Precise determination of $B_K$ and light quark masses in quenched domain-wall QCD

Abstract

We calculate non-perturbative renormalization factors at hadronic scale for $\Delta S=2$ 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) ${\hat{B}}_K$. Applying this to the bare $B_K$ previously obtained by the CP-PACS collaboration at $a^{-1}\simeq 2,3,4$ GeV, we obtain ${\hat{B}}_K=0.782(5)(7)$ (equivalent to $B_K^{\overline{\mathrm{MS}}}(\mathrm{NDR},2\mathrm{GeV})=0.565(4)(5)$ 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 $m_{u,d}^{\mathrm{RGI}}=5.613(66)$ MeV and $m_s^{\mathrm{RGI}}=147.1(17)$ MeV (equivalent to $m_{u,d}^{\overline{\mathrm{MS}}}(2\mathrm{GeV})=4.026(48)$ MeV and $m_s^{\overline{\mathrm{MS}}}(2\mathrm{GeV})=105.6(12)$ MeV by 4-loop running) in the continuum limit.

51 pages, 27 Postscript figures, corrected typos, added reference

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• The Kaon B-parameter from Quenched Domain-Wall QCD
• A precise determination of $B_K$ in quenched QCD
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• Flavour symmetry restoration and kaon weak matrix elements in quenched twisted mass QCD
• Schroedinger functional formalism with Ginsparg-Wilson fermion
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• BK from the lattice with Wilson quarks
• Schroedinger functional formalism with domain-wall fermion

Cited by in corpus (9)

• Review of lattice results concerning low energy particle physics
• Lattice QCD at finite temperature and density
• BK-parameter from Nf = 2 twisted mass lattice QCD
• On the consistency between the observed amount of CP violation in the K- and Bd-systems within minimal flavor violation
• Quenched $B_K$-parameter from Osterwalder-Seiler tmQCD quarks and mass-splitting discretization effects
• Determination of light quark masses in QCD
• A formulation of domain-wall fermions in the Schrödinger functional
• K0-K0bar on the Lattice
• Lattice Kaon Physics