2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/210938A 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 $Δm_K$ and demonstrate that a right-handed gauge boson $W_2$ 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 $150 \sim 300$ GeV. The $W_2$ contribution to $ε_K$ 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 $B^0$ mass difference $Δm_B$, and the mixing-induced CP violation quantity $\sin2β_{J/ψ}$, 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.25 pages, 6 figures, typos corrected, 1 figure added, published versionHigh Energy Physics - Phenomenologytext