A New Prediction for Direct CP Violation ε'/εand ΔI = 1/2 Rule

Abstract

The low energy dynamics of QCD is investigated with special attention paid to the matching between QCD and chiral perturbation theory(ChPT), and also to some useful algebraic chiral operator relations which survive even when we include chiral loop corrections. It then allows us to evaluate the hadronic matrix elements below the energy scale ${\Lambda }_{\chi }\simeq 1$ GeV. Based on the new analyzes, we present a consistent prediction for both direct CP-violating parameter ${\epsilon }^{\prime }/\epsilon$ and $\Delta I=1/2$ rule in the kaon decays. In the leading $1/N_c$ approximation, the isospin amplitudes $A_0$ and $A_2$ are found to agree well with the data, and the direct CP-violating parameter ${\epsilon }^{\prime }/\epsilon$ is predicted to be large, which also confirms our early conclusion. Its numerical value is ${\epsilon }^{\prime }/\epsilon =23.6_{-7.8}^{+12.4}\times 10^{-4}(Im{\lambda }_t/1.2\times 10^{-4})$ which is no longer sensitive to the strange quark mass due to the matching conditions. Taking into account a simultaneous consistent analysis on the isospin amplitudes $A_0$ and $A_2$, the ratio ${\epsilon }^{\prime }/\epsilon$ is in favor of the values ${\epsilon }^{\prime }/\epsilon =(20\pm 9)\times 10^{-4}$.

19 pages, ReVtex, no figures, the corrected version to be published in Phys. Rev. D . A more favorable and consistent prediction for direct CP violation is found: epsilon'(prime) /epsilon = (20 \pm 9) x 10^-4, here the contributions from finite meson masses and new isospin symmetry breaking effects have been included. The uncertainties from QCD (or low energy) scale have been considered. More references are added

Cited by in corpus (14)

• Precise Measurements of Direct CP Violation, CPT Symmetry, and Other Parameters in the Neutral Kaon System
• Measurements of Direct CP Violation, CPT Symmetry, and Other Parameters in the Neutral Kaon System
• The Standard Model Prediction for epsilon'/epsilon
• Symmetry Principle Preserving and Infinity Free Regularization and renormalization of quantum field theories and the mass gap
• Implications of Charmless B Decays with Large Direct CP Violation
• Symmetry-preserving Loop Regularization and Renormalization of QFTs
• Implicit Regularization and Renormalization of QCD
• Two Higgs Bi-doublet Left-Right Model With Spontaneous P and CP Violation
• What is the (epsilon'/epsilon)_exp Telling Us ?
• Exclusive $B\to PV$ Decays and CP Violation in the General two-Higgs-doublet Model
• Large Strong Phases and CP Violation in the Annihilation Processes ${\bar{B}}^0\to K^{+}{K}^{-}$, $K^{\ast \pm }{K}^{\mp }$, $K^{\ast +}{K}^{\ast -}$
• Instantons and the $\Delta I=1/2$ Rule
• The s-d Transition in Heavy Mesons
• Vector Meson Contributions in epsilon'/epsilon