Long-distance contribution to ε K from lattice QCD
A lattice QCD approach to the calculation of the long-distance contributions to ε K is presented. This parameter describes indirect C P violation in K → π π decay. While the short-distance contribution to ε K can be accurately calculated in terms of standard model parameters and a single hadronic matrix element, B K , there is a long-distance part which is estimated to be approximately 5% of the total and is more difficult to determine. A method for determining this small but phenomenologically important contribution to ε K using lattice QCD is proposed and a complete exploratory calculation of the contribution is presented. This exploratory calculation uses an unphysical light quark mass corresponding to a 339 MeV pion mass and an unphysical charm quark mass of 968 MeV, expressed in the MS ¯ scheme at 2 GeV. This calculation demonstrates that future work should be able to determine this long-distance contribution from first principles with a controlled error of 10% or less. Published by the American Physical Society 2024