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

这项工作的目的是阐明强相互作用的性质的格子QCD使用的大规模并行计算机CP-PACS筑波大学开发的。本项目实施三年来取得的主要成果如下：1.利用畴壁费米子作用量的良好手征性质，在1/a= 2GeV和3GeV下，用RG改进的规范作用量计算了K介子B参数.计算结果表明，K→π π衰变的振幅是一个小的标度破坏，利用微扰重整化因子，我们得到了B_k（2G_eV）=0.5746（61）（191），并与以前用KS方法得到的最佳估计值：B_k（2G_eV）=0.628（41）进行了比较。利用手征微扰理论中K→π π与K→π振幅的关系式，我们发现：I）I=2振幅的真实的部分与实验相符，而I=0振幅的实部与实验相符 ...更多信息 只有物理量的一半因此，ΔI=0 = 1/2的增强仅为实验的一半。Ii）虚部表现出类似的特征，即I=0幅度太小;因此直接CP破坏参数e '/e=-1x10 ^<-4>为负且太小。这些不令人满意的结果的根源需要澄清。时空各向异性格点在包括重夸克强子和有限温度QCD计算在内的各种背景下都很有用。利用淬冷各向异性晶格进行了粲正离子光谱和状态方程的研究。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味全QCD作用量的各向异性参数。小夸克质量与手征行为手征外推是目前格点QCD计算中最不确定的外推。在1/a=1GeV的粗格点间距下，对夸克质量减小到m_n/m_p=0.4进行了模拟。在手征极限下的物理预测与m_n/m_p=0.6的模拟结果相差约10%。HMC算法也出现了不稳定性，并对其原因进行了分析.为Nf=2+1的QCD模拟做准备真正真实的QCD模拟需要考虑奇异夸克的动力学效应。我们表明，多项式HMC算法是适合于这个目的。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。这些结果将用于进行Nf=2+1的全QCD模拟，其中包括上夸克、下夸克和奇异夸克的动力学海夸克效应。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