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

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, $\Delta m_{32}^2\approx m_3^2$, $\Delta m_{21}^2\approx m_2^2\gg m_1^2$, and a suppressed $\theta_{13}$ mixing angle. We find configurations where the charged lepton mixing angles are suppressed by powers of the Cabibbo angle ($\lambda_C$) relative to vanilla anarchic partial compositeness, consequently reducing CP and lepton flavor violation. Specifically, the Wilson coefficient for the electron electromagnetic dipole moment exhibits $\lambda_C^2$ suppression, while those governing $\mu\to e\gamma$ and $\mu-e$ vector operators are suppressed by $\lambda_C^{3/2}$ compared to the anarchic scenario without U(1) horizontal symmetry.