Implication of a light radion on the RG evolution of higgs self coupling in the Randall-Sundrum model

In this paper we determine how the beta funtion of the higgs self coupling \lambda 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 <\phi>, both for perturbative and non-perturbative values of \lambda at the ultra violet cut off \Lambda. The lower bound on <\phi> is obtained by demanding that the renormalized coupling \lambda (\mu) at \mu =100 GeV be consistent with the present experimental bound of 110 GeV on the higgs mass from LEP2 searches. We also show that if \lambda (\Lambda) is sufficiently small then an upper bound on <\phi> can be determined by requiring that \beta (\lambda)be positive over the relevant momentum range.