Abstract
We present a new focus point supersymemtry breaking scenario based on the supersymmetric $E_7$ non-linear sigma model. In this non-linear sigma model, squarks and sleptons are identified with (pseudo) Nambu-Goldstone bosons. Their masses are generated only radiatively through gauge and yukawa interactions, and they are much smaller than the gravitino and gaugino masses at a high energy scale. On the other hand, Higgs doublets belong to matter multiplets and hence may have unsuppressed supersymmetry-breaking soft masses. We consider their masses to be equal to the gravitino mass at the high energy scale, assuming the minimal Kahler potential for Higgs doublets. We show that the fine-tuning measure of the electroweak symmetry breaking scale is reduced significantly to $\Delta=30-70$, if the ratio of the gravitino mass to the gaugino mass is around $5/4$. Also, the prospects of the discovery/exclusion of supersymmetric particles at the Large Hadron Collider and dark matter direct detection experiments are discussed.
Highlights
The supersymmetric (SUSY) E7 non-linear sigma (NLS) model based on E7 /SU (5) ×U (1)3 [1, 2] is attractive since it accomodates three generations of quarks and leptons as Nambu-Goldstone (NG) chiral multiplets [3, 4]
We show that the fine-tuning measure of the electroweak symmetry breaking scale is reduced significantly to ∆ = 30-70, if the ratio of the gravitino mass to the gaugino mass is around 5/4
The NLS model approach based on exceptional groups has a potential for predicting the maximal number of generations because the maximal volume of exceptional groups is limited by E8
Summary
The supersymmetric (SUSY) E7 non-linear sigma (NLS) model based on E7 /SU (5) ×U (1)3 [1, 2] is attractive since it accomodates three generations of quarks and leptons as Nambu-Goldstone (NG) chiral multiplets [3, 4]. The supersymmetric (SUSY) E7 non-linear sigma (NLS) model based on E7 /SU (5) ×. The NLS model approach based on exceptional groups has a potential for predicting the maximal number of generations because the maximal volume of exceptional groups is limited by E8. We have four generations and one anti-generation in E8 NLS models. Futhermore, the NLS model may explain the observed small yukawa coupling constants for the first, second and third generations because of the celebrated low energy theorem [5]. It may be intriguing that the basic structure of the E7 NLS model does not change much even if we replace the E7 by E7(7) symmetry found in the N = 8 supergravity [6]
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