Neutrino masses in 5D orbifold SU(5) unification models without right-handed singlets

We explore a mechanism for radiatively generating neutrino Majorana masses in a 5 dimensional orbifold SU(5) unification model without introducing right-handed singlets. The model is non-supersymmetric and the extra dimension is compactified via a S₁/(Z₂ × Z₂') orbifold geometry. The necessary lepton number violating interaction arises from the Yukawa interactions either between a 10-plet or a 15-plet bulk scalar field and the fermion quintuplets which are residents on the SU(5) symmetrical brane located at one of the orbifold fixed points. The model is engineered to give realistic charged fermion masses and mixing and in the same time avoiding the rapid proton and neutron decays by geometric construction. The gauge unification can be maintained by adding extra fermion or scalar fields. The unification scale is found to be larger then 10¹⁵ GeV by adding a bulk vector decuplet pair whose zero mode has masses around 10 ∼ 100 TeV range. We found that neutrino mass matrix of the normal hierarchy type is favored by using 15-plet scalar. We give a solution of this type which has detectable μ→3e transition. On the other hand, by introducing 10-plet scalar, the leading neutrino mass matrix can only be inverted hierarchical and gives at most bi-maximal mixing.