Implications of a light radion on the RG evolution of Higgs self coupling in the Randall–Sundrum model

In this Letter we determine how the beta function of the Higgs self coupling λ at one loop order is modified by a light stabilized radion in the Randall–Sundrum model. We then use the modified beta function to derive a lower bound on the radion vev 〈φ〉, both for perturbative and non-perturbative values of λ at the ultra violet cut off Λ. The lower bound on 〈φ〉 is obtained by demanding that the renormalized coupling λ(μ) at μ=114 GeV be consistent with the present experimental bound of 114 GeV on the Higgs mass from LEPII searches. We also show that important bounds on 〈φ〉 can be derived from the sign of β(λ) in the infrared regime.