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Constraints on the Bulk Standard Model in the Randall-Sundrum Scenario

Gustavo Burdman

TL;DR

This paper analyzes the Randall-Sundrum scenario with the Standard Model fields propagating in the 5D bulk, placing the Higgs on the TeV boundary to avoid tuning issues for the $W$ and $Z$ masses. It extends prior gauge-bulk analyses by incorporating bulk fermions and evaluating both oblique and non-oblique electroweak corrections, including flavor-violating effects, to derive constraints on the low-energy scale $\Lambda_r$ and the KK spectrum. The main result is that non-oblique shifts in gauge-fermion couplings significantly strengthen bounds, yielding $\Lambda_r$ typically above 20 TeV (and up to ~40–50 TeV in some scenarios), which corresponds to KK masses $m_1$ well beyond the LHC reach; flavor violation in the bulk further constrains the flavor structure, especially from kaon processes like $K^+ \to \pi^+ \nu\bar{\nu}$. The findings imply a highly constrained bulk RS setup with near-degenerate bulk masses for down-type fermions and a heavy KK spectrum, underscoring the importance of kaon physics for probing extra-dimensional flavor structures.

Abstract

We derive constraints on the Randall-Sundrum scenario with the standard model fields in the bulk. These result from tree level effects associated with the deformation of the zero mode wave-functions of the W and the Z once electroweak symmetry is broken. Recently Csáki, Erlich and Terning pointed out that this implies large contributions to electroweak oblique parameters. Here we find that when fermions are allowed in the bulk the couplings of the $W$ and the $Z$ to zero-mode fermions are also affected. We perform a fit to electroweak observables assuming universal bulk fermion masses and including all effects and find constraints that are considerably stronger than for the case with fermions localized in the low energy boundary. These put the lowest Kaluza-Klein excitation out of reach of the Large Hadron Collider. We then relax the universality assumption and study the effects of flavor violation in the bulk and its possible signatures.

Constraints on the Bulk Standard Model in the Randall-Sundrum Scenario

TL;DR

This paper analyzes the Randall-Sundrum scenario with the Standard Model fields propagating in the 5D bulk, placing the Higgs on the TeV boundary to avoid tuning issues for the and masses. It extends prior gauge-bulk analyses by incorporating bulk fermions and evaluating both oblique and non-oblique electroweak corrections, including flavor-violating effects, to derive constraints on the low-energy scale and the KK spectrum. The main result is that non-oblique shifts in gauge-fermion couplings significantly strengthen bounds, yielding typically above 20 TeV (and up to ~40–50 TeV in some scenarios), which corresponds to KK masses well beyond the LHC reach; flavor violation in the bulk further constrains the flavor structure, especially from kaon processes like . The findings imply a highly constrained bulk RS setup with near-degenerate bulk masses for down-type fermions and a heavy KK spectrum, underscoring the importance of kaon physics for probing extra-dimensional flavor structures.

Abstract

We derive constraints on the Randall-Sundrum scenario with the standard model fields in the bulk. These result from tree level effects associated with the deformation of the zero mode wave-functions of the W and the Z once electroweak symmetry is broken. Recently Csáki, Erlich and Terning pointed out that this implies large contributions to electroweak oblique parameters. Here we find that when fermions are allowed in the bulk the couplings of the and the to zero-mode fermions are also affected. We perform a fit to electroweak observables assuming universal bulk fermion masses and including all effects and find constraints that are considerably stronger than for the case with fermions localized in the low energy boundary. These put the lowest Kaluza-Klein excitation out of reach of the Large Hadron Collider. We then relax the universality assumption and study the effects of flavor violation in the bulk and its possible signatures.

Paper Structure

This paper contains 5 sections, 51 equations, 2 figures.

Table of Contents

  1. Introduction
  2. The Bulk Standard Model
  3. The effects of non-local wave-function renormalization
  4. Effects of Flavor Violation in the Bulk
  5. Conclusions

Figures (2)

  • Figure 1: Lower bounds ($95\%$ C.L.) on $\Lambda_r$ vs. the fermion bulk mass parameter $\nu$. The top curve corresponds to $m_h=115$ GeV, the lower curve is for $m_h=300$ GeV.
  • Figure 2: Lower bounds ($95\%$ C.L.) on $\Lambda_r$ vs. the fermion bulk mass parameter $\nu$, for the case with the third generation confined to the low energy boundary. The top curve corresponds to $m_h=115$ GeV, the lower curve is for $m_h=300$ GeV.