General CP Violation in Minimal Left-Right Symmetric Model and Constraints on the Right-Handed Scale

In minimal left-right symmetric theories, the requirement of parity invariance allows only one complex phase in the Higgs potential and one in the Yukawa couplings, leading to a two-phase theory with both spontaneous and explicit CP violations. We present a systematic way to solve the right-handed quark mixing matrix analytically in this model and find that the leading order solution has the same hierarchical structure as the left-handed CKM matrix with one more CP-violating phase coming from the complex Higgs vev. Armed with this explicit right-handed mixing matrix, we explore its implications for flavor changing and conserving processes in detail, low-energy CP-violating observables in particular. We report an improved lower bound on the $W_R$ mass of 2.5 TeV from $\Delta M_K$ and $\Delta M_{B}$, and a somewhat higher bound (4 TeV) from kaon decay parameters $\epsilon$, $\epsilon'$, and neutron electric dipole moment. The new bound on the flavor-changing neutral Higgs mass is 25 TeV.