Anomaly-free Froggatt-Nielsen extensions of the Standard Model with two Higgs doublets

Abstract: In this Master thesis we extend the Standard Model with an additional $U(1)$ gauge group and an additional Higgs doublet with a lepton specific $\mathbb{Z}_2$ symmetry. This is used in a gauged version of the Froggatt-Nielsen mechanism to describe the observed masses and mixings among fermions. To reproduce these observables and satisfy the anomaly constraints posed by the new gauge symmetry methods from algebraic geometry are used. By introducing three right-handed neutrinos, an anomaly-free model reproducing the observed masses, PMNS matrix and Cabibbo mixing in the quark sector was found.