We provide detailed estimates of the proton lifetime in the context of simple supersymmetric SU(5) grand unified models with an extra compact spatial dimension, described by the orbifold S 1 /(Z 2 × Z 2 ) and by a large compactification scale M c ≈ 10 14 ÷ 10 16 GeV. We focus on a class of models where the grand unified symmetry is broken by the compactification mechanism and where baryon violation proceeds mainly through gauge vector boson exchange so that the proton lifetime scales as M 4 c . We carefully compute M c from a next-to-leading analysis of gauge coupling unification and we find that M c can only be predicted up to an overall factor 10 ±1 . The simplest model, where the dominant decay mode is π 0 e + and has no flavour suppression, is strongly constrained by existing data, but not totally ruled out. We also analyze models where some of the matter fields are localized in the extra space and proton decay is flavour suppressed. In models associated to anarchy in the neutrino sector the preferred decay channel is K +ν and the lifetime can be within the reach of the next generation of experiments.

We propose a minimal SO(10) model in 5 space-time dimensions. The single extra spatial dimension is compactified on the orbifold S 1 /(Z 2 × Z ′ 2 ) reducing the gauge group to that of Pati-Salam SU (4) C × SU (2) L × SU (2) R . The breaking down to the standard model group is obtained through an ordinary Higgs mechanism taking place at the Pati-Salam brane, giving rise to a proper gauge coupling unification. We achieve a correct description of fermion masses and mixing angles by describing first and second generations as bulk fields, and by embedding the third generation into four multiplets located at the Pati-Salam brane. The Yukawa sector is simple and compact and predicts a neutrino spectrum of normal hierarchy type. Concerning proton decay, dimension five operators are absent and the essentially unique localization of matter multiplets implies that the minimal couplings between the super-heavy gauge bosons and matter fields are vanishing. Non-minimal interactions are allowed but the resulting dimension six operators describing proton decay are too suppressed to produce observable effects, even in future, super-massive detectors.

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.