Two Higgs Bi-doublet Left-Right Model With Spontaneous P and CP Violation

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A left-right symmetric model with two Higgs bi-doublet is shown to be a consistent model for both spontaneous P and CP violation. The flavor changing neutral currents can be suppressed by the mechanism of approximate global U(1) family symmetry. We calculate the constraints from neural K meson mass difference Δmₖ and demonstrate that a right-handed gauge boson W₂ contribution in box-diagrams with mass well below 1 TeV is allowed due to a cancellation caused by a light charged Higgs boson with a mass range 150 300 GeV. The W₂ contribution to εₖ can be suppressed from appropriate choice of additional CP phases appearing in the right-handed Cabbibo-Kobayashi-Maskawa matrix. The model is also found to be fully consistent with B⁰ mass difference ΔmB, and the mixing-induced CP violation quantity 2βⱼ/ψ, which is usually difficult for the model with only one Higgs bi-doublet. The new physics beyond the standard model can be directly searched at the colliders LHC and ILC.