CP-odd effective gluonic Lagrangian in Kobayashi-Maskawa model

Abstract

Schwinger operator method is applied for studying CP-odd pure gluonic effective Lagrangian in the Standard Model at three-loop level. The induced $θ$-term vanishes by the same reasons as EDMs of quark and W-boson to two-loop approximation. A simple way is found to demonstrate these cancellations. All other terms of the effective Lagrangian acquire non-vanishing contributions. The effective operator of dimension six, Weinberg operator, is calculated explicitly. The corresponding contribution to the EDM of neutron is much smaller than that comes from large distances.