at $\xi = 1/2$. But for other valus of $\xi$ except $\xi = 0$ one can also obtain the massless graviton by changing $c$, $g$, and $v$ appropriately to obey Eq.(\[rs2condi\]).

At the pure Dirichlet BC case($\xi = 0$) Eq.(\[rs2condi\]) cannot hold unless $v = \infty$. Thus in this case we can get the massless graviton via a coupling constant renormalization as we did in the previous section.

To show explicitly we have to re-write Eq.(\[rs2schulman\]) by introducing a positive infinitesimal parameter $\epsilon$; $$\label{rs2d1}
\hat{G}_{RS2}^{\xi=0}[a, b; E] = \hat{G}_0^D[a, b; E]
+ \lim_{\epsilon \rightarrow 0^+}
\frac{\hat{G}_0^D[a, c + \epsilon; E] \hat{G}_0^D[c + \epsilon, b; E]}
     {\frac{1}{v} - \hat{G}_0^D[c + \epsilon, c + \epsilon; E]}.$$ Explicit calculation shows that even in this case one can derive a massless graviton when $v^{ren} = -3 / (2 R)$, where $v^{ren}$ is a renormalized coupling constant defined as $$\label{rs2vren}
v^{ren} = \frac{1}{2 \epsilon^2}
\left( \frac{1}{v} - 2 \epsilon \right).$$

The coupling constant renormalization procedure in RS2 is in detail explained in Ref.[@park01-3]. In this case the fixed-energy amplitude and the corresponding gravitational potential is exactly same with that of the original RS result when $v^{ren} = -3 / (2 R)$. This result may provide 