  In this letter we have proposed a natural way of determine the Yukawa
coupling $F(z)\bar\Psi \Psi$ for the 5D bulk action, the form of the $F(z)$
function allows us to localize the spin--$\frac{1}{2}$ fermionic fields in the
paradigm of the 5D braneworld scenarios. The structure acquired by the
$V_{L,R}$ potentials is induced by the ansatz for the $F(z)$ function and we
show that this choice allows the localization of the left-- or right--chiral KK
zero modes $L_{0}(z)$, $R_{0}(z)$ and excludes the tachyonic modes of the KK
mass spectrum $m_{L_{n}}$ and $m_{R_{n}}$. The proposal for the function $F(z)$
leaves behind other speculative proposals since it is independent of the
braneworld model, hence the form for the Yukawa coupling here presented is the
most natural choice. This is shown most evidently if we set $M=\pm 3/2$, which
is a more phenomenologically viable ansatz. This choice allows for a direct
relation between the localization of the ground state for the left-- or
right--chiral KK mass spectrum and the localization of the zero mode for the 4D
graviton in the brane. As a bonus, we include a brief discussion about the
existence of a left-- or right--chiral KK zero mode decoupled from the
corresponding continuous KK mass spectrum, as well as the possible existence of
a mass gap, due to the asymptotic nature of the potentials $V_{R,L}$.

High Energy Physics - Theory