BKfrom Quenched QCD with Exact Chiral Symmetry

We present a calculation of the standard model $\Delta S=2$ matrix element relevant to indirect $CP$ violation in $K\to \pi \pi$ decays which uses Neuberger’s chiral formulation of lattice fermions. The computation is performed in the quenched approximation on a ${16}^3\times 32$ lattice that has a lattice spacing $a\sim 0.1\mathrm{f}\mathrm{m}$. The resulting bare matrix element is renormalized nonperturbatively. Our main result is $B_K^{\mathrm{R}\mathrm{G}\mathrm{I}}=0.87(8{)}_{-1-14}^{+2+14}$, where the first error is statistical, the second is systematic, and the third is Sharpe’s estimate of quenching and flavor-SU(3) breaking uncertainties.