Restoration of Parity and the Right-Handed Analog of the CKM Matrix

In a recent Letter we determined analytically the right-handed quark mixing matrix in the minimal Left-Right symmetric theory with generalized Parity. We derived its explicit form as a series expansion in a small parameter that measures the departure from hermiticity of quark mass matrices. Here we analyze carefully the convergence of the series by including higher order terms and by comparing with numerical results. We apply our findings to some phenomenological applications such as the production and decays of the right-handed gauge boson $W_R$, the neutrinoless double beta decay, the decays of the heavy scalar doublet, the strong CP parameter and the theoretical limits on the new mass scale from the $K$ and $B$-meson physics. In particular, we demonstrate that the relevant coupling for the production of the $W_R$ gauge boson at hadronic colliders and for the neutrinoless double beta decay equals its left-handed counterpart, within a percent. We also demonstrate that the stability of the theoretical lower limit on the $W_R$ mass from the $K$-meson physics is due to a partial cancellation of the external phases of the right-handed mixing matrix.