NUMERICAL STUDY OF LATTICE QUANTUM CHROMODYNAMICS

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Numerical simulations of lattice QCD provides a viable method for determination of the strong interaction corrections to weak amplitudes of hadrons, which is crucial for elucidating unsolved problems of weak interactions of elementary particles including the origin of CP violation. The objective of the present research is to carry out a systematic study of lattice QCD in this direction.In 1994 we applied the method of wall source without gauge fixing, previously developed by us, to the problem of pi-N sigma term and the quark content of proton spin. Both these matrix elements receive contributions from sea quark loops, and how one can evaluate these contributions represents a general problem that also appear in weak matrix element calculations. We found that the method works well, and that the values obtained are consistent with experiments, strongly indicating for the first time that QCD successfully explains the values of these observables long debated in particle theory.In the same … More year we also started preparations for Fujitsu VPP500/80 vector parallel supercomputer, which was scheduled to be installed at KEK in January 1995. A variety of lattice QCD codes were written, and tested intensively in the period January-March 1995.In April 1995 we have initiated large scale lattice QCD calculations of a variety of weak matrix elements of hadrons on VPP.The present status of the calculations are as follows.(1) The K Meson B parameter is one of the fundamental quantity for fixing the Cabibbo-Kobayashi-Maskawa quark mixing matrix. A quenched calculation of this quantity with the Kogut-Susskind quark action is well underway. So far data for 6 values of lattice spacings have been collected, and a calculation for one more value of lattice spacing is planned. Together the data should allow a precision extrapolation of the B parameter to the continuum limit. A similar calculation with the Wilson quark action, based on the method of chiral Ward identities developed this year, is also underway.(2) Another parameter important for CP violation studies is the B meson decay constant. An initial calculation made in the early summer of 1995 revealed large statistical fluctuations. A method of smeared source for reducing the error was tested, and a new calculation has been started late 1995. Data for two values of lattice spacing have been collected and a further calculations with reduced lattics spacing is planned to start soon. This will allow us to estimate the continue m value of the decay constant.(3) Tests of Clover quark action, expected to have a faster approach to the continuum limit, has been completed. Real calculations will start as soon as the Wilson calculation in (2) will be finished.We expect to be able to publish final results of these calculations by summer of 1996. Less