A translational flavor symmetry in the mass terms of Dirac and Majorana fermions

Requiring the effective mass term for a category of fundamental Dirac or Majorana fermions of the same electric charge to be invariant under the translational transformations psi ( alpha L(R)) -> psi ( alpha L(R)) + n ( alpha ) z ( psi L(R)) in the flavor space, where n ( alpha ) and z ( psi L(R)) stand respectively for the flavor-dependent complex numbers and a constant spinor field anticommuting with the fermion fields, we show that n ( alpha ) can be identified as the elements U ( alpha i ) in the ith column of the unitary matrix U used to diagonalize the corresponding Hermitian or symmetric fermion mass matrix M ( psi ), and m ( i ) = 0 holds accordingly. We find that the reverse is also true. Now that the mass spectra of charged leptons, up- and down-type quarks are all strongly hierarchical and current experimental data allow the lightest neutrino to be massless, we argue that the zero mass limit for the first-family fermions and the translational flavor symmetry behind it should be a natural starting point for building viable fermion mass models.

Automated summary

This study investigates the characteristics of the effective mass term of fundamental Dirac or Majorana fermions and proposes that the translational flavor symmetry should be the natural starting point for building viable fermion mass models.