Neutral-Kaon Mixing from (2 + 1)-Flavor Domain-Wall QCD

We present the first results for neutral-kaon mixing using ($2+1$)-flavors of domain-wall fermions. A new approach is used to extrapolate to the physical up and down quark masses from our numerical studies with pion masses in the range 240\char21{}420 MeV; only $SU(2{)}_{L}\ifmmode\times\else\texttimes\fi{}SU(2{)}_{R}$ chiral symmetry is assumed and the kaon is not assumed to be light. Our main result is ${B}_{K}^{\overline{\mathrm{MS}}}(2\text{ }\text{ }\mathrm{GeV})=0.524(10)(28)$ where the first error is statistical and the second incorporates estimates for all systematic errors.