Renormalization of the neutrino mass operators in the multi-Higgs-doublet Standard Model

We derive the renormalization group equations (RGE) for the flavour coupling matrices of the effective dimension-five operators which yield Majorana neutrino masses in the multi-Higgs-doublet Standard Model; in particular, we consider the case where two different scalar doublets occur in those operators. We also write down the RGE for the scalar-potential quartic couplings and for the Yukawa couplings of that model, in the absence of quarks. As an application of the RGE, we consider two models which, based on a mu-tau interchange symmetry, predict maximal atmospheric neutrino mixing, together with U_{e3} = 0, at the seesaw scale. We estimate the change of those predictions due to the evolution of the coupling matrices of the effective mass operators from the seesaw scale down to the electroweak scale. We derive an upper bound on that change, thereby finding that the radiative corrections to those predictions are in general negligible.Comment: 16 pages, LaTe

A non-standard CP transformation leading to maximal atmospheric neutrino mixing

We discuss a neutrino mass matrix $\mathcal{M}_\nu$ originally found by Babu, Ma, and Valle (BMV) and show that this mass matrix can be characterized by a simple algebraic relation. From this relation it follows that atmospheric neutrino mixing is exactly maximal while at the same time an arbitrary mixing angle $\theta_{13}$ of the lepton mixing matrix $U$ is allowed and--in the usual phase convention--CP violation in mixing is maximal; moreover, neither the neutrino mass spectrum nor the solar mixing angle are restricted. We put forward a simple seesaw extension of the Standard Model where the family lepton numbers are softly broken by the Majorana mass terms of the right-handed neutrino singlets and the BMV mass matrix results from a non-standard $CP$ symmetry.Comment: 13 pages, plain LaTeX, no figures; minor modifications, final version for Phys. Lett.

Gauge boson families in grand unified theories of fermion masses: E_6^4 x S_4

In third quantization the origin of fermion families is easy to understand: the electron field, the muon field and the tau field are identical fields in precisely the same sense as three electrons are identical and undistinguishable particles of a theory of second quantization. In both cases, the permutation of these fields or particles leaves the lagrangian invariant. One can also extend the concept of family to gauge bosons. This can be obtained through the semidirect product of the gauge group with the group of permutations of n objects. In this paper we have studied the group E_6^4 x S_4. We explain why we have chosen E_6 as fundamental gauge group factor and why we start with a model with four gauge boson/fermion families to accommodate and to fit the standard model with only three fermion families. We suggest a possible symmetry breaking pattern of E_6^4 x S_4 that could explain quark, lepton and neutrino masses and mixings.Comment: 21 pages, no figur

S3 x Z2 model for neutrino mass matrices

We propose a model for lepton mass matrices based on the seesaw mechanism, a complex scalar gauge singlet and a horizontal symmetry S_3 \times \mathbbm{Z}_2. In a suitable weak basis, the charged-lepton mass matrix and the neutrino Dirac mass matrix are diagonal, but the vacuum expectation value of the scalar gauge singlet renders the Majorana mass matrix of the right-handed neutrinos non-diagonal, thereby generating lepton mixing. When the symmetry $S_3$ is not broken in the scalar potential, the effective light-neutrino Majorana mass matrix enjoys $\mu$--$\tau$ interchange symmetry, thus predicting maximal atmospheric neutrino mixing together with $U_{e3} = 0$. A partial and less predictive form of $\mu$--$\tau$ interchange symmetry is obtained when the symmetry $S_3$ is softly broken in the scalar potential. Enlarging the symmetry group S_3 \times \mathbbm{Z}_2 by an additional discrete electron-number symmetry \mathbbm{Z}_2^{(e)}, a more predicitive model is obtained, which is in practice indistinguishable from a previous one based on the group $D_4$.Comment: 13 pages, 3 figures, final version for publication in JHE

TeV-scale seesaw mechanism catalyzed by the electron mass

We construct a model in which the neutrino Dirac mass terms are of order the electron mass and the seesaw mechanism proceeds via right-handed neutrinos with masses of order TeV. In our model the spectra of the three light and of the three heavy neutrinos are closely related. Since the mixing between light and heavy neutrinos is small, the model predicts no effects in pp and p \bar p colliders. Possible signatures of the model are the lepton-number-violating process e- e- --> H- H-, where H- is a charged scalar particle, lepton-flavour-violating decays like mu- --> e- e+ e-, or a sizable contribution to the anomalous magnetic dipole moment of the muon.Comment: 13 pages, one figure, matches published versio