epsilon'/epsilon at the NLO: 10 Years Later

Abstract

During the last four years several parameters relevant for the analysis of the CP-violating ratio epsilon'/epsilon improved and/or changed significantly. In particular, the experimental value of epsilon'/epsilon and the strange quark mass decreased, the uncertainty in the CKM factor has been reduced, and for a value of the hadronic matrix element of the dominant electroweak penguin operator Q_8, some consensus has been reached among several theory groups. In view of this situation, ten years after the first analyses of epsilon'/epsilon at the next-to-leading order, we reconsider the analysis of epsilon'/epsilon within the SM and investigate what can be said about the hadronic Q_6 matrix element of the dominant QCD penguin operator on the basis of the present experimental value of epsilon'/epsilon and todays values of all other parameters. Employing a conservative range for the reduced electroweak penguin matrix element R_8=1.0+-0.2 from lattice QCD, and present values for all other input parameters, on the basis of the current world average for epsilon'/epsilon, we obtain the reduced hadronic matrix element of the dominant QCD penguin operator R_6=1.23+-0.16 implying <Q_6>_0^NDR(m_c) ~ -0.8 <Q_8>_2^NDR(m_c). We compare these results with those obtained in large-N_c approaches in which generally R_6 ~ R_8 and <Q_6>_0^NDR(m_c) is chirally suppressed relatively to <Q_8>_2^NDR(m_c). We present the correlation between R_6 and R_8 that is implied by the data on epsilon'/epsilon provided new physics contributions to epsilon'/epsilon can be neglected.

arXiv comment18 pages, 1 eps figure, version to appear in JHEP

References in corpus (44)

• The $\Delta S=1$ Effective Hamiltonian Including Next-to-Leading Order QCD and QED Corrections
• Observation of Direct CP Violation in K_{S,L} to ππDecays
• The Anatomy of ${\epsilon }^{\prime }/\epsilon$ Beyond Leading Logarithms with Improved Hadronic Matrix Elements
• The Two-Loop Anomalous Dimension Matrix for $\Delta S=1$ Weak Non-Leptonic Decays I: $\mathcal{O}({\alpha }_s^2)$
• Two--Loop Anomalous Dimension Matrix for $\Delta S=1$ Weak Non-Leptonic Decays II: $\mathcal{O}({\alpha }_e{\alpha }_s)$
• A precision measurement of direct CP violation in the decay of neutral kaons into two pions
• Flavour-symmetry breaking of the quark condensate and chiral corrections to the Gell-Mann-Oakes-Renner relation
• ${\epsilon }^{\prime }/\epsilon$ at the next-to-leading order in QCD and QED
• Measurements of Direct CP Violation, CPT Symmetry, and Other Parameters in the Neutral Kaon System
• Strong Enhancement of ${\epsilon }^{\prime }/\epsilon$ Through Final State Interactions
• A precise measurement of the direct CP violation parameter Re(epsilon'/epsilon)
• Kaon Matrix Elements and CP-violation from Quenched Lattice QCD: (I) the 3-flavor case
• epsilon'/epsilon and Rare K and B Decays in the MSSM
• Estimating epsilon'/epsilon. A Review
• Determination of m_s and |V_us| from hadronic tau decays
• The Standard Model Prediction for epsilon'/epsilon
• Isospin violation in epsilon'
• Light quark masses from scalar sum rules
• Matching the Electroweak Penguins $Q_7$, $Q_8$ and Spectral Correlators
• Decay constants, light quark masses and quark mass bounds from light quark pseudoscalar sum rules
• Standard Model Confronting New Results for epsilon'/epsilon
• Strange Quark Mass from the Invariant Mass Distribution of Cabibbo-Suppressed Tau Decays
• epsilon'/epsilon in the Chiral Limit
• Improved Determination of the Electroweak Penguin Contribution to epsilon'/epsilon in the Chiral Limit
• Final State Interactions in Kaon Decays
• Delta I=1/2 and epsilon'/epsilon in Large-Nc QCD
• pi^0-eta Mixing and CP Violation
• Analysis of ε'/εin the 1/N_c Expansion
• 1/N_c Corrections to the Hadronic Matrix Elements of Q_6 and Q_8 in K --> pi pi Decays
• New QCD estimate of the kaon penguin matrix elements and epsilon'/epsilon
• An updated analysis of eps'/eps in the standard model with hadronic matrix elements from the chiral quark model
• A Critical Reassessment of Q7 and Q8 Matrix Elements
• Chiral Effective Lagrangian and Quark Masses
• A short look at epsilon'/epsilon
• Final State Interactions and epsilon'/epsilon: A Critical Look
• Theoretical status of epsilon'/epsilon
• An Analytic Formula and an Upper Bound for epsilon'/epsilon in the Standard Model
• A note on the dispersive treatment of K -> pi pi with the kaon off-shell
• What is the (epsilon'/epsilon)_exp Telling Us ?
• The Strong Isospin-Breaking Correction for the Gluonic Penguin Contribution to epsilon'/epsilon at Next-to-Leading Order in the Chiral Expansion
• Chiral Limit Prediction for epsilon'/epsilon at NLO in 1/N_c
• Kaon Weak Matrix Elements with Wilson Fermions
• Calculation of $K\to \pi \pi$ decay amplitudes from $K\to \pi$ matrix elements in quenched domain-wall QCD
• On the strange quark mass with improved staggered quarks

Cited by in corpus (40)

• CP Violation and the CKM Matrix: Assessing the Impact of the Asymmetric B Factories
• Kaon Decays in the Standard Model
• General CP Violation in Minimal Left-Right Symmetric Model and Constraints on the Right-Handed Scale
• Anatomy of Prominent B and K Decays and Signatures of CP-Violating New Physics in the Electroweak Penguin Sector
• Anatomy of New Physics in B-Bbar mixing
• On epsilon_K beyond lowest order in the Operator Product Expansion
• Correlations among new CP violating effects in Delta F = 2 observables
• Lattice QCD inputs to the CKM unitarity triangle analysis
• Precise Measurements of Direct CP Violation, CPT Symmetry, and Other Parameters in the Neutral Kaon System
• $K\to \pi \pi$ $\Delta I=3/2$ decay amplitude in the continuum limit
• Flavor Physics in the Randall-Sundrum Model: II. Tree-Level Weak-Interaction Processes
• Quark flavour observables in the Littlest Higgs model with T-parity after LHC Run 1
• $K\to \pi \nu \bar{\nu }$ and ${\epsilon }^{\prime }/\epsilon$ in Simplified New Physics Models
• Z-Z' Mixing and Z-Mediated FCNCs in SU(3)_C x SU(3)_L x U(1)_X Models
• Lattice determination of the $K\to (\pi \pi {)}_{I=2}$ Decay Amplitude $A_2$
• Patterns of Flavour Violation in the Presence of a Fourth Generation of Quarks and Leptons
• Direct CP violation in $K^0\to \pi \pi$: Standard Model Status
• Enhanced KL to pi0 nu nubar from Direct CP Violation in B to K pi with Four Generations
• Radiative Kaon Decays and the Penguin Contribution to the Delta I = 1/2 Rule
• On the consistency between the observed amount of CP violation in the K- and Bd-systems within minimal flavor violation
• Matching factors for Delta S=1 four-quark operators in RI/SMOM schemes
• New Physics Patterns in ${\epsilon }^{\prime }/\epsilon$ and ${\epsilon }_K$ with Implications for Rare Kaon Decays and $\Delta M_K$
• $K\to \pi \nu \overline{\nu }$ in the MSSM in Light of the ${\epsilon }_K^{\prime }/{\epsilon }_K$ Anomaly
• CP Violation and Flavor Mixing in Technicolor Theories
• Correlations between epsilon'/epsilon and Rare K Decays in the Littlest Higgs Model with T-Parity
• Analysis of the semileptonic (B_c -> B_u* l+ l-) decay from QCD sum rules
• Small violations of unitarity, the phase in Bs mixing and visible t->cZ decays at the LHC
• New physics in ε' from chromomagnetic contributions and limits on Left-Right symmetry
• An exploratory lattice study of DI=3/2 K -> pi pi decays at next-to-leading order in the chiral expansion
• CP violation and the 4th generation
• The s ---> d gamma decay in and beyond the Standard Model
• Emerging lattice approach to the K-Unitarity Triangle
• Solving the SUSY CP problem with flavor breaking F-terms
• Scherk-Schwarz Supersymmetry Breaking for Quasi-localized Matter Fields and Supersymmetry Flavor Violation
• $K\to \pi {\ell }^{+}{\ell }^{-}$ form factor in the Large-N${}_c$ and cut-off regularization method
• Direct CP Violation in K-decay and Minimal Left-Right Symmetry Scale
• Kaon weak interactions in powers of 1/Nc
• Vector Meson Contributions in epsilon'/epsilon
• Chiral loop corrections and isospin violation effects in epsilon'/epsilon
• Chiral Logarithms in $\Delta S=1$ Kaon Decay Amplitudes in General Effective Flavor Theories