Probing the Randall-Sundrum geometric origin of flavor with lepton flavor violation

TL;DR

This work analyzes lepton flavor violation within the anarchic Randall-Sundrum framework, where the Standard Model fields live in a warped 5D space and Yukawas are anarchic in the 5D theory. It contrasts two Higgs localization scenarios: brane-localized Higgs yields UV-sensitive, incalculable dipole decays, while a bulk Higgs yields calculable dipole contributions and TeV-scale bounds from μ-e conversion, μ → 3e, and τ decays. A detailed Monte Carlo scan demonstrates that current data require Kaluza-Klein scales in the few- to multi-TeV range, with a notable tension between tree-level and loop-induced LFV processes that constrains the natural parameter space. The study emphasizes that upcoming MEG and PRIME experiments, along with future tau factories, will decisively test the RS geometric origin of flavor at the TeV scale, potentially guiding model-building directions such as custodial symmetries or structured Yukawas.

Abstract

The ``anarchic'' Randall-Sundrum model of flavor is a low energy solution to both the electroweak hierarchy and flavor problems. Such models have a warped, compact extra dimension with the standard model fermions and gauge bosons living in the bulk, and the Higgs living on or near the TeV brane. In this paper we consider bounds on these models set by lepton flavor violation constraints. We find that loop-induced decays of the form l->l'+gamma are ultraviolet sensitive and uncalculable when the Higgs field is localized on a four-dimensional brane; this drawback does not occur when the Higgs field propagates in the full five-dimensional space-time. We find constraints at the few TeV level throughout the natural range of parameters, arising from muon-electron conversion in the presence of nuclei, rare muon decays, and rare tau decays. A "tension" exists between loop-induced dipole decays such as mu->e+gamma and tree-level processes such as muon-electron conversion; they have opposite dependences on the five-dimensional Yukawa couplings, making it difficult to decouple flavor-violating effects. We emphasize the importance of the future experiments MEG and PRIME. These experiments will definitively test the Randall-Sundrum geometric origin of hierarchies in the lepton sector at the TeV-scale.

Figures (9)

• Figure 1: $f_i$, the off-diagonal elements of the gauge boson mass matrix that describe the mixing of the zero-mode with the $i$-th KK-mode.
• Figure 2: The Feynman diagram generating the dipole operator which mediates $l \to l^{'}\gamma$ decays. $l^i$ are the physical KK leptons. We have specialized to $\mu \to e\gamma$ in the figure. There is a similar diagram with $L\leftrightarrow R$.
• Figure 3: The ratios of the zero-mode fermion couplings to $Z^{(1)}$ over their SM values, for $x=e,\mu,\tau$, as functions of the Yukawa couplings $Y_x$.
• Figure 4: Scan of the $\mu \rightarrow 3e$ and $\mu-e$ conversion predictions for $M_{KK}=3,5,10$ TeV. The solid and dashed lines are the PDG and SINDRUM II limits, respectively.
• Figure 5: Scan of the $\tau \rightarrow 3e$ and $\tau \rightarrow 3\mu$ predictions for $M_{KK}=1$ TeV. The solid and dashed lines are the current $B$-factory and projected super-$B$ factory limits, respectively.