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We propose a top quark condensate scenario embedded in grand unified theories (GUTs), stressing that the gauged Nambu-Jona-Lasinio model has a nontrivial continuum limit (``renormalizability) under certain condition which is actually satisfied in all sensible GUTs with simple group. The top quark mass prediction in this scenario is shown to be insensitive to the ultraviolet cutoff $Lambda$ thanks to the ``renormalizability. We also discuss a possibility to reduce the top mass prediction in this scenario.
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Grand unified theories may display multiply interacting fields with strong coupling dynamics. This poses two new problems: (1) What is the nature of chaotic reheating after inflation, and (2) How is reheating sensitive to the mass spectrum of these theories ? We answer these questions in two interesting limiting cases and demonstrate an increased efficiency of reheating which strongly enhances non-thermal topological defect formation, including monopoles and domain walls. Nevertheless, the large fluctuations may resolve this monopole problem via a modified Dvali-Liu-Vachaspati mechanism in which non-thermal destabilsation of discrete symmetries occurs at reheating.
Extensions of the standard model with low-energy supersymmetry generically allow baryon- and lepton-number violating operators of dimension four and five, yielding rapid proton decay. The dimension-four operators are usually forbidden by matter parity. We investigate to what extent the appearance of dimension-five operators at the Planck scale may be constrained by the different grand-unified gauge groups. Dimension-five operators are suppressed in models based on E_6 and SU(3)_C x SU(3)_L x SU(3)_R, where four matter fields do not form a gauge singlet. An intermediate scale offers the possibility to sufficiently suppress these dimension-five operators.
Renormalizable SO(10) grand unified theories (GUTs), extended by $O(N_g)_F$ family gauge symmetry, generate minimal supersymmetric Standard Model flavour structure dynamically via vacuum expectation values of Yukawon Higgs multiplets. For concrete illustration and calculability, we work with the fully realistic minimal supersymmetric GUTs based on the $bf{210 oplus {overline{126}}oplus 126} $ GUT Higgs system - which were already parameter counting minimal relative to other realistic models. $SO(10)$ fermion Higgs channels $bf{{overline{126}},10}$($mathbf{120}$) extend to symmetric(antisymmetric) representations of $O(N_g)_F$, while $mathbf{210,126}$ are symmetric. $N_g=3$ dynamical Yukawa generation reduces the matter fermion Yukawas from 15 to 3 (21 to 5) without (with) the $bf{120}$ Higgs. Yukawon GUTs are thus ultraminimal in parameter counting terms. Consistent symmetry breaking is ensured by a hidden sector Bajc-Melfo(BM) superpotential with a pair of symmetric $O(N_g)$ multiplets $phi,S $, of which the latters singlet part $S_s$ breaks supersymmetry and the traceless part $hat S $ furnishes flat directions to cancel the $O(N_g)$ D-term contributions of the visible sector. Novel dark matter candidates linked to flavour symmetry arise from both the BM sector and GUT sector minimal supersymmetric Standard Model singlet pseudo-Goldstones. These relics may be viable light($< 50 $ GeV) cold dark matter as reported by DAMA/LIBRA. In contrast to the new minimal supersymmetric SO(10) grand unified theory (NMSGUT) even sterile neutrinos can appear in certain branches of the flavour symmetry breaking without the tuning of couplings.
The recently proposed trans-Planckian censorship conjecture (TCC) amounts to the claim that inflation models with an inflationary energy scale larger than Lambda_inf^max ~ 10^9 GeV belong to the swampland, i.e., cannot be embedded into a consistent theory of quantum gravity. In this paper, we point out that this constraint can be readily satisfied in D-term hybrid inflation (DHI), which is a well-motivated inflation scenario in the context of supersymmetric grand unification. In DHI, the amplitude of the primordial scalar power spectrum originates from a Fayet-Iliopoulos term of the order of the unification scale, sqrt{xi} ~ 10^16 GeV. At the same time, the TCC results in an upper bound on the corresponding gauge coupling constant of g_max ~ 10^-14. We are able to show that this constraint translates into an upper bound on the gravitino mass of m_3/2^max ~ 10 MeV, which opens the possibility that dark matter is accounted for by thermally produced gravitinos, if the reheating temperature is close to T_reh ~ 100 TeV. Interestingly enough, a somewhat similar gravitino mass range has recently been derived in a model that aims at explaining dark energy in terms of axion quintessence and resolving the Hubble tension by means of decaying gravitino dark matter.
We use the $SU(5)$ model to show the presence in grand unified theories of an electroweak monopole and a magnetic dumbbell (meson) made up of a monopole-antimonopole pair connected by a $Z$-magnetic flux tube. The monopole is associated with the spontaneous breaking of the weak $SU(2)_L$ gauge symmetry by the induced vacuum expectation value of a heavy scalar $SU(2)_L$ triplet with zero weak hypercharge contained in the adjoint Higgs 24-plet. This monopole carries a Coulomb magnetic charge of $(3/4) (2pi/e)$ as well as $Z$-magnetic charge, where $2pi/e$ denotes the unit Dirac magnetic charge. Its total magnetic charge is $sqrt{3/8}(4pi/e)$, which is in agreement with the Dirac quantization condition. The monopole weighs about 700 GeV, but because of the attached $Z$-magnetic tube it exists, together with the antimonopole, in a magnetic dumbbell configuration whose mass is expected to lie in the TeV range. The presence of these topological structures in $SU(5)$ and $SO(10)$ and in their supersymmetric extensions provides an exciting new avenue for testing these theories in high-energy colliders.
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