[Paper Review] The Impact of Universal Extra Dimensions on FCNC Processes

Andrzej J. Buras, Anton Poschenrieder+2 more|arXiv (Cornell University)|Jul 16, 2003

Quantum Chromodynamics and Particle Interactions3 citations

TL;DR

This paper investigates the impact of Kaluza-Klein (KK) excitations in the Universal Extra Dimensions (UED) model, specifically the Appelquist-Cheng-Dobrescu (ACD) model with one extra dimension, on flavor-changing neutral current (FCNC) processes. It shows that with a compactification scale as low as 250 GeV, the model remains consistent with current FCNC data, predicting measurable enhancements in rare decays like $K^+\to\pi^+\nu\bar{\nu}$ and suppressions in $B\to X_s\gamma$, while preserving the GIM mechanism and KK parity to suppress dangerous flavor-violating contributions.

ABSTRACT

We review the results of two papers on FCNC processes in the Appelquist, Cheng and Dobrescu (ACD) model with one universal extra dimension.

Motivation & Objective

• To assess the viability of the Appelquist-Cheng-Dobrescu (ACD) model with one universal extra dimension in light of current experimental constraints on flavor-changing neutral current (FCNC) processes.
• To determine whether the presence of Kaluza-Klein (KK) modes in the ACD model leads to observable deviations from the Standard Model (SM) predictions in rare decays and mixing processes.
• To identify unique, model-specific correlations between observables such as $\hat{s}_0$ and $Br(B\to X_s\gamma)$ that could test the ACD model at future colliders.
• To evaluate the role of the GIM mechanism and KK parity in suppressing dangerous flavor-changing contributions from KK excitations.

Proposed method

• The analysis is based on the effective four-dimensional theory of the ACD model, where all SM fields propagate in the extra dimension, leading to infinite towers of Kaluza-Klein (KK) partners.
• Feynman rules for SM and KK particle interactions are derived from the bulk and boundary Lagrangians, with flavor-universal boundary terms assumed to minimize FCNC contributions.
• Calculations of one-loop contributions to FCNC processes—such as $B\to X_s\gamma$, $K^+\to\pi^+\nu\bar{\nu}$, $B_d\to\mu^+\mu^-$, and $\varepsilon' / \varepsilon$—are performed using the compactification scale $1/R$ as the sole new parameter.
• The GIM mechanism is applied to the top quark KK modes, which significantly improves convergence and suppresses contributions from lighter quarks and leptons.
• The forward-backward asymmetry $A_{\rm FB}$ in $B\to X_s\ell^+\ell^-$ is studied via the normalized asymmetry $\hat{s}_0$, which is sensitive to new physics.
• Correlations between $\hat{s}_0$ and $Br(B\to X_s\gamma)$ are computed and compared across different values of $1/R$ to identify model-specific signatures.

Experimental results

Research questions

• RQ1 Can the ACD model with one universal extra dimension remain consistent with current experimental data on FCNC processes for compactification scales as low as 250 GeV?
• RQ2 How do Kaluza-Klein excitations modify rare B and K decays such as $B\to X_s\gamma$, $K^+\to\pi^+\nu\bar{\nu}$, and $K_L\to\pi^0e^+e^-$?
• RQ3 To what extent does the GIM mechanism suppress flavor-changing contributions from KK modes in the ACD model?
• RQ4 What are the correlations between $\hat{s}_0$ and $Br(B\to X_s\gamma)$ in the ACD model, and how do they differ from the SM?
• RQ5 Can the suppression of $\varepsilon' / \varepsilon$ in the ACD model provide a useful constraint on $1/R$?

Key findings

• The ACD model is consistent with current FCNC data for a compactification scale as low as 250 GeV, with no significant flavor-changing contributions from KK modes due to the GIM mechanism and KK parity conservation.
• The branching ratio $Br(K^+\to\pi^+\nu\bar{\nu})$ is significantly enhanced in the ACD model, making it a key observable for testing the model.
• The value of $\hat{s}_0$, the zero of the forward-backward asymmetry in $B\to X_s\ell^+\ell^-$, is suppressed in the ACD model and approaches the NLO SM prediction for $1/R = 300$ GeV.
• The branching ratio $Br(B\to X_s\gamma)$ is suppressed in the ACD model, with the suppression increasing as $1/R$ decreases, consistent with the model's constraints from precision electroweak data.
• The ratio $\varepsilon' / \varepsilon$ is suppressed in the ACD model due to enhanced $Z^0$ penguin contributions, but no useful bound on $1/R$ can be derived due to hadronic matrix element uncertainties.
• A strong correlation is found between $\hat{s}_0$ and $\sqrt{Br(B\to X_s\gamma)}$ in the ACD model, which could be used to test the model at future experiments.