Toward Precision Measurement of BK with Quenched Kogut-Susskind Quarks∗ JLQCD Collaboration

The kaon B parameter is one of the crucial hadron weak matrix elements for constraining the CP violation phase of the Cabibbo-KobayashiMaskawa matrix from experiments. A pioneering study was carried out by Gupta, Kilcup, Patel and Sharpe (GKPS)[1–3], which laid a foundation for a lattice QCD determination of this quantity with the Kogut-Susskind quark action. A number of problems, however, are posed to warrant viability of the lattice result in the continuum. While some aspects have been examined previously [4,5], further studies are needed to establish the continuum value of BK . The statistics of GKPS are only 15 (β=6.0) to 24 (β=6.4) configurations: as a consequence the error of BK at β = 6.4 is so large that an O(a) dependence of BK on the lattice spacing inferred from a theoretical analysis[3] can not be ascertained. Furthermore the lattice size of 32 × 48 employed at β = 6.2 and 6.4 may be too small in the temporal direction. We have therefore decided to carry