Study of BK in Lattice QCD with Exact Chiral Symmetry

In this thesis, we calculate the kaon B-parameter BK in quenched lattice QCD with exact chiral symmetry. Our computations are performed at lattice spacing about 0.147(1) fm with gauge configurations generted by Wilson gauge action at β = 5.8 on a 83 × 24 lattice. Our bare BK is renormalized non-perturbatively in the Landau gauge. Our preliminary results are BRI K (1.88GeV ) = 0.6561± 0.2636 at mq = 81.63 MeV and BRI K (1.88GeV ) = 0.8146 ± 0.2468 at mq = 108.84 MeV.1 Introduction 3 1.1 CP symmetry violation in neutral Kaon decays . . . . . . . . 5 1.2 K0 and ‾K 0 mixing and BK parameter1 . . . . . . . . . . . . . 6 2 Dirac Operator Schemes 16 2.1 The lattice formulation . . . . . . . . . . . . . . . . . . . . . . 16 2.2 Wilson-Dirac Operator . . . . . . . . . . . . . . . . . . . . . . 18 2.3 Overlap formulation . . . . . . . . . . . . . . . . . . . . . . . 20 3 Gauge-fixing 25 3.1 Standard Non-Perturbative Gauge Fixing . . . . . . . . . . . . 26 3.2 Landau gauge and Coulomb gauge on the lattice . . . . . . . . 29 4 Renormalization 34 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 4.2 The Renormalised Propagator . . . . . . . . . . . . . . . . . . 35 4.3 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 4.4 K0– ‾K 0 mixing amplitude . . . . . . . . . . . . . . . . . . . . 39 5 Numerical Results 47 6 Conclusion 6