Gauge coupling unification and SO(10) in 5D

Abstract

We analyze the gauge unification in minimal supersymmetric SO(10) grand unified theories in 5 dimensions. The single extra spatial dimension is compactified on the orbifoldThe Standard Model gauge group is achieved by the further branelocalized Higgs mechanism on one of the fixed points. There are two main different approaches developed in literature. Higgs mechanism can take place on the Pati Salam brane, or on the SO(10) preserving brane. We show, both analytically and numerically, that in the first case a natural and succesfull gauge coupling unification can be achieved, while the second case is highly disfavoured. For completeness, we consider either the case in which the brane breaking scale is near the cutoff scale or the case in which it is lower than the compactification scale.

Fermion masses and proton decay in a minimal five-dimensional SO(10) model

“…The requirement of gauge coupling unification gives a prediction on the compactification scale M c which is important for our estimates of proton decay rates. As pointed out in [13], the gauge coupling unification, and consequently M c , depends strongly on the values of u Σ . For this reason, we will consider values of u Σ more general than its naive dimensional value Λ/4π and, in our estimates, we will allow x ≤ 1.…”

“…A next to leading analysis of gauge coupling unification of this model has been discussed in ref. [13]. Here we will summarize the main points and the results.…”

“…However, different choices of Higgs mechanism give completely different predictions for gauge unification, as pointed out in Ref. [13]. It has been shown that only when the Higgses are localized on the PS brane with a VEV near the cutoff scale, gauge coupling unification is naturally preserved at the next to leading order.…”

“…symmetry we give Σ a huge, nonzero VEV, u Σ , along the direction of the SM singlet. The symmetry breaking originated by the VEV of the brane field Σ gives a localized mass to the gauge fields belonging to PS/SM [13,14], without affecting the spectrum of bulk Higgs fields. The effect of this high scale localized mass term is to change the boundary condition for the wave function, in such a way that the masses of the KK tower of gauge bosons are shifted.…”

“…These can be computed in a leading logarithmic approximation, including all states in the Kaluza-Klein towers of gauge bosons and Higgs fields with masses smaller than the cut-off scale Λ. The heavy threshold contributions are given by [13]:…”