New Analysis of the Delta I = 1/2 Rule in Kaon Decays and the B_K Parameter

Abstract

We present a new analysis of the Delta I = 1/2 rule in K --> pi pi decays and the B_K parameter. We use the 1/N_c expansion within the effective chiral lagrangian for pseudoscalar mesons and compute the hadronic matrix elements at leading and next-to-leading order in the chiral and the 1/N_c expansions. Numerically, our calculation reproduces the dominant Delta I = 1/2 K --> pi pi amplitude. Our result depends only moderately on the choice of the cutoff scale in the chiral loops. The Delta I = 3/2 amplitude emerges sufficiently suppressed but shows a significant dependence on the cutoff. The B_K parameter turns out to be smaller than the value previously obtained in the 1/N_c approach. It also shows a significant dependence on the choice of the cutoff scale. Our results indicate that corrections from higher order terms and/or higher resonances are large for the Delta I = 3/2 K --> pi pi amplitude and the (|Delta S| = 2) K^0 -- anti K^0 transition amplitude.

50 pages, LaTeX, 13 eps figures

Cited by in corpus (28)

• Kaon Decays in the Standard Model
• The Standard Model Prediction for epsilon'/epsilon
• CP Violation in the B System and Relations to $K\to \pi \nu \bar{\nu }$ Decays
• K0-anti-K0 mixing in the 1/Nc expansion
• Standard Model Confronting New Results for epsilon'/epsilon
• Final State Interactions in Kaon Decays
• Delta I=1/2 and epsilon'/epsilon in Large-Nc QCD
• 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
• Analysis of ε'/εin the 1/N_c Expansion
• Combined analysis of the unitarity triangle and CP violation in the Standard Model
• Dispersion relations and soft pion theorems for K -> pi pi
• A New Approach to Weak Amplitudes in Large-Nc QCD
• Strong Isospin-Breaking Effects in K-->pi pi at Next-to-Leading Order in the Chiral Expansion
• A New Prediction for Direct CP Violation ε'/εand ΔI = 1/2 Rule
• The Impact of |Delta I|=5/2 Transitions in K-> pi pi Decays
• SU(3) analysis of four-quark operators: $K\to \pi \pi$ and vacuum matrix elements
• The Strong Isospin-Breaking Correction for the Gluonic Penguin Contribution to epsilon'/epsilon at Next-to-Leading Order in the Chiral Expansion
• epsilon'/epsilon in the Standard Model
• CKM matrix and CP violation in B-mesons
• Instantons and the $\Delta I=1/2$ Rule
• Chiral perturbation theory, dispersion relations and final state interactions in K -> pi pi
• B_K in the chiral limit within the 1/Nc expansion
• Penguins diagrams in Delta I=1/2 rule and ε'/εwith σmodels
• Study of Kaon Decay to Two Pions
• Final State Interactions and eps'/eps
• Theoretical status of epsilon'/epsilon
• The Influence of Dimension Eight Operators on Weak Matrix Elements