Abstract
We explore a missing-partner model based on the minimal SU(5) gauge group with mathbf{75} , mathbf{50} and overline{mathbf{50 }} Higgs representations, assuming a super-GUT CMSSM scenario in which soft supersymmetry-breaking parameters are universal at some high scale M_{mathrm{in}} above the GUT scale M_{mathrm{GUT}}. We identify regions of parameter space that are consistent with the cosmological dark matter density, the measured Higgs mass and the experimental lower limit on tau (p rightarrow K^+ nu ). These constraints can be satisfied simultaneously along stop coannihilation strips in the super-GUT CMSSM with tan beta sim 3.5–5 where the input gaugino mass m_{1/2} sim 15–25 TeV, corresponding after strong renormalization by the large GUT Higgs representations between M_{mathrm{in}} and M_{mathrm{GUT}} to m_{mathrm{LSP}}, m_{{tilde{t}}_1} sim 2.5–5 TeV and m_{{tilde{g}}} sim 13–20 TeV, with the light-flavor squarks significantly heavier. We find that tau (p rightarrow K^+ nu ) lesssim 3 times 10^{34} years throughout the allowed range of parameter space, within the range of the next generation of searches with the JUNO, DUNE and Hyper-Kamiokande experiments.
Highlights
The fine-tuning of the hierarchy of the electroweak and grand unification scales is the bane of Grand Unified Theories (GUTs)
We explore a missing-partner model based on the minimal SU(5) gauge group with 75, 50 and 50 Higgs representations, assuming a super-GUT CMSSM scenario in which soft supersymmetry-breaking parameters are universal at some high scale Min above the GUT scale MGUT
One must verify that the predicted value of the lightest Higgs mass is compatible with the experimental measurement [23,24,25]. We investigate how these phenomenological obstacles can be circumvented in a super-GUT version [26,27,28,29,30,31,32,33,34,35,36] of the constrained minimal supersymmetric extension of the Standard Model (CMSSM) [18,20,21,37,38,39,40,41,42,43,44,45,46,47,48], in which universality of the soft supersymmetry-breaking scalar masses is postulated at some high scale Min > MGUT, the GUT scale
Summary
The fine-tuning of the hierarchy of the electroweak and grand unification scales is the bane of Grand Unified Theories (GUTs). As we show here, requiring perturbativity up to the input scale, Min, imposes a strong lower limit on the possible masses of states in the 50 and 50 Higgs representations, M > 2 × 1017 GeV. While the CMSSM needs only four free parameters – a gaugino mass, m1/2, a scalar mass, m0, a trilinear mass term, A0, and the ratio of Higgs vacuum expectation values (vevs), tan β3 – the super-GUT CMSSM based on the missing partner model (MPM) requires several additional parameters – the universality input scale, Min ≥ MGUT, and three extra trilinear couplings, λ , and λ corresponding to the 5 ̄ ·75·50, 5·75·50, and 753 superpotential terms.. We find that throughout the allowed range of parameter space τ ( p → K +ν) 3 × 1034 years, within the discovery reaches of the generation of searches with the JUNO, DUNE and Hyper-Kamiokande experiments, which are estimated to be 1.9 × 1034 years [65], 1.3 × 1034 years [66] and 3.2 × 1034 years [67], respectively
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