θ 13 and charged lepton flavor violation in “warped” A4 models

Abstract

We recently proposed a spontaneous A$_{4}$ flavor symmetry breaking scheme implemented in a warped extra dimensional setup to explain the observed pattern of quark and lepton masses and mixings. The main features of this choice are the explanation of fermion mass hierarchies by wave function overlaps, the emergence of tribimaximal (TBM) neutrino mixing and zero quark mixing at the leading order and the absence of tree-level gauge mediated flavor violation. Quark mixing and deviations from TBM neutrino mixing are induced by the presence of bulk A$_4$ flavons, which allow for "cross-brane" interactions and a "cross-talk" between the quark and neutrino sectors. In this work, we study the constraints associated with the recent measurements of $\theta_{13}\approx 9^\circ$ by RENO and Daya Bay, forcing every model that predicts TBM neutrino mixing to account for the significant deviation of $\theta_{13}$ from 0, while keeping the values of $\theta_{12}$ and $\theta_{23}$ close to their central experimental values. We then proceed to study in detail the RS-A$_4$ contributions to $\mu\to e,3e$, generated at the tree level by virtue of anomalous $Z$ couplings. These couplings arise from gauge and fermionic KK mixing effects after electroweak symmetry breaking. Since the experimental sensitivity for $BR(\mu\to e,3e)$ is expected to increase by five orders of magnitude within the next decade, it is shown that the RS-A$_4$ lepton sector can be significantly constrained. Finally, we show that when "cross-brane" interactions are turned off, the $Z$ couplings are protected against all anomalous contributions and a strong correlation between $\theta_{13}$ and the deviation from maximality of $\theta_{23}$ is found.