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Recent theoretical and computational advances have enabled the precision determination of multiparticle Standard Model amplitudes using lattice QCD. In particular the measure of direct CPviolation in kaon decays, ε ′, has now been computed with errors that are 40% of the experimental value; this quantity is highly sensitive to BSM sources of CP-violation and may help shed light on the origin of the matter-antimatter asymmetry in the Universe. We will discuss this calculation of ε ′ and our present and future efforts in improving our result. We will also briefly discuss our ongoing calculations of other long-distance contributions to kaonic amplitudes sensitive to new physics.

Standard Model Prediction for Direct CP-violation in K-decays, and Long-Distance Contributions to Kaonic Ampltiudes