Radion effects on unitarity in gauge-boson scattering(6)

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

the Higgs contribution of Figs.1(d)and(e),the amplitude becomes

−i M SM=−m2h s−m2

h +

t

v2

for m2h≪s,|t|.(12)

A light Higgs boson thus naturally restores partial wave unitarity,through a precise cancellation of the high energy divergence of the gauge boson scattering amplitude against the additional physical Higgs contribution.This mysterious cancellation becomes transparent by simply replacing the full massive spin-1external gauge bosonfields by the scalar Goldstone bosons,as dictated by the equivalence theorem[18,17,19].However,this also implies an upper bound on the Higgs boson mass m h<900GeV if perturbative unitarity is maintained to arbitrarily high energies[18].

Although the unitarity bound cannot predict any specific form of new physics in the elec-troweak symmetry breaking sector,it does provide a general argument for a scale(around1TeV) at which the physics responsible for EWSB must show up.Furthermore,any new physics that couples to the EWSB sector significantly at high energies may be subject to constraints from partial wave unitarity.

3The radion effects

In Randall-Sundrum scenarios,the low energy4-d effective theory includes the ordinary4-d graviton,the radion,and the KK excitations of the graviton and the bulk scalar.Here we are assuming the SM remains on the TeV brane(see e.g.,Refs.[14,20]for alternatives).At energies well below the cutoffscale,we need only consider the radion as the additional degree of freedom in our effective theory.As we approach(or exceed)the cutoffscaleΛ,additional contributions from the KK modes(and perhaps other quantum gravity states)must be included in the calculations.However,including these contributions is subtle and model-dependent.For example,in the holographic viewpoint[21],the holographic dual4-d theory is becoming strongly coupled in the transition to a4-d conformalfield theory aboveΛ.In any case,we will restrict ourselves to energies below the cutoffscale,and consider only the contribution from the radion.

As stated in the introduction,the radion couples tofields localized on the SM brane through

−γ

v

r W+µW−µ−γM2Z