Flavor violating $Z^{\mathrm{\prime }}$ from $SO(10)$ SUSY GUT in High-Scale SUSY

We propose an $SO(10)$ supersymmetric grand unified theory (SUSY GUT), where the $SO(10)$ gauge symmetry breaks down to $SU(3)_c \times SU(2)_L \times U(1)Y\times U(1){X}$attheGUTscaleand$U(1)X$ is radiatively broken at the SUSY-braking scale. In order to achieve the observed Higgs mass around $126$ GeV and also to satisfy constraints on flavor- and/or CP-violating processes, we assume that the SUSY-breaking scale is $O(100)$ TeV, so that the $U(1{)}_X$ breaking scale is also $O(100)$ TeV. One big issue in the SO(10) GUTs is how to realize realistic Yukawa couplings. In our model, not only ${\bf 16}$-dimensionalbutalso${\bf 10}$-dimensional matter fields are introduced to predict the observed fermion masses and mixings. The Standard-Model quarks and leptons are linear combinations of the $\mathbf{16}$- and ${\bf 10}$-dimensionalfieldssothatthe$U(1){X}$ gauge interaction may be flavor-violating. We investigate the current constraints on the flavor-violating $Z^{\mathrm{\prime }}$ interaction from the flavor physics and discuss prospects for future experiments.