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

Figure7:Constraints on the radion and Higgs masses from the perturbative unitarity bound. For this graph,we set

√

s<m r(or m r<√

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

√

Figure8:The partial wave amplitude as a function of

s<m r,due to the differing sign of the(leading)pole contributions,which contrasts with the asymptoticallyflat behavior of the partial wave amplitude in the SM.

of orderΛ,no significant bounds can be obtained when the Higgs and radion are mass eigenstates with no mixing.This linear contribution is exactly analogous to the Higgs,but unlike the Higgs there is no gauge cancellation between this term and ordinary gauge boson exchange.

Including curvature-Higgs mixing into the4-d effective theory dramatically affects the gauge boson scattering cross section.In particular,we found that the mixing coefficient|ξ|must be less than3so that perturbative unitarity is not violated prior to reaching the TeV brane cutoffscale Λ,independent of the mass of the radion and Higgs as seen in Fig.5.It is interesting to remark that with the curvature-Higgs mixing coefficientξ∼−1/(6γ),electroweak precision constraints can be satisfied with m h,m r≫M W[7].Wefind,however,that this large mixing implies the theory must also become non-perturbative at a scale significantly below the TeV brane cutoffscale.We also calculated the partial wave amplitude including the radion and Higgs masses,and we found that the allowed region of(γ,ξ)satisfying perturbative unitarity is further reduced. Mass bounds on the Higgs boson and the radion can be inferred for largeξ,as shown in Fig.7. Via our explicit calculations,we verified the validity of the Goldstone boson equivalence theorem with the existence of the curvature-Higgs mixing.

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