Kaon<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="italic">B</mml:mi></mml:math>Parameter from Quenched Lattice QCD

Abstract

We present results of a large-scale simulation for the kaon $B$ parameter ${B}_{K}$ in quenched lattice QCD with the Kogut-Susskind quark action. Calculating ${B}_{K}$ at 1% statistical accuracy for seven values of lattice spacing in the range $a\ensuremath{\approx}0.24--0.04\mathrm{fm}$ on lattices up to ${56}^{3}\ifmmode\times\else\texttimes\fi{}96$, we verify the theoretically predicted quadratic $a$ dependence. Strong indications are found that, with our level of accuracy, ${\ensuremath{\alpha}}_{\overline{\mathrm{MS}}}(1/a{)}^{2}$ terms arising from our one-loop matching procedure have to be included in the continuum extrapolation. We present ${B}_{K}(\mathrm{NDR},2\mathrm{GeV})\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.628(42)$ as our final value, where NDR indicates naive dimensional regularization.