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Register a new userInsensitive Unification of Gauge Couplings
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Authors
Radovan Dermisek
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The standard model extended by three vector-like families with masses of order 1 TeV -- 100 TeV allows for unification of gauge couplings. The values of gauge couplings at the electroweak scale are highly insensitive to fundamental parameters. The grand unification scale is large enough to avoid the problem with fast proton decay. The electroweak minimum of the Higgs potential is stable.
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We argue that in the two-loop approximation gauge coupling unification in the exceptional supersymmetric standard model can be achieved for any phenomenologically reasonable value of strong gauge coupling at the electroweak scale consistent with the experimentally measured central value.
We analize the impact of two-loop renormalization group equations on the $SU(3)_ctimes SU(2)_wtimes U(1)_Y$ gauge couplings unification in various supersymmetric theories. In general the presence of superfields in higher representation than the doublet spoil the gauge couplings unification at one-loop. The situation is more interesting when the renormalization group equations are calculated at two-loop. In this case we show that the unification of the gauge couplings can be achieved for models with triplet superfield(s). In the analysis of the models with triplet superfield(s) we show that the dimensionless couplings do not have a Landau pole in their evolution at high energies but they run to a nontrivial ultraviolet fixed point.
We discuss gauge coupling unification in models with additional 1 to 4 complete vector-like families, and derive simple rules for masses of vector-like fermions required for exact gauge coupling unification. These mass rules and the classification scheme are generalized to an arbitrary extension of the standard model. We focus on scenarios with 3 or more vector-like families in which the values of gauge couplings at the electroweak scale are highly insensitive to the grand unification scale, the unified gauge coupling, and the masses of vector-like fermions. Their observed values can be mostly understood from infrared fixed point behavior. With respect to sensitivity to fundamental parameters, the model with 3 extra vector-like families stands out. It requires vector-like fermions with masses of order 1 TeV - 100 TeV, and thus at least part of the spectrum may be within the reach of the LHC. The constraints on proton lifetime can be easily satisfied in these models since the best motivated grand unification scale is at $sim 10^{16}$ GeV. The Higgs quartic coupling remains positive all the way to the grand unification scale, and thus the electroweak minimum of the Higgs potential is stable.
When the extra dimensional space is not simply-connected, dynamics of the AB phase in the extra dimension can induce dynamical gauge symmetry breaking by the Hosotani mechanism. This opens up a new way of achieving unification of gauge forces. It leads to the gauge-Higgs unification. The Hosotani mechanism can be established nonperturbatively by lattice simulations, in which measurements of the Polyakov line give a clue.
Gauge-Higgs grand unification is formulated. By extending $SO(5) times U(1)_X$ gauge-Higgs electroweak unification, strong interactions are incorporated in $SO(11)$ gauge-Higgs unification in the Randall-Sundrum warped space. Quarks and leptons are contained in spinor and vector multiplets of $SO(11)$. Although the KK scale can be as low as $10 $ TeV, proton decay is forbidden by a conserved fermion number in the absence of Majorana masses of neutrinos.
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