$K_L \to \pi^o \nu \overline{\nu}$ in Extended Higgs Models

Abstract

The decay $K_L\rightarrow \pi^o\nu\overline{\nu}$ is an excellent probe of the nature of CP violation. It is almost entirely CP-violating, and hadronic uncertainties are negligible. Experiments which hope to detect the decay are currently being planned. We calculate the decay rate in several extensions of the standard model Higgs sector, including the Liu-Wolfenstein two-doublet model of spontaneous CP-violation and the Weinberg three-doublet model. In a model with an extra doublet, with CP-violation arising from the CKM sector, the rate can increase by up to 50\%. However, in models in which the CP violation arises either entirely or predominantly from the Higgs sector, we find that the decay rate is much smaller than that of the standard model, unless parameters of the model are fine-tuned.