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

Abstract

In this paper we derive a quasi unitarity bound on the radion mass ($\text{mphi}$) from the process $hh\to \varphi \varphi$. We find that at sufficiently high energies (i.e. when $s\gg m_h^2,{\text{mphi}}^2$) the J=0 partial wave amplitude for the above process violates unitarity if ${\text{mphi}}^2>m_h^2+16\pi {\text{vphi}}^2$. Combining this result with the unitarity bound $m_h^2<\frac{16\pi v\text{vphi}}{3}$ obtained from the process $hh\to h\varphi$ we get an upper bound of $4\sqrt{\pi }\text{vphi}[1+\frac{v}{3\text{vphi}}{]}^{\frac{1}{2}}$ 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.

Comments: The contents and the title have been changed to take into account an error in the calculation. Plain Tex, 8 pages, no figures