Novel Development of Research of the Standard Model on the Lattice using the Massively Parallel Computer CP-PACS

这项工作旨在利用筑波大学开发的大规模并行计算机CP-PACS阐明基于晶格QCD的强相互作用的本质。在本赠款援助的三年期间取得的主要成果如下：用畴壁费米子形式计算弱矩阵元。利用畴壁费米子作用良好的手性，在1/a=2 GeV和3GeV条件下，利用rg改进的规范作用对kaon B参数进行了评价。结果显示只有很小的尺度违规，并且使用微扰重整化因子，我们得到B_k(2G_eV)=0.5746(61)(191)，与之前使用KS形式的最佳估计B_k(2G_eV)=0.628（41）进行比较。另一个要解决的问题是K→π π衰减幅度。利用K→π π与K→π振幅的手性摄动理论公式，我们发现：I=2振幅的实部与实验一致，而I=0振幅的实部只有物理的一半左右。因此theΔI=0 = 1/2增强只是实验的一半。Ii)虚部也表现出I=0幅值过小的相似特征；因此直接CP违背参数e'/e=-1x10^<-4>为负且太小。这些令人不满意的结果的起因需要澄清。各向异性晶格上的晶格QCD时空各向异性晶格在各种情况下都很有用，包括重夸克强子和有限温度QCD的计算。采用各向异性淬火晶格进行了夏蒙光谱和状态方程研究。为了推进各向异性晶格在全QCD中的应用，首次尝试确定了两种风味全QCD作用的各向异性参数。小夸克质量和手性行为在今天的晶格QCD计算中，手性外推是最不确定的外推。在1/a=1GeV的粗晶格间距下，将夸克质量降低到m_n/m_p=0.4。与低至m_n/m_p=0.6的模拟相比，手性极限的物理预测相差约10%。HMC算法还产生了一种不稳定性，并对其来源进行了研究。Nf=2+1全QCD模拟的准备真正真实的QCD模拟需要包括奇异夸克的动力学效应。我们证明了多项式HMC算法适合于此目的。为了使用rg改进的动作对Nf=2+1进行完全O(a)改进的模拟，确定了Nf=3理论的三叶草系数。研究结果将用于结合上、下、奇夸克海夸克效应的Nf=2+1全QCD模拟。少

This work aimed to elucidate the nature of strong interactions based on lattice QCD using the massively parallel computer CP-PACS developed at University of Tsukuba. The main results achieved over the three year period of the present Grant-in-aid are as follows :1. Calculation of weak matrix elements using the domain wall fermion formalism.Taking advantage of the good chiral property of the domain wall fermion action, the kaon B parameter was evaluated using RG-improved gauge action at 1/a=2 GeV and 3GeV. The results showed only small scaling violations, and using perturbative renormalization factor, we obtained B_k(2G_eV)=0.5746(61)(191), to be compared with the previous best estimate using the KS formalism : B_k(2G_eV)=0.628(41).Another problem addressed is K→π π decay amplitudes. Using chiral perturbation theory formuli which relates K→π π to K→π amplitudes, we found the following : I) The real part of the I=2 amplitude is consistent with experiment, while that of the I=0 amplitude … More is only about half of the physical one. Thus theΔI=0 = 1/2 enhancement is only half of experiment. Ii) The imaginary Part exhibits a similar feature that the I=0 amplitude is too small ; consequently the direct CP violation parameter e'/e=-1x10^<-4> is negative and too small. The origin of these unsatisfactory results needs to be clarified.2. Lattice QCD on anisotropic latticesSpace-time anisotropic lattices are useful in a variety of contexts including calculations of heavy quark hadrons and finite-temperature QCD. Charmonium spectroscopy and equation of state studies were made using quenched anisotropic lattices. To advance the use of anisotropic lattices in full QCD, first attempt to determine the anisotropy parameters of the action was made for two flavor full QCD.3. Small quark mass and chiral behaviorChiral estrapolation is the most uncertain of the extrapolations in today's lattice QCD calculations. Simulations reducing the quark mass as small as m_n/m_p=0.4 were attempted at a coarse lattice spacing of 1/a=1GeV. Compared to simulations down to m_n/m_p=0.6, physical predictions in the chiral limit differ by about 10%. The HMC algorithm also develop an instability whose origin was investigated.4. Preparations toward Nf=2+1 full QCD simulationsTruly realistic simulations of QCD requires including dynamical effects of strange quark. We showed that the polynomial HMC algorithm is suitable for this purpose. To carry out a fully O(a) improved simulation for Nf=2+1 using the RG-improved action, the clover coefficient for Nf=3 theory was determined. The results will be used to carry out Nf=2+1 full QCD simulations which incorporates dynamical sea quark effects of up, down and strange quark. Less