Flavor Physics in the Randall-Sundrum Model: I. Theoretical Setup and Electroweak Precision Tests

TL;DR

This work develops an exact, non-perturbative treatment of tree-level flavor effects in the minimal RS model with bulk gauge and fermion fields and a brane-localized Higgs. By solving the full 5D equations of motion and boundary conditions, the authors derive KK decompositions, bulk profiles, and exact sums over KK towers, enabling precise predictions for gauge, Higgs, and fermion interactions. They show that fermion mass hierarchies and CKM structure emerge from anarchic 5D Yukawas and wave-function overlaps, with reparametrization invariances that preserve masses/mixings while reshaping flavor couplings. Electroweak precision tests constrain the KK scale but permit relatively low $M_{ m KK}$ if a heavy Higgs or custodial protection is employed, while RS-GIM suppression softens many FCNCs. The paper also analyzes flavor-changing $Z^0$ and Higgs couplings, non-unitarity of CKM, KK-fermion mixing, and rare top decays, laying a comprehensive foundation for RS flavor physics and guiding future loop-level studies.

Abstract

A complete discussion of tree-level flavor-changing effects in the Randall-Sundrum (RS) model with brane-localized Higgs sector and bulk gauge and matter fields is presented. The bulk equations of motion for the gauge and fermion fields, supplemented by boundary conditions taking into account the couplings to the Higgs sector, are solved exactly. For gauge fields the Kaluza-Klein (KK) decomposition is performed in a covariant R_xi gauge. For fermions the mixing between different generations is included in a completely general way. The hierarchies observed in the fermion spectrum and the quark mixing matrix are explained naturally in terms of anarchic five-dimensional Yukawa matrices and wave-function overlap integrals. Detailed studies of the flavor-changing couplings of the Higgs boson and of gauge bosons and their KK excitations are performed, including in particular the couplings of the standard W and Z bosons. A careful analysis of electroweak precision observables including the S and T parameters and the Zbb couplings shows that the simplest RS model containing only Standard Model particles and their KK excitations is consistent with all experimental bounds for a KK scale as low as a few TeV, if one allows for a heavy Higgs boson and/or for an ultra-violet cutoff below the Planck scale. The study of flavor-changing effects includes analyses of the non-unitarity of the quark mixing matrix, anomalous right-handed couplings of the W bosons, tree-level flavor-changing neutral current couplings of the Z and Higgs bosons, the rare decays t-->c(u)+Z and t-->c(u)+h, and the flavor mixing among KK fermions. The results obtained in this work form the basis for general calculations of flavor-changing processes in the RS model and its extensions.

Figures (12)

• Figure 1: Examples of one-loop contributions to the renormalization of the Higgs-boson mass (left) and of the Yukawa couplings, involving a Higgs-boson (middle) and a gluon as well as its KK excitations (right).
• Figure 2: Tree-level contributions to $\mu^-\to e^-\nu_\mu\bar{\nu}_e$ arising from the exchange of a $W^-$ boson and its KK excitations.
• Figure 3: Regions of 68%, 95%, and 99% probability in the $m_t$--$m_W$ plane following from the direct measurements of $m_W$ and $m_t$ at LEP2 and the Tevatron. The black dot corresponds to the SM prediction based on the value of $G_F$ for our reference input values, while the green (medium gray) shaded band shows the SM expectation for values of the Higgs-boson mass $m_h\in [60,1000]$ GeV. The blue (dark gray) line and points represent the RS prediction for $M_{\rm KK}\in [1,10]$ TeV. See text for details.
• Figure 4: Regions of 68%, 95%, and 99% probability in the $S$--$T$ plane. The green (medium gray) shaded stripes in both panels indicate the SM predictions for $m_t=(172.6\pm 1.4)$ GeV and $m_h\in [60,1000]$ GeV. The blue (dark gray) shaded area in the left/right panel represents the RS corrections without/with custodial protection for $M_{\rm KK}\in [1,10]$ TeV and $L\in [5,37]$. See text for details.
• Figure 5: Regions of 68%, 95%, and 99% probability in the $m_h$--$M_{\rm KK}$ (left panel) and $m_h$--$L$ (right panel) plane in the RS scenario without custodial protection. The upper (lower) area in the left and right panel corresponds to $L=\ln(10^{16})$ ($L=\ln(10^3)$) and $M_{\rm KK}=3$ TeV ($M_{\rm KK}=1.5$ TeV), respectively. See text for details.