Flavor violating Z' from SO(10) SUSY GUT in High-Scale SUSY

Abstract

We propose an SO(10) supersymmetric grand unified theory (SUSY GUT), where the SO(10) gauge symmetry breaks down to SU (3) c × SU (2) L × U (1) Y × U (1) X at the GUT scale and 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 16-dimensional but also 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 16-and 10-dimensional fields so that the U (1) X gauge interaction may be flavor-violating. We investigate the current constraints on the flavor-violating Z ′ interaction from the flavor physics and discuss prospects for future experiments. 1 I. INTRODUCTIONThe Grand Unified Theories (GUTs) are longstanding hypotheses, and continue to fascinate us because of the excellent explanation of mysteries in the Standard Model (SM). The GUTs unify not only the gauge groups but also quarks and leptons, and reveal the origin of the structure of the SM, such as the hypercharge assignment for the SM particles.The gauge groups in the SM areThe minimal candidate for the unified gauge group is SU(5), which was originally proposed by Georgi and Glashow [1]. There, quarks and leptons belong to 10-and 5-dimensional representations in SU (5), and the SM Higgs doublet is embedded into 5, introducing additional colored Higgs particle. One big issue is the unification of the SM gauge coupling constants, and it could be realized in the supersymmetric (SUSY) extension. It is well-known that the minimal SU(5) SUSY GUT realizes the gauge coupling unification around 2 × 10 16 GeV, if SUSY particle masses are around 1 TeV [2].Another candidate for the unified gauge group would be SO(10). It is non-minimal, but it would be an attractive extension because the SO(10) GUT explains the anomalyfree conditions in the SM. Furthermore, all leptons and quarks, including the right-handed neutrinos, in one generation may belong to one 16-dimensional representation in the minimal setup [3].On the other hand, the GUTs face several problems, especially because of the experimental constraints. One stringent constraint is from nonobservation of proton decay [1,4]. While the GUT scale in the SUSY GUT may be high enough to suppress the proton decay induced by the so-called X-boson exchange, the dimension-five operator generated by the colored Higgs exchange is severely constrained. Another stringent constraint is from the observed fermion masses and mixings. The SU(5) GUT predicts a common mass ratio of down-type quark and charged lepton in each generation. Furthermore, in the SO(10) GUT, the up-type, down-type quarks, and charged lepton in each generation would have common mass ratios if the all mat...