[Paper Review] K and B Physics in the Custodially Protected Randall-Sundrum Model

Monika Blanke|arXiv (Cornell University)|Aug 19, 2009

Particle physics theoretical and experimental studies16 references4 citations

TL;DR

This paper investigates flavor-changing effects in the custodially protected Randall-Sundrum model, showing that tree-level exchanges of Kaluza-Klein gluons and a heavy $Z_H$ boson generate significant contributions to $K$- and $B$-meson mixing and rare decays. It demonstrates that the model can simultaneously explain anomalies in $B_s$ mixing and enhance $K\to\pi\nu\bar{\nu}$ decays by 100–200% over the SM, offering a distinctive flavor structure distinguishable from other new physics frameworks.

ABSTRACT

The Randall-Sundrum framework provides an appealing solution to both the gauge hierarchy and the flavour problem. The model with enlarged custodial symmetry is consistent with electroweak precision observables for Kaluza-Klein (KK) scales as low as 2-3 TeV, so that the lowest-lying KK modes could be observed at the LHC. The presence of the heavy KK gauge bosons induces new tree level contributions to flavour violating observables. We summarise the main results for K and B physics observables in the Delta F = 2 and Delta F = 1 sectors. The specific pattern of new physics effects can be used to distinguish this model from other new physics frameworks.

Motivation & Objective

• To assess the viability of the custodially protected Randall-Sundrum model in explaining electroweak precision data and flavor-violating observables.
• To analyze tree-level contributions from Kaluza-Klein gauge bosons and gluons to $\Delta F=2$ and $\Delta F=1$ processes in $K$ and $B$ systems.
• To test whether the model can simultaneously accommodate constraints from $\varepsilon_K$, $S_{\psi\phi}$, $A^{s}_{\text{SL}}$, and rare decays like $K\to\pi\nu\bar{\nu}$.
• To identify unique flavor and CP-violating correlations that distinguish this model from other new physics scenarios such as the Littlest Higgs with T-parity.
• To evaluate the degree of fine-tuning required in the 5D Yukawa couplings when KK scales are lowered to the LHC-accessible range (~2.5 TeV).

Proposed method

• Uses a custodially protected Randall-Sundrum model with bulk fermions and a warped extra dimension to generate hierarchical Yukawa couplings via wave function localization.
• Applies the RS-GIM mechanism to suppress tree-level FCNCs, relying on wave function overlap hierarchies to naturally suppress flavor violation.
• Computes contributions to $K$- and $B$-meson mixing via exchange of KK gluons and the heavy $Z_H$ boson, focusing on scalar left-right operators.
• Evaluates rare decays such as $K\to\pi\nu\bar{\nu}$ and $B_{s,d}\to\mu^+\mu^-$ using tree-level $Z$-boson couplings to right-handed down quarks.
• Performs a global fit to $\varepsilon_K$, $S_{\psi\phi}$, $A^{s}_{\text{SL}}$, and branching ratios, using constraints from experimental data.
• Analyzes correlations between observables to identify model-specific signatures, particularly in the $K\to\pi\nu\bar{\nu}$ plane and $B_{s}\to\mu^+\mu^-$ decay rates.

Experimental results

Research questions

• RQ1 Can the custodially protected Randall-Sundrum model simultaneously explain the measured $\varepsilon_K$ and the observed $S_{\psi\phi}$ and $A^{s}_{\text{SL}}$ anomalies in $B_s$ mixing?
• RQ2 What is the minimal Kaluza-Klein scale consistent with electroweak precision data and flavor constraints, and how much fine-tuning is required?
• RQ3 How do the new physics contributions to $K\to\pi\nu\bar{\nu}$ decays compare to the SM, and can they be enhanced by 100–200% as predicted?
• RQ4 What distinctive flavor correlations arise in this model, and how can they be used to distinguish it from other new physics frameworks like the Littlest Higgs with T-parity?
• RQ5 Why are NP effects in rare $K$ decays significantly larger than in rare $B$ decays, and what role does the right-handed quark sector play?

Key findings

• The model can achieve consistency with $\varepsilon_K$ data at a Kaluza-Klein scale as low as $M_{\text{KK}} \simeq 2.5\,\text{TeV}$ without requiring large fine-tuning in the 5D Yukawa couplings.
• Tree-level exchanges of KK gluons generate strong enhancements in the scalar left-right operator, leading to significant NP contributions to $K$-meson mixing.
• $K\to\pi\nu\bar{\nu}$ branching ratios can be enhanced by up to 100–200% over the SM due to new contributions from the $Z$ boson to right-handed quark currents.
• The model predicts no strict correlation between $K\to\pi\nu\bar{\nu}$ and other observables, distinguishing it from models like the Littlest Higgs with T-parity that exhibit a two-branch correlation.
• NP effects in rare $B$ decays such as $B_{s,d}\to\mu^+\mu^-$ are small, at the $\mathcal{O}(10\%)$ level, making them difficult to distinguish from the SM.
• Large enhancements in $K$ decays and large non-SM $S_{\psi\phi}$ values cannot coexist, indicating a complementary role for $K$ and $B_s$ observables in testing the model.