Luca Merlo

Revisiting Bimaximal Neutrino Mixing in a Model with S(4) Discrete Symmetry

In view of the fact that the data on neutrino mixing are still compatible with a situation where Bimaximal mixing is valid in first approximation and it is then corrected by terms of (λC) (with λC being the Cabibbo angle), arising from the diagonalization of the charged lepton masses, such that δsin2θ12 ~ sinθ13 ~ (λC) while δsin2θ23 ~ (λC2), we construct a model based on the discrete group S4 where those properties are naturally realized. The model is supersymmetric in 4-dimensions and the complete flavour group is S4 × Z4 × U(1)FN, which also allows to reproduce the hierarchy of the charged lepton spectrum. The only fine tuning needed in the model is to reproduce the small observed value of r = Δm2sun/Δm2atm. Once the relevant parameters are set to accommodate r then the spectrum of light neutrinos shows a moderate normal hierarchy and is compatible, within large ambiguities, with the constraints from leptogenesis as an explanation of the baryon asymmetry in the Universe.

Fermion masses and mixings in a S4 based model

It has been recently claimed that the symmetry group S4 yields to the Tri-bimaximal neutrino mixing in a “natural” way from the group theory point of view. Approving of this feature as an indication, we build a supersymmetric model of lepton and quark masses based on this family symmetry group. In the lepton sector, a correct mass hierarchy among the charged leptons is achieved together to a neutrino mass matrix which can be diagonalized by the Tri-bimaximal pattern. Our model results to be phenomenologically inequivalent with respect to other proposals based on different flavour groups but still predicting the Tri-bimaximal mixing. In the quark sector a realistic pattern for masses and mixing angles is obtained. The flavour structures of the mass matrices in both the sectors come from the spontaneously symmetry breaking of S4, due to several scalar fields, which get non-zero vacuum expectation values. A specific vacuum alignment is required and it is shown to be a natural results of the minimization of the scalar potential and, moreover, to be stable under the corrections from the higher order terms.

Phenomenological consequences of the seesaw mechanism in S-4 based models

We thank M. Hirsch and Y. Lin for useful comments and ndiscussions. The work of F. B. has been partially supported nby MEC-Valencia MEC Grant No. FPA2008-00319/FPA, nby European Commission Contract Nos. MRTN-CT-2004- n503369 and ILIAS/N6 RII3-CT-2004-506222 and by the nfoundation for Fundamental Research of Matter and the nNational Organization for Scientific Research. L. M. recognizes nthat this work has been partly supported by the nEuropean Commission under Contract No. MRTN-CT- n2006-035505. The work of S. M. supported by MECValencia nMEC Grant No. FPA2008-00319/FPAand by nEuropean Commission Contract Nos. MRTN-CT-2004- n503369 and ILIAS/N6 RII3-CT-2004-506222.

The interplay between GUT and flavour symmetries in a Pati-Salam × S4 model

Both Grand Unified symmetries and discrete flavour symmetries are appealing ways to describe apparent structures in the gauge and flavour sectors of the Standard Model. Both symmetries put constraints on the high energy behaviour of the theory. This can give rise to unexpected interplay when building models that possess both symmetries. We investigate on the possibility to combine a Pati-Salam model with the discrete flavour symmetry S4 that gives rise to quark-lepton complementarity. Under appropriate assumptions at the GUT scale, the model reproduces fermion masses and mixings both in the quark and in the lepton sectors. We show that in particular the Higgs sector and the running Yukawa couplings are strongly affected by the combined constraints of the Grand Unified and family symmetries. This in turn reduces the phenomenologically viable parameter space, with high energy mass scales confined to a small region and some parameters in the neutrino sector slightly unnatural. In the allowed regions, we can reproduce the quark masses and the CKM matrix. In the lepton sector, we reproduce the charged lepton masses, including bottom-tau unification and the Georgi-Jarlskog relation as well as the two known angles of the PMNS matrix. The neutrino mass spectrum can present a normal or an inverse hierarchy, and only allowing the neutrino parameters to spread into a range of values between λ−2 and λ2, with λ ≃ 0.2. Finally, our model suggests that the reactor mixing angle is close to its current experimental bound.

Vacuum alignment in SUSY A4 models

In this note we discuss the vacuum alignment in globally supersymmetric models with spontaneously broken flavour symmetries in the presence of generic soft supersymmetry (SUSY) breaking terms. We show that the inclusion of these soft SUSY breaking terms can give rise to non-vanishing vacuum expectation values (VEVs) for the auxiliary components of the flavon fields. These non-zero VEVs can have an important impact on the phenomenology of this class of models, since they can induce an additional flavour violating contribution to the sfermion soft mass matrix of right-left (RL) type. We carry out an explicit computation in a class of globally SUSY A4 models predicting tribimaximal mixing in the lepton sector. The flavour symmetry breaking sector is described in terms of flavon and driving supermultiplets. We find non-vanishing VEVs for the auxiliary components of the flavon fields and for the scalar components of the driving fields which are of order mSUSY × 〈φ〉 and mSUSY, respectively. Thereby, mSUSY is the generic soft SUSY breaking scale which is expected to be around 1 TeV and 〈φ〉 is the VEV of scalar components of the flavon fields. Another effect of these VEVs can be the generation of a μ term.

Tri/Bi-maximal lepton mixing and leptogenesis

In models with flavour symmetries added to the gauge group of the Standard Model the CP-violating asymmetry necessary for leptogenesis may be related with low-energy parameters. A particular case of interest is when the flavour symmetry produces exact Tri/Bi-maximal lepton mixing leading to a vanishing CP-violating asymmetry. In this paper we present a model-independent discussion that confirms this always occurs for unflavoured leptogenesis in type I see-saw scenarios, noting however that Tri/Bi-maximal mixing does not imply a vanishing asymmetry in general scenarios where there is interplay between type I and other see-saws. We also consider a specific model where the exact Tri/Bi-maximal mixing is lifted by corrections that can be parametrised by a small number of degrees of freedom and analyse in detail the existing link between low and high-energy parameters — focusing on how the deviations from Tri/Bimaximal are connected to the parameters governing leptogenesis.

Lepton Flavour Violation in a Supersymmetric Model with A 4 Flavour Symmetry

Abstract We compute the branching ratios for μ → e γ , τ → μ γ and τ → e γ in a supersymmetric model invariant under the flavour symmetry group A 4 × Z 3 × U ( 1 ) FN , in which near tri-bimaximal lepton mixing is naturally predicted. At leading order in the small symmetry breaking parameter u, which is of the same order as the reactor mixing angle θ 13 , we find that the branching ratios generically scale as u 2 . Applying the current bound on the branching ratio of μ → e γ shows that small values of u or tan β are preferred in the model for mass parameters m SUSY and m 1 / 2 smaller than 1000 GeV. The bound expected from the on-going MEG experiment will provide a severe constraint on the parameter space of the model either enforcing u ≈ 0.01 and small tan β or m SUSY and m 1 / 2 above 1000 GeV. In the special case of universal soft supersymmetry breaking terms in the flavon sector a cancellation takes place in the amplitudes and the branching ratios scale as u 4 , allowing for smaller slepton masses. The branching ratios for τ → μ γ and τ → e γ are predicted to be of the same order as the one for μ → e γ , which precludes the possibility of observing these τ decays in the near future.

Fermion Masses and Mixings in a S(4)-based Model

It has been recently claimed that the symmetry group S4 yields to the Tri-bimaximal neutrino mixing in a “natural” way from the group theory point of view. Approving of this feature as an indication, we build a supersymmetric model of lepton and quark masses based on this family symmetry group. In the lepton sector, a correct mass hierarchy among the charged leptons is achieved together to a neutrino mass matrix which can be diagonalized by the Tri-bimaximal pattern. Our model results to be phenomenologically inequivalent with respect to other proposals based on different flavour groups but still predicting the Tri-bimaximal mixing. In the quark sector a realistic pattern for masses and mixing angles is obtained. The flavour structures of the mass matrices in both the sectors come from the spontaneously symmetry breaking of S4, due to several scalar fields, which get non-zero vacuum expectation values. A specific vacuum alignment is required and it is shown to be a natural results of the minimization of the scalar potential and, moreover, to be stable under the corrections from the higher order terms.

Discrete Flavour Groups, \theta_13 and Lepton Flavour Violation

A bstractDiscrete flavour groups have been studied in connection with special patterns of neutrino mixing suggested by the data, such as Tri-Bimaximal mixing (groups A4, S4…) or Bi-Maximal mixing (group S4…) etc. We review the predictions for sin θ13 in a number of these models and confront them with the experimental measurements. We compare the performances of the different classes of models in this respect. We then consider, in a supersymmetric framework, the important implications of these flavour symmetries on lepton flavour violating processes, like μ → eγ and similar processes. We discuss how the existing limits constrain these models, once their parameters are adjusted so as to optimize the agreement with the measured values of the mixing angles. In the simplified CMSSM context, adopted here just for indicative purposes, the small tan β range and heavy SUSY mass scales are favoured by lepton flavour violating processes, which makes it even more difficult to reproduce the reported muon g − 2 discrepancy.

Running effects on lepton mixing angles in flavour models with type I seesaw

Abstract We study renormalization group running effects on neutrino mixing patterns when a (type I) seesaw model is implemented by suitable flavour symmetries. We are particularly interested in mass-independent mixing patterns to which the widely studied tribimaximal mixing pattern belongs. In this class of flavour models, the running contribution from neutrino Yukawa coupling, which is generally dominant at energies above the seesaw threshold, can be absorbed by a small shift on neutrino mass eigenvalues leaving mixing angles unchanged. Consequently, in the whole running energy range, the change in mixing angles is due to the contribution coming from charged lepton sector. Subsequently, we analyze in detail these effects in an explicit flavour model for tribimaximal neutrino mixing based on an A 4 discrete symmetry group. We find that for normally ordered light neutrinos, the tribimaximal prediction is essentially stable under renormalization group evolution. On the other hand, in the case of inverted hierarchy, the deviation of the solar angle from its TB value can be large depending on mass degeneracy, putting strong constraints on the flavour model.