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The low energy dynamics of QCD is investigated with special attention paid tothe matching between QCD and chiral perturbation theory(ChPT), and also to someuseful algebraic chiral operator relations which survive even when we includechiral loop corrections. It then allows us to evaluate the hadronic matrixelements below the energy scale $\Lambda_{\chi} \simeq 1$ GeV. Based on the newanalyzes, we present a consistent prediction for both direct CP-violatingparameter $\epsilon'/\epsilon$ and $\Delta I =1/2$ rule in the kaon decays. Inthe leading $1/N_c$ approximation, the isospin amplitudes $A_0$ and $A_2$ arefound to agree well with the data, and the direct CP-violating parameter$\epsilon'/\epsilon$ is predicted to be large, which also confirms our earlyconclusion. Its numerical value is $\epsilon'/\epsilon =23.6^{+12.4}_{-7.8}\times 10^{-4}(Im\lambda_t/1.2\times 10^{-4})$ which is nolonger sensitive to the strange quark mass due to the matching conditions.Taking into account a simultaneous consistent analysis on the isospinamplitudes $A_0$ and $A_2$, the ratio $\epsilon'/\epsilon$ is in favor of thevalues $\epsilon'/\epsilon = (20\pm 9)\times 10^{-4}$.Comment: 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 adde

physical review. d. particles, fields, gravitation, and cosmology/physical review. d. particles and fields

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