Fermion mass hierarchy and proton stability from nonanomalous $U(1{)}_F$ in supersymmetric $SU(5)$

We present a realistic supersymmetric $SU(5)$ model combined with a nonanomalous $U(1{)}_F$ symmetry. We find a set of $U(1{)}_F$ charges which automatically lead to the realistic mass hierarchy and mixing patterns for quarks, leptons, and neutrinos. All gauge anomalies, including the $[U(1{)}_F{]}^3$ anomaly, are canceled in our model without invoking the Green-Schwarz mechanism or having exotic fields. Proton decay mediated by dimension-5 operators is automatically suppressed in our model, because the scale set by the largest right-handed neutrino mass is much less than the GUT scale.

Figure 1

Feynman diagrams of dimension-5 operators that lead to proton decay mediated by color triplet Higgsinos. (a) Dimension-5 proton decay operators in the usual minimal SUSY $SU(5)$ model [23]. (b), (c) In the presence of the $U(1{)}_F$, these operators are absent because the Yukawa couplings that are circled are highly suppressed.