Proton lifetime from SU(5) unification in extra dimensions

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 S1/(Z2 × Z2') and by a large compactification scale Mc ≈ 1014÷1016 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 Mc4. We carefully compute Mc from a next-to-leading analysis of gauge coupling unification and we find that Mc can only be predicted up to an overall factor 10±1. The simplest model, where the dominant decay mode is π0e+ 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+ and the lifetime can be within the reach of the next generation of experiments.