Calculations of Kaon electro - weak matrix elements in lattice QCD

树世代标准模型中的Kobayashi-Maskawa矩阵可以导致直接CP破坏，这在最近的实验中已经被测量到。为了证实所观测到的CP运动是否确实可以用标准模型的Kobyashi-Maskawa矩阵来解释，必须对K介子电弱矩阵元进行非微扰计算。在本研究中，我利用格点QCD的数值模拟计算了与CP破坏相关的K介子电弱矩阵元。在这样的计算中，重要的是保持手征对称性，然而，由于费米子加倍问题，手征对称性在以前的晶格计算中被明确打破。利用最近提出的畴壁费米子，在计算中保持了手征对称性。K介子在晶格上衰变到2皮欧也是很难处理的。我利用手征微扰理论把K到2 π介子矩阵元与K到π介子矩阵元联系起来，这在格点上更容易计算。在这项研究中，我得到了以下结果。(1)在连续极限下，精确地计算了与K ~+的CP破坏有关的K ~+ B参数。(2)微扰计算了K介子电弱矩阵元所需的重整化因子。在畴壁费米子的情况下，也提出了非微扰的重整化因子方法。(3)本文用非微扰方法研究了畴壁费米子的手征性质。(4)数值计算了与K介子衰变直接CP破坏有关的矩阵元。

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.