CP violation in $\eta \to \pi \pi$ by Higgs - $\eta$ mixing through two-loop quantum effects

Abstract

Strictly within the standard electro-weak interaction, CP violation in the flavour conserving process $η\ra π+ π$ could originate from the mixing of the $\eta$ meson with the virtual scalar Higgs $H^0$ via $W^{+}+W^{-}$ and $Z^0+Z^0$ exchange. The parity-violation carried by these weak gauge bosons makes the mixing possible at two-loop level. Nowhere the Kobayashi-Maskawa (KM) phase mechanism is needed. For the Higgs mass between 100-600 GeV, the $η\ra π+π$ branching ratio is found to be $3\cdot 10^{-26}-2\cdot 10^{-29}$, hence unconventional CP violation mechanisms are the only ones that could give rise to its observation at the existing or near future $\eta$ factories, unless the Higgs mass is improbably as light as 10 MeV.

7 Pages use LaTex, + 1 figure ( Postscript file )