Calculations of Kaon electro - weak matrix elements in lattice QCD

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The Kobayashi-Maskawa matrix in the standard model with tree generations can induce the direct CP violation, which has been measured in the recent expeminents. To confirm if the observe CP viloation is indeed explained by the standard model with the Kobyashi-Maskawa matrix, the K meson electro-weak matrix elements must be non-perturbatively evaluated. In this research, I have calculated the K meson electro-weak matrix elements relevant for the CP violation, using numerical simulations of lattice QCD. In such calculations it it important to keep the chral symmetry, which was however explicitly broken in the previous lattice calculations due to the fermion doubling problem. By using the domain-wall fermions recently proposed, I can keep the chiral symmetry in the calculation. It is also difficult to treat the decay of K meson to 2 piohs on the lattice. I employed the chiral perturbation theory to connect the K to 2 pions matrix elements with those of the K to pi, which can be calulated more easily on the lattice. In this research I obtained the following results. (1) The Kaon B paramters, related to the indirect CP violation of Kaon, has been precisely evaluated in the continuum limit. (2) The renormalization factors necessary for the Kaon electro-weak matrix elements have been calculated perturbatively. The non-perturbative mehod for the renormalization factors has also been proposed in the case of the domain-wall fermion. (3) The chiral properties of the domain-wall fermion has been investigated non-perturbatiyely. (4) The matrix elements relevant for the direct CP violation of the Kaon decays have been calculated numerically.