Nearest-Neighbour-Interactions from a minimal discrete flavour symmetry within SU(5) Grand Unification

Understand

A flavour symmetry based on Z_4 is analysed in the context of SU(5) Grand Unification with the standard fermionic content plus three right-handed neutrinos.

• The role of Z_4 is to forbid some Yukawa couplings of up- and down-quarks to Higgs scalars such that the quark mass matrices M_u, M_d have Nearest-Neighbour-Interaction (NNI) structure, once they are generated through the electroweak symmetry breaking.
• It turns out in this framework that Z_4 is indeed the minimal discrete symmetry and its implementation requires the introduction of at least two Higgs quintets, which leads to a two Higgs doublet model at low energy scale.
• Due to the SU(5) unification, it is shown that the charged lepton mass matrix develops also NNI form.