Constraints on radion vev from the beta functions for top yukawa coupling and higgs self coupling in the Randall-Sundrum model

Abstract

In this paper we determine how the beta function for the top Yukawa coupling to one loop is modified by a light stabilized radion in the Randall-Sundrum model. We then use this beta function together with β(λ) to deteremine lower bounds on the radion vev <ϕ> for different values of λ(m_z) and m_ϕ by demanding that both g_t(μ) and λ(μ) should remain perturbative from m_z up ot the cut off Λ. We find that the lower bounds on <ϕ> that follow from the condition λ(Λ)<\sqrt{4π} nearly agree with those that follow from g_t(Λ)<\sqrt{4π}. We have also determined the critical value of <ϕ> for different values of λ(m_z) and m_ϕ from the line of fixed points which is given by β(g_t)=0.