$K$ to $\pi\pi$ Decay amplitudes from Lattice QCD

Understand

We report a direct lattice calculation of the $K$ to $\pi\pi$ decay matrix elements for both the $\Delta I=1/2$ and 3/2 amplitudes $A_0$ and $A_2$ on 2+1 flavor, domain wall fermion, $16^3\times32\times16$ lattices.

• This is a complete calculation in which all contractions for the required ten, four-quark operators are evaluated, including the disconnected graphs in which no quark line connects the initial kaon and final two-pion states.
• These lattice operators are non-perturbatively renormalized using the Rome-Southampton method and the quadratic divergences are studied and removed.
• This is an important but notoriously difficult calculation, requiring high statistics on a large volume.