  Requiring the effective mass term for a category of fundamental Dirac or
Majorana fermions of the same electric charge to be invariant under the
transformation $\psi^{}_{\alpha \rm L (R)} \to \psi^{}_{\alpha \rm L (R)} +
n^{}_{\alpha} z^{}_\psi$ in the flavor space, where $n^{}_\alpha$ and
$z^{}_\psi$ stand respectively for the flavor-dependent complex numbers and the
spacetime- and flavor-independent element of the Grassmann algebra, we show
that $n^{}_\alpha$ can be identified as the elements $U^{}_{\alpha i}$ in the
$i$-th 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. Given the very facts that
the charged leptons, up- and down-type quarks all have a strong mass hierarchy
and current experimental data allow the lightest neutrino to be (almost)
massless, the zero mass limit for the first-family fermions and the
translational flavor symmetry behind it are expected to be a natural starting
point for model building.
