Calculations of Kaon electro - weak matrix elements in lattice QCD

树代标准模型中的Kobayashi-Maskawa矩阵可以引起直接CP违背，这在最近的实验中已经被测量到。为了确认观测到的CP波动是否确实可以用Kobyashi-Maskawa矩阵的标准模型来解释，必须对K介子电弱矩阵元素进行非摄动评估。在本研究中，我利用晶格QCD的数值模拟计算了与CP违背相关的K介子电弱矩阵元素。在这样的计算中，保持chral对称性是很重要的，然而在之前的晶格计算中，由于费米子加倍问题，chral对称性被明确地打破了。利用最近提出的畴壁费米子，可以保持计算中的手性对称性。在晶格上处理K介子衰减到2 piohs也很困难。我使用手性微扰理论将K到2 π π的矩阵元素与K到π的矩阵元素连接起来，这可以更容易地在晶格上计算。在这项研究中，我得到了以下结果。(1)与Kaon的间接CP违背有关的Kaon B参数在连续体极限下得到了精确的评价。(2)对Kaon电弱矩阵元素的重整化因子进行了微扰计算。对于畴壁费米子，也提出了重整化因子的非摄动方法。(3)对畴壁费米子的手性进行了非摄动研究。(4)用数值方法计算了与Kaon衰变直接CP破坏相关的矩阵元。

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.