Matching the Electroweak Penguins $Q_7$, $Q_8$ and Spectral Correlators

Abstract

Exact analytical expressions for the $\Delta S=1$ coupling $\im G_E$ in terms of observable spectral functions are given. This coupling determines the size of the $\Delta I=3/2$ contribution to ${\epsilon }^{\prime }$. We show analytically how the scheme-dependence and scale dependences vanish to all orders in $1/N_c$ and NLO in ${\alpha }_S$ explicitly both for $Q_7$ and $Q_8$. Numerical results are derived for both $Q_7$ and $Q_8$ from the $\tau$-data and known results on the scalar spectral functions. In particular we study the effect of all higher dimension operators. The coefficients of the leading operators in the OPE of the needed correlators are derived to NLO in ${\alpha }_S$.

38 pages, JHEP.cls,Changes: mistake in the calculations of the OPE coefficients corrected, numerical results: OPAL data discussed more extensively and analysis of ALEPH data extended and comparison with earlier work rewritten

Cited by in corpus (68)

• CP Violation and the CKM Matrix: Assessing the Impact of the Asymmetric B Factories
• Kaon Decays in the Standard Model
• Precision Tau Physics
• The Physics of Hadronic Tau Decays
• Anatomy of Prominent B and K Decays and Signatures of CP-Violating New Physics in the Electroweak Penguin Sector
• Mesonic low-energy constants
• Flavor Physics in the Randall-Sundrum Model: II. Tree-Level Weak-Interaction Processes
• Duality violations and spectral sum rules
• Chiral dynamics in form factors, spectral-function sum rules, meson-meson scattering and semilocal duality
• A Rational Approach to Resonance Saturation in large-Nc QCD
• V-A hadronic tau decays : a laboratory for the QCD vacuum
• Unraveling duality violations in hadronic tau decays
• QCD Short-distance Constraints and Hadronic Approximations
• Direct CP violation in $K^0\to \pi \pi$: Standard Model Status
• Delta I=1/2 and epsilon'/epsilon in Large-Nc QCD
• QCD Condensates for the Light Quark V-A Correlator
• Improved Determination of the Electroweak Penguin Contribution to epsilon'/epsilon in the Chiral Limit
• K^0-\bar K^0 mixing beyond the standard model and CP-violating electroweak penguins in quenched QCD with exact chiral symmetry
• Neural network parametrization of spectral functions from hadronic tau decays and determination of QCD vacuum condensates
• Determination of the Chiral Couplings L_10 and C_87 from Semileptonic Tau Decays
• Possible duality violations in tau decay and their impact on the determination of alpha_s
• Finite energy chiral sum rules in QCD
• Determination of <2pi_{I=2}|Q_{7,8}|K0> in the Chiral Limit
• epsilon'/epsilon at the NLO: 10 Years Later
• S-parameter and pseudo-Nambu-Goldstone boson mass from lattice QCD
• Chiral Condensates, Q_7 and Q_8 Matrix Elements and Large-N_c QCD
• Pinched weights and Duality Violation in QCD Sum Rules: a critical analysis
• Violation of Quark-Hadron Duality and Spectral Chiral Moments in QCD
• Chiral condensates from tau decay: a critical reappraisal
• Updated determination of chiral couplings and vacuum condensates from hadronic tau decay data
• New Physics Patterns in ${\epsilon }^{\prime }/\epsilon$ and ${\epsilon }_K$ with Implications for Rare Kaon Decays and $\Delta M_K$
• Isospin-Violating Contributions to ${\epsilon }^{\prime }/\epsilon$
• Upper Bounds on epsilon'/epsilon Parameters B_6^{(1/2)} and B_8^{(3/2)} from Large N QCD and other News
• Anomalous $A{V}^{\ast }V$ vertex function in the soft-wall holographic model of QCD
• Operator Product Expansion with analytic QCD in tau decay physics
• Correlations between epsilon'/epsilon and Rare K Decays in the Littlest Higgs Model with T-Parity
• Remarks on the hadronic matrix elements relevant to the SUSY K-Kbar mixing amplitude
• Low-energy constants and condensates from the tau hadronic spectral functions
• Spin-1 Correlators at Large NC: Matching OPE and Resonance Theory up to O(alpha_s)
• Charged Kaon K \to 3 pi CP Violating Asymmetries at NLO in CHPT
• Non-factorization of four-quark condensates at low energies within Chiral Perturbation Theory
• An exploratory lattice study of DI=3/2 K -> pi pi decays at next-to-leading order in the chiral expansion
• Analytic Approaches to Kaon Physics
• QCD Description of Hadronic Tau Decays
• The Strange Quark Mass, alpha_s and the Chiral Limit Electroweak Penguin Matrix Elements From Hadronic Tau Decay Data
• V-A sum rules with D=10 operators
• A joint analysis of the S-wave in the pi+pi- and pi0pi0 data
• SU(3) analysis of four-quark operators: $K\to \pi \pi$ and vacuum matrix elements
• Comment on `Analysis of O(p^2) Corrections to <2pi|Q_{7,8}|K>'
• The $B_K$ Kaon Parameter in the Chiral Limit
• QCD condensates from tau-decay data: A functional approach
• QCD condensates of dimension D=6 and D=8 from hadronic tau-decays
• Relations between vacuum condensates and low energy parameters from a rational approach
• Weinberg like sum rules revisited
• Perturbative QCD in acceptable schemes with holomorphic coupling
• Hadronic Matrix Elements for Kaons
• Matching the Electroweak Penquins Q_7 and Q_8
• The neural network approach to parton distribution functions
• Isospin symmetry breaking and the neutron-proton mass difference
• Electroweak penguins and SUSY K^0-\bar K^0 mixing with Neuberger quarks
• Estimate of the systematic error in tau decay due to duality violations
• Contribution from Duality Violations to the theoretical error on alpha_s
• Kaon weak interactions in powers of 1/Nc
• Duality violation in QCD Sum Rules with the LR correlator
• From hadronic tau decays to the chiral couplings L_10 and C_87
• Chiral loop corrections and isospin violation effects in epsilon'/epsilon
• K -> pi pi Electroweak Penguins in the Chiral Limit
• Impact of Duality Violations on Spectral Sum Rule Analyses