Effective Hamiltonian for Non-Leptonic |Delta F| = 1 Decays at NNLO in QCD

Abstract

We compute the effective hamiltonian for non-leptonic |Delta F| = 1 decays in the standard model including next-to-next-to-leading order QCD corrections. In particular, we present the complete three-loop anomalous dimension matrix describing the mixing of current-current and QCD penguin operators. The calculation is performed in an operator basis which allows to consistently use fully anticommuting gamma_5 in dimensional regularization at an arbitrary number of loops. The renormalization scheme dependences and their cancellation in physical quantities is discussed in detail. Furthermore, we demonstrate how our results are transformed to a different basis of effective operators which is frequently adopted in phenomenological applications. We give all necessary two-loop constant terms which allow to obtain the three-loop anomalous dimensions and the corresponding initial conditions of the two-loop Wilson coefficients in the latter scheme. Finally, we solve the renormalization group equation and give the analytic expressions for the low-energy Wilson coefficients relevant for non-leptonic B meson decays beyond next-to-leading order in both renormalization schemes.

arXiv comment46 pages, 6 figures; typos in Eqs. (27) and (37) corrected (thanks to Guido Bell and Diego Guadagnoli for pointing them out) and numerically irrelevant typos/mistakes in Eqs. (26), (29), (48), (102), and (A.27) corrected (thanks to Xinqiang Li for bringing them to our attention)

References in corpus (40)

• A complete analysis of FCNC and CP constraints in general SUSY extensions of the standard model
• Systematic approach to exclusive B ->V l^+l^-, V gamma decays
• Weak Radiative B-Meson Decay Beyond Leading Logarithms
• The $\Delta S=1$ Effective Hamiltonian Including Next-to-Leading Order QCD and QED Corrections
• Photonic penguins at two loops and m_t-dependence of BR[ B -> X_s l^+ l^-]
• The Anatomy of ${\epsilon }^{\prime }/\epsilon$ Beyond Leading Logarithms with Improved Hadronic Matrix Elements
• Two-Loop QCD Anomalous Dimensions of Flavour-Changing Four-Quark Operators Within and Beyond the Standard Model
• The Two-Loop Anomalous Dimension Matrix for $\Delta S=1$ Weak Non-Leptonic Decays I: $\mathcal{O}({\alpha }_s^2)$
• Weak Hamiltonian, CP Violation and Rare Decays
• Two-loop mixing of dimension-five flavor-changing operators
• $O(\alpha {\alpha }_s^2)$ correction to the electroweak $\rho$ parameter
• Beta functions and anomalous dimensions up to three loops
• Anomalous Dimension Matrix for Radiative and Rare Semileptonic B Decays up to Three Loops
• MATAD: a program package for the computation of MAssive TADpoles
• Evanescent Operators, Scheme Dependences and Double Insertions
• Complete NNLO QCD Analysis of B -> X_s l^+ l^- and Higher Order Electroweak Effects
• Massive 3-loop Feynman diagrams reducible to SC* primitives of algebras of the sixth root of unity
• The Impact of Universal Extra Dimensions on B -> X_s gamma, B -> X_s gluon, B -> X_s mu^+ mu^-, K_L -> pi^0 e^ +e^-, and epsilon'/epsilon
• Corrections of order ${\cal O}(G_F M_t^2 \as^2)$ to the $\rho$ parameter
• Connections between epsilon'/epsilon and Rare Kaon Decays in Supersymmetry
• |Delta F| = 1 Nonleptonic Effective Hamiltonian in a Simpler Scheme
• Three-loop matching of the dipole operators for b -> s gamma and b -> s g
• epsilon'/epsilon and Rare K and B Decays in the MSSM
• Can ε'/εbe supersymmetric?
• Supersymmetric corrections to $ε^\prime /εat the leading order in QCD and QED
• Flavour changing neutral currents and CP violating processes in generalized supersymmetric theories
• Fermionic NNLL corrections to b -> s γ
• Recurrence Relations for Three-Loop Prototypes of Bubble Diagrams with a Mass
• Electroweak Penguin Contributions to Non-Leptonic Delta F = 1 Decays at NNLO
• Equations of Motion for Effective Lagrangians and Penguins in Rare B-Decays
• Large Delta(I)=3/2 Contribution to epsilon'/epsilon in Supersymmetry
• Virtual- and bremsstrahlung corrections to b -> d l+ l- in the standard model
• Epsilon' from supersymmetry with non universal A terms?
• A short look at epsilon'/epsilon
• Application of conformal mapping and Padé approximants $(\omega P^{\prime }s)$ to the calculation of various two-loop Feynman diagrams
• Probing Supersymmetric Flavor Models with ${\epsilon }^{\prime }/\epsilon$
• Constraints on the Mass and Mixing of the 4th Generation Quark From Direct CP Violation${\epsilon }^{\prime }/\epsilon$ and Rare K Decays
• Contribution to ${\epsilon }^{\prime }/\epsilon$ from anomalous gauge couplings
• ${\epsilon }^{\prime }/\epsilon$ And Anomalous Gauge Boson Couplings
• Enhancement of epsilon'/epsilon in the SU(2)_L times SU(2)_R times U(1) model

Cited by in corpus (179)

• Estimate of BR(B -> X_s gamma) at O(alpha_s^2)
• Symmetries and Asymmetries of B -> K* mu+ mu- Decays in the Standard Model and Beyond
• SuperIso v3.0: A program for calculating flavor physics observables in 2HDM and supersymmetry
• Optimizing the basis of B->K*ll observables in the full kinematic range
• Two-Loop Electroweak Corrections for the K -> pi nu anti-nu Decays
• NNLO QCD corrections to the B -> X_s gamma matrix elements using interpolation in m_c
• $K^{+}\to {\pi }^{+}\nu \bar{\nu }$ and $K_L\to {\pi }^0\nu \bar{\nu }$ in the Standard Model: Status and Perspectives
• Implications from clean observables for the binned analysis of B -> K*ll at large recoil
• Flavor Physics in the Quark Sector
• Electromagnetic Logarithms in B -> X_s l+ l-
• 50 Years of Quantum Chromodynamics
• On the Importance of NNLO QCD and Isospin-breaking Corrections in ${\epsilon }^{\prime }/\epsilon$
• B->V gamma Beyond QCD Factorisation
• Next-to-Next-to-Leading-Order Charm-Quark Contribution to the CP Violation Parameter epsilon_K and Delta M_K
• Complete Anatomy of B -> K*ll and its angular distribution
• Theory of B -> K(*)l+l- decays at high q^2: OPE and quark-hadron duality
• Charm Quark Contribution to K+ -> pi+ nu anti-nu at Next-to-Next-to-Leading Order
• The Rare Decay K^+ -> pi^+ nu nubar at the Next-to-Next-to-Leading Order in QCD
• Rare $B$ Decays as Tests of the Standard Model
• B physics Beyond the Standard Model at One Loop: Complete Renormalization Group Evolution below the Electroweak Scale
• Epsilon_K at Next-to-Next-to-Leading Order: The Charm-Top-Quark Contribution
• ${\Lambda }_b\to \Lambda {\ell }^{+}{\ell }^{-}$ form factors, differential branching fraction, and angular observables from lattice QCD with relativistic $b$ quarks
• Towards the Identification of New Physics through Quark Flavour Violating Processes
• Constraints on New Physics in MFV models: a model-independent analysis of Delta F=1 processes
• Improved Theory Predictions and Global Analysis of Exclusive $\mathbf{b}\to \mathbf{s}{\mathbf{\mu }}^{+}{\mathbf{\mu }}^{-}$ Processes
• Flavor Physics in the Randall-Sundrum Model: II. Tree-Level Weak-Interaction Processes
• Electroweak Corrections to the Charm Quark Contribution to K+ -> pi+ nu nu-bar
• Toward a NNLO calculation of the B-->X_s gamma decay rate with a cut on photon energy: I. Two-loop result for the soft function
• Constraining the Two-Higgs-Doublet-Model parameter space
• Analysis of Br(B-->X_s gamma) at NNLO with a Cut on Photon Energy
• B, D and K decays
• Logarithmically Enhanced Corrections to the Decay Rate and Forward Backward Asymmetry in anti-B --> X(s) l+ l-
• NNLO vertex corrections to non-leptonic B decays: Tree amplitudes
• Measurements of the B -> X_s gamma Branching Fraction and Photon Spectrum from a Sum of Exclusive Final States
• On the LHCb anomaly in B -> K* l+ l-
• Flavor & new physics opportunities with rare charm decays into leptons
• $K\to \pi \nu \bar{\nu }$ and ${\epsilon }^{\prime }/\epsilon$ in Simplified New Physics Models
• Improved anatomy of epsilon'/epsilon in the Standard Model
• Three-Loop Mixing of Dipole Operators
• Four-Loop Anomalous Dimensions for Radiative Flavour-Changing Decays
• Three-loop QCD corrections to B_s -> mu^+ mu^-
• Bound on minimal universal extra dimensions from Bbar -> X_s gamma
• Indirect probes of the trilinear Higgs coupling: $gg\to h$ and $h\to \gamma \gamma$
• Two-loop current-current operator contribution to the non-leptonic QCD penguin amplitude
• Analytic calculation of two-loop QCD corrections to b\to s\ell^+\ell^- in the high q^2 region
• The photon energy spectrum in B-> X_s + γin perturbative QCD through O(α_s^2)
• Radiative and Electroweak Penguin Decays of B Mesons
• QCD Corrections to Radiative B Decays in the MSSM with Minimal Flavor Violation
• Upper Bounds on Rare K and B Decays from Minimal Flavour Violation
• Exploring New Physics in the C7-C7' plane
• New Physics at a Super Flavor Factory
• Direct CP violation in $K^0\to \pi \pi$: Standard Model Status
• D-meson lifetimes within the heavy quark expansion
• NNLO vertex corrections in charmless hadronic B decays: Real part
• Probing the Flavour Structure of Supersymmetry Breaking With Rare B-Processes - A Beyond Leading Order Analysis
• Master formula for ${\epsilon }^{\prime }/\epsilon$ beyond the Standard Model
• Direct CP violation and the $\Delta I=1/2$ rule in $K\to \pi \pi$ decay from the Standard Model
• Towards $B\to V\gamma$ Decays at NNLO in SCET
• Two-body non-leptonic heavy-to-heavy decays at NNLO in QCD factorization
• NNLO fermionic corrections to the charm quark mass dependent matrix elements in B -> X_s gamma
• EOS -- A Software for Flavor Physics Phenomenology
• Singularity-free Next-to-leading Order $\Delta S=1$ Renormalization Group Evolution and ${\epsilon }_K^{\prime }/{\epsilon }_K$ in the Standard Model and Beyond
• The impact of flavour data on global fits of the MFV SMEFT
• $B\to K^{\ast }{\ell }^{+}{\ell }^{-}$ in soft-collinear effective theory
• Bayesian Fit of Exclusive $b\to s\bar{\ell }\ell$ Decays: The Standard Model Operator Basis
• Exclusive radiative B-meson decays within the aligned two-Higgs-doublet model
• The supersymmetric Higgs sector and B-Bbar mixing for large tan beta
• The electromagnetic dipole operator effect on B -> Xs gamma at O(alpha_s^2)
• Flavor Anomalies in Heavy Quark Decays
• Footprints of leptoquarks: from $R_{K^{(\ast )}}$ to $K\to \pi \nu \bar{\nu }$
• NNLL QCD Contribution of the Electromagnetic Dipole Operator to Gamma(anti-B -> X(s) gamma)
• A puzzle in ${\bar{B}}_{(s)}^0\to D_{(s)}^{(\ast )+}\{{\pi }^{-},K^{-}\}$ decays and extraction of the $f_s/f_d$ fragmentation fraction
• Magnetic dipole operator contributions to the photon energy spectrum in anti-B -> X(s) gamma at O(alpha(s)^2)
• B- -> pi- pi0/rho- rho0 to NNLO in QCD factorization
• Extracting short distance information from b -> s l+ l- effectively
• Exploiting dijet resonance searches for flavor physics
• Precise predictions for B -> Xs l+ l- in the large q^2 region
• Charm quark mass dependence of the electromagnetic dipole operator contribution to anti-B -> X(s) gamma at O(alpha**2(s))
• Lepton polarization asymmetries in rare semi-tauonic $b\to s$ exclusive decays at FCC-$ee$
• Anatomy of ${\epsilon }^{\prime }/\epsilon$ beyond the Standard Model
• Two- and three-loop anomalous dimensions of Weinberg's dimension-six CP-odd gluonic operator
• Isospin-Violating Contributions to ${\epsilon }^{\prime }/\epsilon$
• New Physics Patterns in ${\epsilon }^{\prime }/\epsilon$ and ${\epsilon }_K$ with Implications for Rare Kaon Decays and $\Delta M_K$
• Rates and Asymmetries of B --> pi l+ l- Decays
• Probing anomalous $t\bar{t}Z$ interactions with rare meson decays
• Implications for new physics from a novel puzzle in ${\bar{B}}_{(s)}^0\to D_{(s)}^{(\ast )+}\{{\pi }^{-},K^{-}\}$ decays
• Theoretical and experimental status of rare charm decays
• 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 $(m_c/m_b{)}^1$
• FCNC $B_s$ and ${\Lambda }_b$ transitions: Standard Model versus a single Universal Extra Dimension scenario
• Completing the Calculation of BLM corrections to B -> Xs gamma
• Fermionic corrections to the interference of the electro- and chromomagnetic dipole operators in anti-B --> X(s) gamma at O(alpha(s)**2)
• Radiative B decay spectrum: DGE at NNLO
• Disintegration of beauty: a precision study
• Anti-B --> X(s) gamma in two universal extra dimensions
• Chromomagnetic Dipole-Operator Corrections in Bbar -> X_sgamma at O(beta_0 alpha_s^2)
• Large-m_c Asymptotic Behaviour of O(alpha_s^2) Corrections to B -> X_s gamma
• Higher-order Wilson coefficients for c $\to$ u transitions in the Standard Model
• Phenomenology of inclusive $\bar{B}\to X_s{\ell }^{+}{\ell }^{-}$ for the Belle II era
• Flavour Theory: 2009
• Higher order QCD corrections in exclusive charmless B decays
• Penguin contribution to width difference and CP asymmetry in $B_q$-${\bar{B}}_q$ mixing at order ${\alpha }_s^2{N}_f$
• Disentangling QCD and New Physics in $D^{+}\to {\pi }^{+}{\ell }^{+}{\ell }^{-}$
• Two-loop non-leptonic penguin amplitude in QCD factorization
• Towards NNLO accuracy for ${\epsilon }^{\prime }/\epsilon$
• Amplitude analysis of the $B^0\to K^{\ast 0}{\mu }^{+}{\mu }^{-}$ decay
• Precision Global Determination of the $B\to X_s\gamma$ Decay Rate
• Radiative Decays of Charged Leptons in the Seesaw Effective Field Theory with One-loop Matching
• Standard Model evaluation of ${\epsilon }_K$ using lattice QCD inputs for ${\hat{B}}_K$ and $V_{cb}$
• Towards a Next-to-Next-to-Leading Order analysis of matching in $B^0$-${\bar{B}}^0$ mixing
• Factorization in B -> K pi e+e- decays
• ${\epsilon }_K^{\prime }/{\epsilon }_K$ and $K\to \pi \nu \bar{\nu }$ in a two-Higgs doublet model
• Constraining new physics with B to K* mu+ mu- in the early LHC era
• Reduction of Charm Quark Mass Scheme Dependence in $\bar{B}\to X_s\gamma$ at the NNLL Level
• Long distance effects in inclusive rare $B$ decays and phenomenology of $\bar{B}\to X_d{\ell }^{+}{\ell }^{-}$
• Renormalization and non-renormalization of scalar EFTs at higher orders
• NLO QCD Renormalization Group Evolution for Non-Leptonic $\Delta F=2$ Transitions in the SMEFT
• The width difference in the $B-\bar{B}$ system at next-to-next-to-leading order of QCD
• Complete (O_7,O_8) contribution to B -> X_s gamma at order alpha_s^2
• Electroweak Corrections to the Charm-Top-Quark Contribution to ${\epsilon }_K$
• Zooming in on $B\to K^{\ast }\ell \ell$ decays at low recoil
• Status of SM calculations of b > s transitions
• Effective electroweak Hamiltonian in the gradient-flow formalism
• Simple Rules for Evanescent Operators in One-Loop Basis Transformations
• Determination of short- and long-distance contributions in $B^0\to K^{\ast 0}{\mu }^{+}{\mu }^{-}$ decays
• Four-body contributions to B -> Xs gamma at NLO
• $B_{s,d}-{\bar{B}}_{s,d}$ mixings and $B_{s,d}\to {\ell }^{+}{\ell }^{-}$ decays within the Manohar-Wise model
• Dipole operators in Fierz identities
• Bounding the Minimal 331 Model through the Decay B -> X_s gamma
• Constraints on anomalous $tcZ$ coupling from $\bar{B}\to {\bar{K}}^{\ast }{\mu }^{+}{\mu }^{-}$ and $B_s\to {\mu }^{+}{\mu }^{-}$ decays
• Renormalization scheme factorization of one-loop Fierz identities
• Anomalous $tq\gamma$ coupling effects in exclusive radiative B-meson decays
• Next-to-Leading-Order QCD Matching for $\Delta F=2$ Processes in Scalar Leptoquark Models
• The LFU Ratio $R_{\pi }$ in the Standard Model and Beyond
• Predictions of Angular Observables for ${\bar{B}}_s\to K^{\ast }\ell \ell$ and $\bar{B}\to \rho \ell \ell$ in Standard Model
• Status of rare exclusive $B$ meson decays in 2018
• Theoretical status of ${\epsilon }^{\prime }/\epsilon$
• Renormalization-group equations of the LEFT at two loops: dimension-five effects
• Decay Rate Difference in the Neutral B-System: Delta Gamma Bs and Delta Gamma Bd
• $\Delta I=3/2$ and $\Delta I=1/2$ channels of $K\to \pi \pi$ decay at the physical point with periodic boundary conditions
• $B\to K{\eta }^{(\prime )}\gamma$ decays in the standard model and in scenarios with universal extra dimensions
• Study on pure annihilation type B to V gamma decays
• On the two-loop penguin contributions to the Anomalous Dimensions of four-quark operators
• Decay b -> (c\bar{c}) s in the leading logarithm approximation
• Selected Topics in Heavy Flavour Physics
• Renormalization-group equations of the LEFT at two loops: dimension-six operators
• Probing new physics in class-I $B$-meson decays into heavy-light final states
• Renormalisation group evolution for the $\Delta S=1$ effective Hamiltonian with $N_f=2+1$
• Semileptonic weak Hamiltonian to $\mathcal{O}(\alpha {\alpha }_s({\mu }_{\mathrm{Lattice}}))$ in momentum-space subtraction schemes
• Top-quark flavor-changing $tqZ$ couplings and rare $\Delta F=1$ processes
• Searching for New physics in Charm Radiative decays
• Improved analysis of the (O_7, O_7) contribution to $\bar{B}\to X_s\gamma \gamma$ at $O({\alpha }_s)$
• Magnetic-dipole corrections to $R_K$ and $R_{K^{\ast }}$ in the Standard Model and Dark Photon scenarios
• The Dual QCD @ Work
• QCD Corrections to the Radiative Decay B -> X_s gamma
• Charmless Non-Leptonic Multi-Body B decays
• Weak hamiltonian Wilson Coefficients from Lattice QCD
• Bounds on the compactification scale of two universal extra dimensions from exclusive $b\to s\gamma$ decays
• Towards a Global Analysis of the $b\to c\bar{u}q$ Puzzle
• Angular analysis of $B^0\to K^{\ast 0}{e}^{+}{e}^{-}$ decays
• Recent developments in radiative B decays
• Developments in the evaluation of m_c dependent matrix elements in B -> Xs gamma at NNLO
• Recent progress in decays of $b$ and $c$ hadrons
• General non-leptonic $\Delta F=1$ WET at the NLO in QCD
• Two-loop Electroweak Corrections to the Top-Quark Contribution to ${\epsilon }_K$
• Towards a non-perturbative calculation of Weak Hamiltonian Wilson coefficients
• The width difference in the $B_s$-${\bar{B}}_s$ system: towards NNLO
• Kaon Flavour Physics Strikes Back
• The Revival of Kaon Flavour Physics
• Kaon physics overview
• Isospin-breaking contributions to ${\epsilon }^{\prime }/\epsilon$
• The electroweak Hamiltonian in the gradient flow formalism
• Re-evaluation of the isoscalar mixing angle within selected mesonic nonets
• Complete next-to-next-to-leading order QCD corrections to the decay matrix in $\mathbf{B}$-meson mixing at leading power
• Investigating non-local contributions in $B_s\to \varphi \bar{\ell }\ell$ including higher-twist effects
• Non-leptonic B-decays at two loops in QCD Factorization
• Estimating QCD-factorization amplitudes through $SU(3)$ symmetry in $B\to PP$ decays
• The gradient flow formulation of the electroweak Hamiltonian
• Multi-parton contributions to $\bar{B}\to X_s\gamma$ at NLO
• The Optimal Strategy for ${\epsilon }^{\prime }/\epsilon$ in the SM: 2019