Precise determination ofBKand light quark masses in quenched domain-wall QCD

Abstract

We calculate non-perturbative renormalization factors at hadronic scale for ∆S = 2 four-quark operators in quenched domain-wall QCD using the Schrödinger functional method. Combining them with the non-perturbative renormalization group running by the Alpha collaboration, our result yields the fully non-perturbative renormalization factor, which converts the lattice bare B K to the renormalization group invariant (RGI) B K . Applying this to the bare B K previously obtained by the CP-PACS collaboration at a −1 ≃ 2, 3, 4 GeV, we obtain B K = 0.782(5)(7) (equivalent to B MS K (NDR, 2GeV) = 0.565(4)(5) by 2-loop running) in the continuum limit, where the first error is statistical and the second is systematic due to the continuum extrapolation. Except the quenching error, the total error we have achieved is less than 2%, which is much smaller than the previous ones. Taking the same procedure, we obtain m

Kaon physics from lattice

“…obtained by JLQCD [48] using the chirally symmetric domain wall fermion formulation, gives continuum limit consistent with various earlier calculations. This includes RBC who used a different gauge action thus displaying universality.…”

BK-parameter fromNf=2twisted mass lattice QCD

“…of eq. (2.20) turns out to be very 6 When extending the analysis of ref. [24] to the OS doublet case one finds that, in contrast to the situation in the twisted mass doublet case, matrix elements with both one insertion of the d = 6 Symanzik local effective action term and two insertions of the d = 5 term contribute to the cutoff effects in (M 12 ) 2 .…”

“…The latter, being expressed in terms of quark fields with standard Wilson action, is known [14,15] to be multiplicatively renormalizable. Moreover, the argument implies that the renormalized operator is given by the formula 6) where, for consistency with literature on Wilson fermions, the renormalization constant is named after the form (V A + AV ) the operator takes in the "twisted" basis.…”

“…Relying on arguments similar to those given in ref. [24], one can however conjecture that the large discretization error in M 12 is due to dynamically large matrix elements entering the Symanzik description of the lattice OS pseudoscalar meson mass, rather than to large coefficients in front of some terms of the Symanzik local effective action for OS valence fermions 6 . This conjecture suggests that the large cutoff effect detected in the lattice OS pseudoscalar meson mass is peculiar to this quantity (or to others directly related to it) but not a general feature of physical observables built in terms of OS valence quarks.…”

“…A compilation of recent data is provided in Fig. 1 [4][5][6][7][8][9][10][11][12], respectively. The symbol ⋆ denotes determinations where the continuum extrapolation was carried out.…”