Kaon mixing and the charm mass

Abstract

We study contributions to the Delta S=2 weak Chiral Lagrangian producing K0-K0bar mixing which are not enhanced by the charm mass. For the real part, these contributions turn out to be related to the box diagram with up quarks but, unlike in perturbation theory, they do not vanish in the limit m_u->0. They increase the leading contribution to the K_L-K_S mass difference by ~10%. This means that short distances amount to (90+-15)% of this mass difference. For the imaginary part, we find a correction to the lambda_c^2 m_c^2 term of -5% from the integration of charm, which is a small contribution to epsilon_K. The calculation is done in the large-Nc limit and we show explicitly how to match short and long distances.