Renormalization of the S Parameter in Holographic Models of Electroweak Symmetry Breaking

TL;DR

This paper investigates the divergence and renormalization of the S parameter in holographic models of electroweak symmetry breaking, revealing that the S parameter's dependence on the Higgs mass can be removed through renormalization.

Contribution

It demonstrates the non-finiteness of the S parameter in certain holographic models and proposes a renormalization approach that removes Higgs mass dependence from electroweak constraints.

Findings

The S parameter is logarithmically divergent and requires renormalization.

Renormalization can eliminate Higgs mass dependence in S.

Electroweak bounds on the S parameter are affected by the renormalization scheme.

Abstract

We show that the S parameter is not finite in theories of electroweak symmetry breaking in a slice of anti--de Sitter five-dimensional space, with the light fermions localized in the ultraviolet. We compute the one-loop contributions to S from the Higgs sector and show that they are logarithmically dependent on the cutoff of the theory. We discuss the renormalization of S, as well as the implications for bounds from electroweak precision measurements on these models. We argue that, although in principle the choice of renormalization condition could eliminate the S parameter constraint, a more consistent condition would still result in a large and positive S. On the other hand, we show that the dependence on the Higgs mass in S can be entirely eliminated by the renormalization procedure, making it impossible in these theories to extract a Higgs mass bound from electroweak precision constraints.