Anomaly-free 2HDMs with a gauged Abelian symmetry and two generations of right-handed neutrinos

Despite the popularity of two-Higgs-doublet models (2HDMs) with a gauged Abelian flavor symmetry, the allowed Yukawa textures have only been partly explored so far. In this work, we classify and compare every anomaly-free instance, in the case of having two generations of right-handed neutrinos and a type-I seesaw mechanism. We found 16 valid implementations in total, out of which 11 agree well with current experimental bounds. To our knowledge, neither of these models have been considered previously.