Universal spin-1/2 fermion field localization on a 5D braneworld

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 $V_{R,L}$.