Two Higgs bi-doublet left-right model with spontaneous P and CP violation

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. The constraints from neural K meson mass difference Δm _K are calculated and it is demonstrated that a right-handed gauge boson W ₂ contribution in box-diagrams with mass well below 1 TeV is allowed due to a cancelation caused by a light-charged Higgs boson with a mass range of 150–300 GeV. The W ₂ contribution to ε _K can be suppressed from an 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 B ⁰ mass difference Δm _B and the mixing induced CP violation sin2β _{J/ 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. Supported by the National Natural Science Foundation of China (NSFC) (Grant Nos. 10475105 and 10491306) and the Key Project of Chinese Academy of Sciences (CAS)