Title: Kaon to Two Pion decay from Lattice QCD and CP violation
Description: We report a direct lattice calculation of the K to ππ (ΔI=1/2) decay amplitude A₀ on a 32³×64 ensemble, with 2+1 flavor Möbius Domain Wall Fermion, with a⁻¹=1.379(9) GeV. This is a complete and physical calculation: chiral symmetry breaking is controlled by the Möbius Domain Wall formalism; pion and kaon masses are simulated at their near-physical values, mκ≅490 MeV and mπ≅140 MeV. G-parity boundary conditions are used to realize correct kinematics for the final two-pion state and give E_{ππ(I=0)}≅498 MeV, while keeping isospin symmetry; all 10 ΔS=1 operators are considered, each of which involve the notorious disconnected diagrams. With this setup, we are able to resolve, for the first time, the physical decay amplitudes Re(A₀) and Im(A₀) from 0. The Re(A₀) amplitude agrees with its experimental value, The result for Im(A₀) is used, in combination with the lattice calculated decay amplitude A₂, to compute Re(ϵ'/ϵ), which evaluates to 1.38(5.08)×10⁻⁴ and agrees at the 2σ level with the experimental value 1.66(0.23)×10⁻³.

This is a major step towards understanding and testing CP violation in the standard model. Several measurement techniques are used to increase computational efficiency. We use all-to-all propagators to construct finite sized mesons, which have a better overlap with the meson ground state and reducing statistical noise from the vacuum graphs. This also saves matrix-inversion overhead when constructing mesons with different momenta. The other technical improvements include the mixed-precision conjugate gradient algorithm, and optimized fast Fourier transformation. We also discuss the cross-checks on the use of G-parity boundary conditions, and estimate several important systematic errors.