NUMERICAL STUDY OF LATTICE QUANTUM CHROMODYNAMICS

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Study of weak interation matrix elements of hadrons is an important subject in lattice QCD in view of its possible impact on research of the Standard Model of particles as a whole. This project aimed to extract weak matrix elements of mesons, sufficiently accurate for use in phenomenological analyzes, through systematic large scale numerical simulation of lattice QCD.The main results of the project are as follows.(1) Precision measurement of K meson B parameter in quenched QCDSimulations have been made both for the Kogut-Susskind and Wilson quark actions.For the Kogut-Susskind quark action, the matrix element was measured using two types of lattice operators for seven lattice spacings ranging over 0.24fm to 0.041fm, which yielded the value B_K (2GeV,NDR) =0.628 (42).For the Wilson quark action, the method based on chiral Ward identities have been developed and applied to simulations for 4 values of lattice spacing, yielding B_K (2GeV,NDR) =0.62 (10).The values from the two types of act … More ions show a good agreement. Our values represent the best result obtained so far for this important quantity.(2) Precision measurement of the B meson decay constant in quenched QCDThe difficulty with this quantity stems from systematic errors associated with heavy mass of the b quark. In this project, a parallel set of simulations have been carried out, one using the Wilson quark action and the other employing the clover action which is expected to have reduced magnitude of scaling violation effects. Carrying out simulations for 3 lattice spacings and invoking the method of El-Khadra-Kronfeld-Mackenzie for estimating systematic errors associated with b quark, we have obtained the following values for the decay constant as our best estimate : f_B=173 (5) (9) (14) MeV,f_<Bs>=199 (3) (10) (16) MeV,f_D=197 (3) (14) (17) MeV,f_<Ds>=224 (3) (16) (18) MeV.(3) Form factors for weak decaysWe have also examined the feasibility of calculating semi-leptonic weak decay form factors. Our study shows that the form factor depends significantly on the meson mass, and that statistical signals deteriorate rapidly for non-zero momenta. Further check of these points and development of a new technique appear needed for real progress in this area.Results above have been reported as annual Lattice conference series. For the B parameter of K meson and the decay constant of B meson, our simulations have been completed. Journal articles have been prepared and submitted in this fiscal year. Less