Proton decay, fermion masses and texture from extra dimensions in SUSY GUT's

In supersymmetry, there are gauge invariant dimension 5 proton decay operators which must be suppressed by a mass scale much larger than the Planck mass. It is natural to expect that this suppression should be explained by a mechanism that explains the hierarchical structure of the fermion mass matrices. We apply this argument to the case where wave functions of chiral multiplets are localized under a kink background along an extra spatial dimension and the Yukawa couplings as well as the coefficients of the proton decay operators are determined by the overlap of the relevant wave functions. A configuration is found in the context of SU(5) supersymmetric grand unified theory that yields realistic values of quark masses, mixing angles, CP phase and charged lepton masses and sufficiently small genuine dimension 5 proton decay operators. Inclusion of SU(5) breaking effects is essential in order to obtain non-vanishing CP phase as well as correct lepton masses. The resulting mass matrix has a texture structure in which texture zeros are a consequence of extremely small overlap of the wave functions. Our approach requires explicit breaking of supersymmetry in the extra dimension, which can be realized in (de)constructing extra dimension.