[@tp1]: $$\begin{aligned}
   m_{rad}^2 = \frac{20}{\sqrt{3}}\frac{\alpha k^4}{M^6} \epsilon^2 e^{-2kr_c\pi} v_h^2v_v^2 
   \bigg[1 + \frac{40}{\sqrt{3}}\alpha k^2\kappa v_h\bigg] \bigg[\frac{v_h}{v_v} - 1\bigg]^2
   \label{radion_mass}
  \end{aligned}$$ It is evident that $m_{rad}$ increases with the increasing value of $\alpha$ and becomes zero as $\alpha$ tends to zero. It is expected because without any higher curvature term, the gravitational action contains only Einstein-Hilbert term and thus the mass of radion becomes zero (see [@GW_radion]).\
As the ratio, $\frac{\lambda_{L,R}}{m_{rad}}$ determines the fermion to radion scattering amplitude, we plot this in the figure (\[plot ratio\]) with respect to the parameter $\alpha$.\

![$\frac{\lambda_{L,R}}{m_{rad}}$ vs $\alpha$ in $F(R)$ theory for $M=1$, $\Lambda=-1$ and $m_5=0$[]{data-label="plot ratio"}](amplitude.eps){width="3.0in" height="2.0in"}

It is evident from figure (\[plot ratio\]) that the contribution of radion in scattering amplitude of fermions decreases as the value of the higher curvature parameter $\alpha$ increases. Thus the presence of higher curvature term reduces the signature in such scattering processes.\

Massive KK mode
---------------

In this section, we study the localization of higher Kaluza-Klein modes. For massive KK modes, equation of motion for fermionic wave function is given as, $$\begin{aligned}
   &e&^{-A(y)}e^{-\frac{2\kappa}{\sqrt{3}}\big(<\Phi>+\xi(y)\big)}
   \bigg[\pm e^{\frac{\kappa}{2\sqrt{3}}\big(<\Phi>+\xi(y)\big)}\bigg(\partial_{y}-2A'(y)\nonumber\\ 
   &-&\frac{\kappa}{\sqrt{3}}\xi'(y)\bigg) + m_5\bigg]\zeta^n_{R,L}(y) = -m_n\zeta^n_{L,R}(y)
   \label{eom for wave function2}
  \end{aligned}$$

$m_n$ is the mass of nth KK mode. Using the rescaling $$\begin{aligned}
   