Abstract
We reconsider the minimal SU(5) grand unified theory (GUT) in the context of no-scale supergravity inspired by string compactification scenarios, assuming that the soft supersymmetry-breaking parameters satisfy universality conditions at some input scale M_mathrm{in} above the GUT scale M_{mathrm{GUT}}. When setting up such a no-scale super-GUT model, special attention must be paid to avoiding the Scylla of rapid proton decay and the Charybdis of an excessive density of cold dark matter, while also having an acceptable mass for the Higgs boson. We do not find consistent solutions if none of the matter and Higgs fields are assigned to twisted chiral supermultiplets, even in the presence of Giudice–Masiero terms. However, consistent solutions may be found if at least one fiveplet of GUT Higgs fields is assigned to a twisted chiral supermultiplet, with a suitable choice of modular weights. Spin-independent dark matter scattering may be detectable in some of these consistent solutions.
Highlights
The construction of no-scale supergravity grand unified theory (GUT) encounters significant hurdles, such as fixing the compactification moduli
With m0 = A0 = B0 = 0, the particle spectrum almost inevitably contains either a stau lightest supersymmetric particle (LSP) or tachyonic stau. This problem can be alleviated if the universal boundary conditions are applied above the GUT scale [62]
Working within a no-scale supergravity framework inspired by string compactification scenarios, we have shown in this paper that, if the matter and Higgs supermultiplets are all untwisted, super-GUT SU(5) models are unable to provide simultaneously a long enough proton lifetime, a small enough relic LSP density and an acceptable Higgs mass in the framework of no-scale supergravity, even in the presence of a Giudice–Masiero term in the Kähler potential
Summary
The construction of no-scale supergravity GUTs encounters significant hurdles, such as fixing the compactification moduli. Pure no-scale boundary conditions require that all the quadratic, bilinear and trilinear scalar couplings m0, B0 and A0 vanish, leading to phenomenology that is in contradiction with experimental constraints This issue may be avoided in models with (untwisted or twisted) matter fields with non-vanishing modular weights as we show below. Another one-parameter theory in this context is pure gravity mediation [42,43,44,45,46,47], in which the gaugino masses, A and B terms are determined by anomaly mediation [49,50,51,52,53] leaving only the gravitino mass, m3/2 = m0 as a free parameter These boundary conditions may be too restrictive if they are imposed at the GUT scale, MGUT, defined as the renormalization scale where the two electroweak gauge couplings.
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