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Register a new userTwo-Loop Renormalization Group Equations and Gauge Couplings Unification
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Authors
Antonio Costantini
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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.
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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.
We present the full two-loop $beta$-functions for the minimal supersymmetric standard model couplings, extended to include R-parity violating couplings through explicit R-parity violation.
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.
We explore the potential of ultimate unification of the Standard Model matter and gauge sectors into a single $E_8$ superfield in ten dimensions via an intermediate Pati-Salam gauge theory. Through a consistent realisation of a $mathbb{T}^6/(mathbb{Z}_6times mathbb{Z}_2)$ orbifolding procedure accompanied by the Wilson line breaking mechanism and Renormalisation Group evolution of gauge couplings, we have established several benchmark scenarios for New Physics that are worth further phenomenological exploration.
We discuss the gauge-Higgs unification in a framework of Lifshitz type gauge theory. We study a higher dimensional gauge theory on R^{D-1}times S^{1} in which the normal second (first) order derivative terms for scalar (fermion) fields in the action are replaced by higher order derivative ones for the direction of the extra dimension. We provide some mathematical tools to evaluate a one-loop effective potential for the zero mode of the extra component of a higher dimensional gauge field and clarify how the higher order derivative terms affect the standard form of the effective potential. Our results show that they can make the Higgs mass heavier and change its vacuum expectation value drastically. Some extensions of our framework are briefly discussed.
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