A new CP violation mechanism generated by the standard neutral Higgs   boson : the $\eta \to \pi + \pi $ case
  Strictly within the standard electro-weak interaction, CP violation in the flavour conserving process $\eta \rightarrow \pi + \pi $ could originate from the mixing of the $\eta$ meson with the virtual scalar Higgs boson $ H^{0}$ via $W$ and top quark exchange. The parity-violation carried by weak gauge bosons makes the mixing possible by quantum effect at two-loop level. Nowhere the Kobayashi-Maskawa (KM) phase mechanism is needed. The phenomenon reveals an unexpected new role of the Higgs boson in the CP symmetry breaking. For the Higgs mass between 100-600 GeV, the $\eta \rightarrow \pi +\pi $ branching ratio is found to be $3.6 \cdot 10^{-26} - 2.4 \cdot 10^{-29}$ , hence CP violation mechanisms beyond the Standard Model are the only ones that could give rise to its observation at existing or near future $\eta$ factories, unless the Higgs mass is improbably as light as 550 $MeV$. 
X. Y. Pham and M. Gourdin