Long-distance contribution to ϵK from lattice QCD

A lattice QCD approach to the calculation of the long-distance contributions to eK is presented. This parameter describes indirect CP violation in K -> 7v7v decay. While the short -distance contribution to eK can be accurately calculated in terms of standard model parameters and a single hadronic matrix element, BK, 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 eK 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.