Neutral Kaon Mixing from Lattice QCD

In this work, we report the lattice calculation of two important quantities which emerge from second order, K0 − ¯ K0 mixing : ∆MK and K. The RBC-UKQCD collaboration has performed the first calculation of ∆MK with unphysical kinematics [1]. We now extend this calculation to near-physical and physical ensembles. In these physical or near-physical calculations, the two-pion energies are below the kaon threshold, and we have to examine the two-pion intermediate states contribution to ∆MK, as well as the enhanced finite volume corrections arising from these two-pion intermediate states. We also report the first lattice calculation of the long-distance contribution to the indirect CP violation parameter, the K. This calculation involves the treatment of a short-distance, ultra-violet divergence that is absent in the calculation of ∆MK, and we will report our techniques for correcting this divergence on the lattice. In this calculation, we used unphysical quark masses on the same ensemble that we used in [1]. Therefore, rather than providing a physical result, this calculation demonstrates the technique for calculating K, and provides an approximate understanding the size of the long-distance contributions. Various new techniques are employed in this work, such as the use of All-Mode-Averaging (AMA), the All-to-All (A2A) propagators and the use of super-jackknife method in analyzing the data.