Bino-wino coannihilation as a prediction in the E7 unification of families

<jats:title>A<jats:sc>bstract</jats:sc> </jats:title> <jats:p>We study the phenomenological consequences of the supersymmetric (SUSY) <jats:italic>E</jats:italic> <jats:sub>7</jats:sub> <jats:italic>/</jats:italic>SU(5) <jats:italic>×</jats:italic> U(1)<jats:sup>3</jats:sup> 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 <jats:inline-formula> <jats:alternatives> <jats:tex-math>$$ \mathcal{O} $$</jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>O</mml:mi> </mml:math> </jats:alternatives> </jats:inline-formula>(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 <jats:inline-formula> <jats:alternatives> <jats:tex-math>$$ \mathcal{O} $$</jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>O</mml:mi> </mml:math> </jats:alternatives> </jats:inline-formula>(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.</jats:p>