The scalar field associated with fluctuations in the positions of the two branes, the ``radion'', plays an important role determining the cosmology and collider phenomenology of the Randall-Sundrum solution to the hierarchy problem. It is now well known th

Since the radion contributions to the gauge boson scattering amplitude are suppressed by γ2∝1/Λ2,there is no region where a large contribution is expected in the 4-d effective theory,

despite the O (s/M 2W

)divergence.This same result can be trivially applied to all other gauge boson scattering amplitudes involving the exchange of an (internal)radion.Fundamentally this result is straightforward to see from the radion interactions –the radion contribution is always suppressed by 1/Λinstead of 1/v .There is,however,one important difference between the Higgs and the radion interactions:At one-loop the radion couples to trace anomaly gauge interaction [11,12].

Here,the

strength of the interaction is γb a g 2a /16π2,where b a

is one-loop beta function coefficient for the a coupling.This is generally much larger than the analogous one-loop coupling to the Higgs [at least for a =SU(3)],scaling roughly with the number of heavy fermions running in the loop.Nevertheless,this is still suppressed relative to the size of tree-level couplings and thus does not give rise to any new unitarity problems.

4Curvature-Higgs mixing

The couplings of the radion that we have used to calculate gauge boson scattering were indepen-dent of the Higgs couplings.This need not be the case,however.In particular,on the TeV brane we ought to add all terms to the action that are not forbidden by symmetries.One important term is a curvature-Higgs mixing operator [11]

S mixing = d 4x √

r +3ξγ2(∂r )2 .(21)

This mixing can be diagonalized by appropriate field redefinitions and rotations,resulting in the following relations between the interaction and mass eigenstates [7]

h →Ah m +Br m

−γr →Ch m +Dr m

(22)where A =cos θ−

6ξγZ cos θC =sin θ

Z γ

(23)9