpus (3)

• Enhancement of the $K_L$ -- $K_S$ Mass Difference by Short Distance QCD Corrections Beyond Leading Logarithms
• The Rare Decays $K^{+}\to {\pi }^{+}\nu \bar{\nu }$\ and $K_L\to {\mu }^{+}{\mu }^{-}$\ Beyond Leading Logarithms
• Direct CP Violation in K_L --> π^0 e^+e^- Beyond Leading Logarithms

Cited by in corpus (113)

• Weak Decays Beyond Leading Logarithms
• Weak Radiative B-Meson Decay Beyond Leading Logarithms
• Photonic penguins at two loops and m_t-dependence of BR[ B -> X_s l^+ l^-]
• 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
• Anomalous Dimension Matrix for Radiative and Rare Semileptonic B Decays up to Three Loops
• Next-to-Leading Order QCD Corrections to the Lifetime Difference of $B_s$ Mesons
• Automated one-loop computations in the SMEFT
• The Complete |Delta S|=2 Hamiltonian in the Next-To-Leading Order
• Low-energy effective field theory below the electroweak scale: matching at one loop
• B-parameters of the complete set of matrix elements of (Delta B = 2) operators from the lattice
• Charm Quark Contribution to K+ -> pi+ nu anti-nu at Next-to-Next-to-Leading Order
• Epsilon_K at Next-to-Next-to-Leading Order: The Charm-Top-Quark Contribution
• Electroweak Corrections to the Charm Quark Contribution to K+ -> pi+ nu nu-bar
• The Standard Model effective field theory at work
• Matching scalar leptoquarks to the SMEFT at one loop
• Sudakov Resummation for Subleading SCET Currents and Heavy-to-Light Form Factors
• EFT approach to the electron Electric Dipole Moment at the two-loop level
• Elementary derivation of a recently proposed integral representation for permanents
• Two-loop matching of the dipole operators for $b\to s\gamma$ and $b\to sgluon$
• The B^+ B_d^0 Lifetime Difference Beyond Leading Logarithms
• Precision calculations of $B\to V$ form factors in QCD
• NNLO Vertex Corrections in charmless hadronic B decays: Imaginary part
• A Subleading Operator Basis and Matching for $gg\to H$
• Evanescent Effects Can Alter Ultraviolet Divergences in Quantum Gravity without Physical Consequences
• Dimension-six matrix elements for meson mixing and lifetimes from sum rules
• A Complete Basis of Helicity Operators for Subleading Factorization
• Dispersive calculation of B_7^{3/2} and B_8^{3/2} in the chiral limit
• Building Blocks for Subleading Helicity Operators
• Electroweak Penguin Contributions to Non-Leptonic Delta F = 1 Decays at NNLO
• The QCD heavy-quark potential to order v^2: one loop matching conditions
• Two-Loop Renormalization of Quantum Gravity Simplified
• Singularity-free Next-to-leading Order $\Delta S=1$ Renormalization Group Evolution and ${\epsilon }_K^{\prime }/{\epsilon }_K$ in the Standard Model and Beyond
• Penguin Diagrams, Charmless B-Decays and the ``Missing Charm Puzzle''
• Three-Loop Anomalous Dimension of the Heavy Quark Pair Production Current in Non-Relativistic QCD
• Nucleon Form Factors and Distribution Amplitudes in QCD
• The supersymmetric Higgs sector and B-Bbar mixing for large tan beta
• Subleading Power Factorization with Radiative Functions
• Evanescent Operators in One-Loop Matching Computations
• Effective field theory for radiative corrections to charged-current processes I: Vector coupling
• Complete NLO QCD Corrections for Tree Level Delta F = 2 FCNC Processes
• A Subleading Power Operator Basis for the Scalar Quark Current
• The leading twist light-cone distribution amplitudes for the S-wave and P-wave quarkonia and their applications in single quarkonium exclusive productions
• Loop Corrections to Heavy-to-Light Form Factors and Evanescent Operators in SCET
• Perturbative Renormalization of Neutron-Antineutron Operators
• On the effective theory of neutrino-electron and neutrino-quark interactions
• Matching factors for Delta S=1 four-quark operators in RI/SMOM schemes
• Top quark decay at next-to-leading order in the Standard Model Effective Field Theory
• Towards next-to-next-to-leading-log accuracy for the width difference in the $B_s-{\bar{B}}_s$ system: fermionic contributions to order $(m_c/m_b{)}^0$ and $(m_c/m_b{)}^1$
• A low-energy perspective on the minimal left-right symmetric model
• Subleading power corrections to the pion-photon transition form factor in QCD
• What is Leading Order for LFV in SMEFT?
• Renormalizing Love: tidal effects at the third post-Newtonian order
• Majorana Neutrino Masses in the RGEs for Lepton Flavour Violation
• Two-loop renormalization of three-quark operators in QCD
• Scaling dimensions in QED${}_3$ from the $\epsilon$-expansion
• Four loop MSbar mass anomalous dimension in the Gross-Neveu model
• Perturbative renormalization factors of three- and four-quark operators for domain-wall QCD
• Four quark operators for kaon bag parameter with gradient flow
• Functional Matching and Renormalization Group Equations at Two-Loop Order
• Universal Scalar Leptoquark Action for Matching
• The Kaon B-parameter with the Wilson Quark Action using Chiral Ward Identities
• Low-energy effective field theory below the electroweak scale: one-loop renormalization in the 't Hooft-Veltman scheme
• Three loop renormalization of the SU(N_c) non-abelian Thirring model
• Electroweak effects in the $B^0-{\bar{B}}^0$ mixing
• Heavy Pair Production Currents with General Quantum Numbers in Dimensionally Regularized NRQCD
• Towards a Next-to-Next-to-Leading Order analysis of matching in $B^0$-${\bar{B}}^0$ mixing
• Operator mixing in $\mathbf{\epsilon }$-expansion: scheme and evanescent (in)dependence
• Phase space analysis for three and four massive particles in final states
• $B^0$-${\bar{B}}^0$ mixing: matching to HQET at NNLO
• R-Parity Violation and the Decay b to s gamma
• Electroweak input schemes and universal corrections in SMEFT
• Computing Tools for Effective Field Theories
• The Effective Electroweak Chiral Lagrangian: The Matter Sector
• Non-perturbative renormalization scheme for the CP-odd three-gluon operator
• Electric dipole moment constraints on CP-violating heavy-quark Yukawas at next-to-leading order
• Nucleon Form Factors to Next-to-Leading Order with Light-Cone Sum Rules
• Simple Rules for Evanescent Operators in One-Loop Basis Transformations
• Effective electroweak Hamiltonian in the gradient-flow formalism
• Two-loop QCD penguin contribution to the width difference in $B_s-{\bar{B}}_s$ mixing
• Dipole operators in Fierz identities
• Short-distance QCD corrections to $K^0{\bar{K}}^0$ mixing at next-to-leading order in Left-Right models
• Renormalization scheme factorization of one-loop Fierz identities
• AutoEFT: Automated Operator Construction for Effective Field Theories
• A Procedure g5anchor to Anchor ${\gamma }_5$ in Feynman Diagrams for the Standard Model
• One-loop matching of $CP$-odd four-quark operators to the gradient-flow scheme
• Four Fermion Operator Matching with NRQCD Heavy and AsqTad Light Quarks
• The heavy quark expansion for lifetimes: Towards the QCD corrections to power suppressed terms
• Renormalization-group equations of the LEFT at two loops: dimension-six baryon-number-violating operators
• Unitarity violation in non-integer dimensional Gross-Neveu-Yukawa model
• Weak mixing below the weak scale in dark-matter direct detection
• One-loop matching of the $CP$-odd three-gluon operator to the gradient flow
• Top mass dependent alpha_s^3 corrections to B-meson mixing in the MSSM
• Gluonic evanescent operators: classification and one-loop renormalization
• On operator mixing in fermionic CFTs in non-integer dimensions
• Completing NLO QCD Corrections for Tree Level Non-Leptonic Delta F = 1 Decays Beyond the Standard Model
• One-loop matching of Delta S=2 four-quark operators with improved staggered fermions
• Power corrections to the pion transition form factor from higher-twist distribution amplitudes of photon
• Renormalization-group equations of the LEFT at two loops: dimension-six operators
• Gluonic evanescent operators: two-loop anomalous dimensions
• Perturbative renormalization factors of four-quark operators for improved Wilson fermion action and Iwasaki gauge action
• Renormalization of three-quark operators at two loops in the RI${}^{\prime }$/SMOM scheme
• Radiative corrections to neutron beta decay and (anti)neutrino-nucleon scattering from low-energy effective field theory
• Disturbing news about the $d=2+\epsilon$ expansion
• Power expansion for heavy quarkonium production at next-to-leading order in ${\mathrm{e}}^{+}{\mathrm{e}}^{-}$ annihilation
• The anomalous dimension of spin-1/2 baryons in many flavors QCD
• Towards a Global Analysis of the $b\to c\bar{u}q$ Puzzle
• The electroweak Hamiltonian in the gradient flow formalism
• Symmetry Restoration in the SMEFT: Finite Counterterms for a Non-Anticommuting ${\gamma }_5$
• Constraints on lepton-flavor mixing with third-generation new physics
• The Simplest B Decay, Precisely
• One-loop matching of the LEFT to the QCD gradient flow
• The gradient flow formulation of the electroweak Hamiltonian