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

Abstract

In this talk, we investigate predictions of the SO(10) Grand Unified Theory (GUT), where an extra U(1)' gauge symmetry remains up to the supersymmetry (SUSY) breaking scale. The minimal setup of SO(10) GUT unifies quarks and leptons into a 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 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)' 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)' charges. The mixing also depends on the flavor. Consequently, the U(1)' 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.