Abelian symmetries in the two-Higgs-doublet model with fermions

Understand

We classify all possible implementations of an abelian symmetry in the two-Higgs-doublet model with fermions.

• We identify those symmetries which are consistent with non-vanishing quark masses and a CKM matrix which is not block-diagonal.
• Our analysis takes us from a plethora of possibilities down to 246 relevant cases, requiring only 34 distinct matrix forms.
• We show that applying Z_n with n \geq 4 to the scalar sector leads to a continuous U(1) symmetry in the whole Lagrangian.