A minimal supersymmetric E6 unified theory

Abstract

We show explicitly that supersymmetric E 6 Grand Unified Theory with a Higgs sector consisting of {27 + 27 + 351 ′ + 351 ′ + 78} fields provides a realistic scenario for symmetry breaking and fermion mass generation. While gauge symmetry breaking can be achieved without the 78 field, its presence is critical for a successful doublet-triplet mass splitting. The Yukawa sector of the model consists of only two symmetric matrices describing all of quark, lepton and neutrino masses and mixings. The fermion mass matrices are computed at low energy and a fit to the second and third generation masses and mixings is performed. We find a good numerical fit to the low-energy data. Thus, this model, having 11 superpotential parameters, alongside the two symmetric Yukawa matrices, seems to be the best realistic candidate for a minimal renormalizable supersymmetric E 6 unified theory.

New signals for vector-like down-type quark in U(1) of $$E_6$$

“…This will allow us to have a large doublet-triplet splitting scale, which prevents rapid proton decay if the E 6 Yukawa relations were enforced. This will require either two pairs of (27,27) and one pair of (351 , 351 ) dimensional Higgs representations, or one pair of (27, 27), 78, and one pair of (351 , 351 ) dimensional Higgs representations (detailed studies of E 6 theories with broken Yukawa relations can be found in [49][50][51]). For our model, the unbroken symmetry at the TeV scale is…”

Asymptotically safe grand unification

“…Embedding SO (10) in larger gauge groups, for example E 6 cannot help [27,28] because the resulting theory is even less asymptotically free. One could envision different ways to go around this issue, for example one could push the unification scale closer to the gravity one via specific threshold corrections and hope that gravity will work its magic.…”

“…If a singlet scalar gauge invariant operator of the chiral ring 28) at the fixed point acquires 29) unitarity is violated unless it becomes free. If this occurs one needs to modify the a function accordingly [94] …”

“…We focussed in this initial work on grand unified theories on the SO(10) theory but we plan to extend the analysis to similar E 6 realizations [27,28] as well as SU(5) [112][113][114].…”

Isospin-violating dark matter in a U(1)′ model inspired by E6

“…This allows us to have a large doublet-triplet splitting scale, which prevents rapid proton decay if the E 6 Yukawa relations were enforced. This will need either two pairs of (27,27) or one pair of (27,27), 78, in addition to one pair of (351 ′ , 351 ′ ) dimensional Higgs representations (Detailed studies of E 6 theories with broken Yukawa relations can be found in [36,37].) For our model, the unbroken symmetry at the…”