# Bino-wino coannihilation as a prediction in the $E_7$ unification of families

## TL;DR

This paper explores a supersymmetric $E_7$ unification model where bino-wino coannihilation naturally predicts dark matter relic abundance, unifies gauge and Yukawa couplings, and suggests testable signals at colliders.

## Contribution

It introduces a novel $E_7$ based SUSY model with pseudo-Nambu-Goldstone multiplets, predicting bino-wino coannihilation and gauge-Yukawa unification within a testable framework.

## Key findings

- Bino-wino mass difference is within 1% at low energy.
- Dark matter relic abundance explained by bino-wino coannihilation.
- Gauge and bottom-tau Yukawa couplings are unified to within 1%.

## Abstract

We study the phenomenological consequences of the supersymmetric (SUSY) $E_7/SU(5)\times U(1)^3$ non-linear sigma model coupled to supergravity, where the three generations 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 introduce 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.