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.
Highlights
We study the constraints associated with the recent measurements of θ13 ≈ 9◦ by RENO and Daya Bay, forcing every model that predicts TBM neutrino mixing to account for the significant deviation of θ13 from 0, while keeping the values of θ12 and θ23 close to their central experimental values
The global fits based on the recent measurements of νμ → νe appearance in the RENO, Daya Bay, T2K, MINOS and other experiments, allow one to obtain a significance of 10σ for θ13 > 0, with best fit points at around θ13 0.15, depending on the precise treatment of reactor fluxes [18, 19]
We have shown that cross-talk operators in the charged lepton sector and brane localized higher order corrections to the Majorana and Dirac mass matrices induce significant deviations from TBM neutrino mixing, such that the experimental bounds can be rather satisfied
Summary
The RS-A4 setup [1] is illustrated in figure 1. The scalar sector contains the IR peaked Higgs field and the UV and IR peaked flavons, χ and Φ, respectively All fermionic zero modes acquire masses through Yukawa interactions with the Higgs field and the A4 flavons after SSB. The VEV and physical profiles for the bulk scalars are obtained by solving the corresponding equations of motion with a UV/IR localized quartic potential term and an IR/UV localized mass term [30]. The Higgs VEV is in charge of the SSB pattern SU(2)L × SU(2)R → SU(2)D, which is peaked towards the IR brane. The right diagonalization matrices in the quark and charged lepton sectors, to first order in fχui,di,ei (xui ,d, , yiu,d, ) are given by:. The suppression by quark mass ratios of the off-diagonal elements in VRu,d, stemming from the degeneracy of LH bulk masses, turned out to play an important role in relaxing the flavor violation bounds on the KK mass scale, as compared to flavor anarchic frameworks [10]
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