Bulk Standard Model in the Randall-Sundrum Background

TL;DR

This paper investigates embedding the Standard Model in a five-dimensional Randall-Sundrum background with bulk fermions and gauge bosons. It demonstrates that bulk fermion zero modes localize near the TeV brane due to the RS geometry, causing KK gauge bosons to couple to fermion zero modes and leading to significant electroweak constraints that push the first KK mode above ~9 TeV. A crucial result is that a bulk Higgs fails to maintain the RS hierarchy without extreme fine-tuning, whereas confining the Higgs to the TeV brane yields a viable scenario with moderate tuning. Taken together, the findings indicate that preserving the RS mechanism favors a brane-localized Higgs in a bulk-SM framework, while bulk-Higgs scenarios are disfavored by hierarchy considerations and precision data.

Abstract

We discuss issues in an attempt to put the Standard Model (SM) in five-dimensional anti-de Sitter spacetime compactified on $S^1/Z_2$. The recently-proposed approach to the gauge hierarchy problem by using this background geometry, with the SM confined on a boundary, is extended to a situation where (some of) the SM particles reside in the five dimensional bulk. In particular, we find a localization of zero modes of bulk fermions near the boundary with a negative tension. Unlike the compactification with the flat metric, these fermion zero modes couple to Kaluza-Klein (KK) excitations of the SM gauge bosons. Interestingly, only low-lying modes of such KK gauge bosons have non-negligible couplings. Current electroweak precision data give a constraint that the first KK mode be heavier than 9 TeV. We also argue that at least the Higgs field should be confined on the brane to utilize the Randall-Sundrum background as a solution to the gauge hierarchy.

Figures (2)

• Figure 1: Plot of the masses of the $n$-th Kaluza-Klein modes of the gauge bosons in units of $10^{-16}k$. We take $kr_c=12$.
• Figure 2: Plot of the couplings $g_n$ of the $n$-th Kaluza-Klein modes to the bilinear of the zero modes of the bulk fermions relative to the gauge coupling constant $g$.