We study the fermion mass and mixing hierarchy problems within the context of the $SU(5)$ $4+1\mathrm{d}$ domain-wall brane model of Davies, George, and Volkas. In this model, the ordinary fermion mass relations of $SU(5)$ grand unified theories are avoided, since the masses are proportional to overlap integrals of the profiles of the electroweak Higgs and the chiral components of each fermion, which are split into different $3+1\mathrm{d}$ hyperplanes according to their hypercharges. We show that the fermion mass hierarchy without electroweak mixing can be generated naturally from these splittings, that generation of the Cabibbo-Kobayashi-Maskawa matrix looks promising, and that the Cabibbo angle, along with the mass hierarchy, can be generated for the case of Majorana neutrinos from a more modest hierarchy of parameters. We also show that, under some assumptions made on the parameter space, the generation of realistic lepton mixing angles is not possible without fine-tuning, which argues for a flavor symmetry to enforce the required relations.

• Received 26 August 2010

DOI:https://doi.org/10.1103/PhysRevD.83.056004