Continuum Limit of $B_K$ from 2+1 Flavor Domain Wall QCD

Understand

We determine the neutral kaon mixing matrix element $B_K$ in the continuum limit with 2+1 flavors of domain wall fermions, using the Iwasaki gauge action at two different lattice spacings.

• These lattice fermions have near exact chiral symmetry and therefore avoid artificial lattice operator mixing.
• We introduce a significant improvement to the conventional NPR method in which the bare matrix elements are renormalized non-perturbatively in the RI-MOM scheme and are then converted into the MSbar scheme using continuum perturbation theory.
• In addition to RI-MOM, we introduce and implement four non-exceptional intermediate momentum schemes that suppress infrared non-perturbative uncertainties in the renormalization procedure.