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

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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