Scheme Dependence of Weak Matrix Elements in the $1/N_c$ Expansion

Abstract

We show how the scheme- and scale-dependence of the short-distance operator product expansion with four-quark operators can be correctly accounted for in the framework of the $1/N_c$-expansion once the hadronization of two-quark currents has been fixed. We show formulas explicitly in the case of the $B_K$-parameter. We then use them with our earlier estimates of the long-distance effects. We compare Chiral Perturbation Theory at Leading- and Next-to-Leading-Order with the ENJL model results in the chiral limit. Good matching between the long- and short-distance regimes is obtained and our final value for the physical scheme independent ${\hat{B}}_K$ is $0.77\pm 0.05\pm 0.05$.

20 pages, use JHEP.cls and axodraw.sty; small error detected, numerical results changed with about quoted error

Cited by in corpus (25)

• Kaon Decays in the Standard Model
• Mesonic low-energy constants
• CP Violation in the B System and Relations to $K\to \pi \nu \bar{\nu }$ Decays
• QCD Short-distance Constraints and Hadronic Approximations
• Final State Interactions in Kaon Decays
• Four-point functions and kaon decays in a minimal AdS/QCD model
• Constraining models with vector-like fermions from FCNC in K and B physics
• K^0-\bar K^0 mixing beyond the standard model and CP-violating electroweak penguins in quenched QCD with exact chiral symmetry
• Impact of the finite volume effects on the chiral behavior of fK and BK
• Kaon B Parameter in Quenched QCD
• An updated analysis of eps'/eps in the standard model with hadronic matrix elements from the chiral quark model
• Unquenched determination of the kaon parameter B_K from improved staggered fermions
• Long-distance dimension-eight operators in B_K
• Correlators of left charges and weak operators in finite volume chiral perturbation theory
• B_K from quenched QCD with exact chiral symmetry
• Theoretical status of epsilon'/epsilon
• Analytic Approaches to Kaon Physics
• A New Prediction for Direct CP Violation ε'/εand ΔI = 1/2 Rule
• The $B_K$ Kaon Parameter in the Chiral Limit
• Chiral Limit Prediction for epsilon'/epsilon at NLO in 1/N_c
• Lattice Matrix Elements and CP Violation in B and K Physics: Status and Outlook
• Hadronic Matrix Elements for Kaons
• Matching the Electroweak Penquins Q_7 and Q_8
• Kaon weak interactions in powers of 1/Nc
• Kaon Decays from AdS/QCD