A quasi unitarity bound on the radion mass in the Randall-Sundrum model

In this paper we derive a quasi unitarity bound on the radion mass ($\mphi$) from the process $hh\to \phi\phi$. We find that at sufficiently high energies (i.e. when $ s\gg m_h^2, \mphi^2 $) the J=0 partial wave amplitude for the above process violates unitarity if $\mphi^2 > m_h^2+16 \pi \vphi^2 $. Combining this result with the unitarity bound $m_h^2<{16\pi v\vphi\over 3}$ obtained from the process $hh\to h\phi$ we get an upper bound of $4\sqrt {\pi}\vphi [1+{v\over 3 \vphi}]^{1\over 2}$ on the radion mass. This bound is however valid only in the low energy effective theory where we can ignore the effects of the gravitational KK modes and the string/M theoretic excitations.