Right-Handed Quark Mixing in Left-Right Symmetric Theory

We give exact formulas for the right-handed analog of the Cabibbo-Kobayashi-Maskawa (CKM) matrix in the minimal left-right symmetric theory, for the case when the left-right symmetry is generalized parity as in the original version of the theory. We derive its explicit form and give a physical reason for the known and surprising fact that the right-handed mixing angles are close to the CKM ones, in spite of the left-right symmetry being badly broken in nature. We exemplify our results on the production of the right-handed charged gauge boson and the computation of $K_L-K_S$ mass difference.

Figure 1

The differences between the right-and left-handed mixing angles and the KM phases (${\delta }_R-{\delta }_L$ is multiplied with the accompanying $\sin {\theta }_L^{13}$). The first order terms are given by red lines, the blue dots denote exact numerical solutions. The agreement is striking in all of the allowed region $s_a{t}_{2\beta }\lesssim 0.055$.

Figure 2

Right-handed external phases. Again, in red lines we give the first order expressions and with blue dots the exact numerical solutions; they start diverging only for larger values $s_a{t}_{2\beta }\gtrsim 0.03$. The inclusion of the higher order terms in green gives an excellent agreement with the exact results.