Lepton flavor from a horizontal symmetry in a slice of AdS$_5$

TL;DR

This work presents a warped extra-dimensional model in a slice of AdS$_5$ where bulk SM fields experience a horizontal U(1) symmetry with a flavon, and EW and FN breaking occurs on the IR boundary. By leveraging flavor-anarchic 5D Yukawas together with FN charges and localization, the model generates realistic lepton masses and the PMNS matrix, with neutrinos realized as Dirac states in a normal hierarchy. Importantly, charged-lepton mixing and LFV are suppressed by Cabibbo-angle factors relative to anarchic partial compositeness, enabling lighter KK resonances without conflicting with precision bounds, as demonstrated by analytic estimates and numerical scans. The results indicate a viable framework for leptonic flavor in warped extra dimensions and motivate further exploration of the scalar sector and quark-sector extension.

Abstract

We build a model of lepton flavor in a slice of AdS$_5$. We add to the 5D SM fields a set of neutrino fields, as well as a horizontal U(1) symmetry and a flavon field, all propagating in the bulk. The electroweak and U(1) symmetries are spontaneously broken by a potential localized on the infrared boundary. We show that in a flavor anarchic scenario, by suitable choice of the 5D masses and the U(1) charges, the masses of the SM leptons and the PMNS matrix can be naturally generated. The neutrino masses are Dirac like, with a normal ordered hierarchical spectrum, $Δm_{32}^2\approx m_3^2$, $Δm_{21}^2\approx m_2^2\gg m_1^2$, and a suppressed $θ_{13}$ mixing angle. We find configurations where the charged lepton mixing angles are suppressed by powers of the Cabibbo angle ($λ_C$) relative to vanilla anarchic partial compositeness, consequently reducing CP and lepton flavor violation. Specifically, the Wilson coefficient for the electron electromagnetic dipole moment exhibits $λ_C^2$ suppression, while those governing $μ\to eγ$ and $μ-e$ vector operators are suppressed by $λ_C^{3/2}$ compared to the anarchic scenario without U(1) horizontal symmetry.

Figures (6)

• Figure 1: KK wave functions of the first and second scalar modes: $s^{(1)}$ and $s^{(2)}$, respectively.
• Figure 2: Numerical predictions of the neutrino observables with BM1 of the model, performing a random scan over the Yukawa couplings. On the left we show the mass-squared differences and in the centre and in the right the mixing angles of the PMNS matrix.
• Figure 3: Numerical predictions of the masses of the charged leptons with BM1 of the model, performing a random scan over the Yukawa couplings. Orange lines show the analytical estimates.
• Figure 4: Numerical predictions of the Wilson coefficients of dipole operators with BM1 of the model, normalized with respect to APC, performing a random scan over the Yukawa couplings. Orange lines show the analytical estimates. On the top-left panel we show the neutral and charged Higgs contributions to the $e$EDM, on the top-right we show the different chiralities in $\mu\to e\gamma$, as on the bottom-left and bottom-right panels, where we show respectively $\tau\to \mu\gamma$ and $\tau\to e\gamma$.
• Figure 5: Numerical predictions of the Wilson coefficients of vector operators with BM1 of the model, normalized with respect to APC, performing a random scan over the Yukawa couplings. Orange lines show the analytical estimates. On the top-left and top-right panels we show the results for $\mu e$ and $\tau\mu$ operators,respectively, and on the bottom one for $\tau e$.