Fermion mass hierarchies from supersymmetric gauged flavour symmetry in 5D

A mechanism to generate realistic fermion mass hierarchies based on supersymmetric gauged $U(1)_F$ symmetry in flat five-dimensional (5D) spacetime is proposed. The fifth dimension is compactified on $S^1/Z_2$ orbifold. The $U(1)_F$ gauge filed and the standard model fermions charged under the extra abelian symmetry along with their superpartners live in the 5D bulk. Bulk masses of fermions are generated by the vacuum expectation value of $N=2$ superpartner of $U(1)_F$ gauge field, and they are proportional to $U(1)_F$ charges of respective fermions. This decides localization of fermions in the extra dimension, which in turn gives rise to exponentially suppressed Yukawa couplings in the effective 4D theory. Anomaly cancellation puts stringent constraints on the allowed $U(1)_F$ charges which leads to correlations between the masses of quarks and leptons. We perform an extensive numerical scan and obtain several solutions for anomaly-free $U(1)_F$, which describe the observed pattern of fermion masses and mixing with all the fundamental parameters of order unity. It is found that the possible existence of SM singlet neutrinos substantially improves the spectrum of solutions by offering more freedom in choosing $U(1)_F$ charges. The model predicts $Z^\prime$ boson mediating flavour violating interactions in both the quark and lepton sectors with the couplings which can be explicitly determined from the Yukawa couplings.