Flavor physics induced by light $Z'$ from SO(10) GUT

In this paper, we investigate predictions of the SO(10) Grand Unified Theory (GUT), where an extra U(1)$^\prime$ gauge symmetry remains up to the supersymmetry (SUSY) breaking scale. The minimal setup of SO(10) GUT unifies quarks and leptons into a ${\bf 16}$-representational field in each generations. The setup, however, suffers from the realization of the realistic Yukawa couplings at the electroweak scale. In order to solve this problem, we introduce ${\bf 10}$-representational matter fields, and then the two kinds of matter fields mix with each other at the SUSY breaking scale, where the extra U(1)$^\prime$ gauge symmetry breaks down radiatively. One crucial prediction is that the Standard Model quarks and leptons are given by the linear combinations of the fields with two different U(1)$^\prime$ charges. The mixing also depends on the flavor. Consequently, the U(1)$^\prime$ interaction becomes flavor violating, and the flavor physics is the smoking-gun signal of our GUT model. The flavor violating $Z'$ couplings are related to the fermion masses and the CKM matrix, so that we can derive some explicit predictions in flavor physics. We especially discuss $K$-$\overline{K}$ mixing, $B_{(s)}$-$\overline{B_{(s)}}$ mixing, and the (semi)leptonic decays of $K$ and $B$ in our model. We also study the flavor violating $\mu$ and $\tau$ decays and discuss the correlations among the physical observables in this SO(10) GUT framework.