Kaon $B$-parameter from quenched domain-wall QCD

Kaon $B$ -parameter from quenched domain-wall QCD

Y. Aoki, T. Blum, N. H. Christ, C. Dawson, T. Izubuchi, R. D. Mawhinney, J. Noaki, S. Ohta, K. Orginos, A. Soni, and N. Yamada

Phys. Rev. D 73, 094507 – Published 19 May 2006

Abstract

We present numerical results for the kaon $B$ -parameter, $B_{K}$ , determined in the quenched approximation of lattice QCD. Our simulations are performed using domain-wall fermions and the renormalization group improved, DBW2 gauge action which combine to give quarks with good chiral symmetry at finite lattice spacing. Operators are renormalized nonperturbatively using the RI/MOM scheme. We study scaling by performing the simulation on two different lattices with $a^{- 1} = 1.982 (30)$ and 2.914(54) GeV. We combine this quenched scaling study with an earlier calculation of $B_{K}$ using two flavors of dynamical, domain-wall quarks at a single lattice spacing to obtain $B_{K}^{\bar{MS} NDR} (μ = 2 GeV) = 0.563 (21) (39) (30)$ , were the first error is statistical, the second systematic (without quenching errors) and the third estimates the error due to quenching.

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Received 26 August 2005

DOI:https://doi.org/10.1103/PhysRevD.73.094507

Authors & Affiliations

Y. Aoki¹, T. Blum^2,3, N. H. Christ⁴, C. Dawson², T. Izubuchi^2,5, R. D. Mawhinney⁴, J. Noaki^2,*, S. Ohta^2,6,7, K. Orginos⁸, A. Soni⁹, and N. Yamada^6,7

¹Physics Department, University of Wuppertal, Gaussstr. 20, 42119, Wuppertal, Germany
²RIKEN BNL Research Center, Brookhaven National Laboratory, Upton, New York 11973, USA
³Physics Department, University of Connecticut, Storrs, Connecticut 06269-3046, USA
⁴Physics Department, Columbia University, New York, New York 10027, USA
⁵Institute of Theoretical Physics, Kanazawa University, Ishikawa 920-1192, Japan
⁶Institute of Particle and Nuclear Studies, KEK, Ibaraki 305-0801, Japan
⁷The Graduate University for Advanced Studies (SOKENDAI), Tsukuba, Ibaraki 305-0801, Japan
⁸Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
⁹Physics Department, Brookhaven National Laboratory, Upton, New York 11973, USA

^*Present address: School of Physics and Astronomy, University of Southampton, Southampton, SO17 1BJ, England

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Vol. 73, Iss. 9 — 1 May 2006

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