Abstract
Abstract We consider the generation of the hierarchical charged lepton spectrum and anarchic neutrino masses and mixing angles in warped extra dimensional models with Randall-Sundrum metric. We have classified all possible cases giving rise to realistic spectra for both Dirac and Majorana neutrinos. An anarchic neutrino spectrum requires a convenient bulk symmetry broken by boundary conditions on both UV and IR branes. We have in particular considered the case of Majorana neutrinos with a continuous bulk symmetry. To avoid unwanted massless extra gauge bosons the 4D group should be empty. If the 4D coset is not vanishing it can provide a Wilson Line description of the neutrino Majorana mass matrix. We have studied an example based on the bulk gauge group $\mathrm{U}{(3)_{\ell }}\otimes \mathrm{U}{(3)_{\mathcal{N}}}{\otimes_i}\mathrm{U}{(1)_{{{\varepsilon^i}}}}$ with the Wilson Line in $\mathrm{SO}{(3)_{\mathcal{N}}}$ satisfying all required conditions. A χ 2-fit to experimental data exhibits 95% CL region in the parameter space with no fine- tuning. As a consequence of the symmetries of the theory there is no tree-level induced lepton flavor violation and so one-loop processes are consistent with experimental data forKK-modes about a few TeV. The model is easily generalizable to models with IR deformed metrics with similar conclusions.
Highlights
Quark sector in WED theories both for an AdS metric [2, 3], as in the original RandallSundrum (RS) model, and for asymptotically AdS metrics [4,5,6,7]
Its 4D Yukawa coupling, is controlled by their 5D Dirac mass c such that for different values of c we obtain hierarchically different values of the corresponding quark masses and small mixing angles. Due to their different localizations the quark flavors couple differently to KK modes of gauge bosons generating dimensionsix flavor changing neutral current (FCNC) operators. While these flavor violations are suppressed by the so-called RS-GIM mechanism [8,9,10] the KK masses have to be heavier than ∼ 20 TeV to suppress FCNC processes in the RS theory [6, 11] while this bound can be lowered to 4-5 TeV in the case of IR deformed metrics [5, 6]
FCNC higher dimensional operators involving light fermions and generated by exchange of gauge boson KK-modes are protected by the so-called RS-GIM mechanism as massive KK-modes are leaning towards the IR brane
Summary
We will compute the neutrino mass matrix (2.9) separately for the cases of bulk and brane Yukawa couplings. The neutrino mass matrix for bulk Yukawa coupling is given by miνj = v Y ij ǫcil−1/2ǫcjN −1/2 (cjN > 1/2). Even for cN > 1/2 this gives too small neutrino masses unless we consider ǫ 10−12, which implies k 1015 GeV ≪ MP , in which case we do not solve the grand hierarchy problem (as in little RS models [35]). To summarize the case of Dirac neutrinos, its mass matrix and mixing angles can be realistically described by different localization of leptonic fields in the bulk of AdS space provided there is a symmetry imposing cil ≡ cl and ciN ≡ cN for ∀i and both cl, cN > 1/2. We will come back to the issue of the bulk symmetry later on in this paper
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