Bino-wino coannihilation as a prediction in the E ₇ unification of families

We study the phenomenological consequences of the supersymmetric (SUSY) E₇/SU(5) × U(1)³ non-linear sigma model coupled to supergravity, where the three gen- erations of quark and lepton chiral multiplets appear as (pseudo) Nambu Goldstone (NG) multiplets, that is, the origin of the three families is explained. To break SUSY, we intro- duce a SUSY breaking field charged under some symmetry avoiding the Polonyi problem. The gaugino mass spectrum is almost uniquely determined when one requires the electroweak vacuum to be (meta)stable: it would be a miracle that the mass difference between the bino and wino turns out to be within O(1)% at the low energy. Thus, a bino-wino coannihilation is naturally predicted, which can explain the correct relic abundance of dark matter. Moreover, we find that the bottom-tau Yukawa couplings and the gauge couplings are unified up to O(1)% in most of the viable region. This scenario can be fully tested at the LHC and future collider experiments since the gauginos and some of the pseudo-NG bosons are light. An axion-like multiplet, which can be identified with the QCD axion, is also predicted.