Neutrino masses from operator mixing

Abstract

We show that in theories that reduce, at the Fermi scale, to an extension of the standard model with two doublets, there can be additional dimension five operators giving rise to neutrino masses. In particular there exists a singlet operator which can not generate neutrino masses at tree level but generates them through operator mixing. Under the assumption that only this operator appears at tree level we calculate the neutrino mass matrix. It has the Zee mass matrix structure and leads naturally to bimaximal mixing. However, the maximal mixing prediction for solar neutrinos is very sharp even when higher order corrections are considered. To allow for deviations from maximal mixing a fine tuning is needed in the neutrino mass matrix parameters. However, this fine tuning relates the departure from maximal mixing in solar neutrino oscillations with the neutrinoless double beta decay rate.PACS numbers: 14.60. Pq, 14.60.St, 14.80.Cp, 12.60.Fr The simplest model for neutrino masses is based on the seesaw mechanism [1][2][3]. In the seesaw mechanism the standard model (SM) is enlarged with singlet right-handed neutrinos. Then, a Dirac mass term, M D , mixing left-handed and right-handed neutrinos is possible. In addition, since right-handed neutrinos do not carry any gauge charge, they can have a Majorana mass, M R , without compromising the gauge symmetry. If the right-handed Majorana mass term is very large, as expected for a singlet mass term, very light Majorana neutrino masses for left-handed neutrinos are obtained through the diagonalization of the full mass matrix of neutral fermions, m ν = M 2 D /M R , thus justifying the small size of neutrino masses. Since the Dirac mass term is proportional to the standard Higgs vacuum expectation value, this mechanism provides masses which are m ν ≈ Λ 2 F /Λ, being Λ F the Fermi scale and Λ the lepton number breaking scale. This type of behaviour is much more general and, in fact, many neutrino mass models can be cast into this form. This can be understood in the following way: if the SM is just the low energy effective manifestation of some underlying theory, the effects of new physics can be represented by a series of gauge invariant operators 1 containing the SM fields with higher dimension operators suppressed by powers of the scale of new physics [4][5][6]. At low energies, the most relevant operators will be those with the lowest dimension, that is dimension five operators. One can easily see that there is only one gauge invariant operator of dimension five one can build with the field content of the standard model [5]where ℓ is the standard left-handed doublet of leptons, ℓ = iτ 2 ℓ c , ℓ c = Cℓ T ( C is the charge conjugation operator), ϕ is the Higgs doublet and ϕ = iτ 2 ϕ * , τ are the Pauli matrices in SU(2) space, F is a complex symmetric matrix in flavour space (SU(2) and flavour indices have been suppressed) and Λ is a scale related to the scale of new physics. It is clear that this Lagrangian does not conserve generational lepton numbers, but in a...

Prospects for the Zee-Babu model at the CERN LHC and low energy experiments

“…The simplest model of neutrino masses is the Zee-Babu 3 (ZB) model [18,19,20] which just adds two complex singlet scalar fields to the SM (that is, just 4 new degrees of freedom) with neutrino masses generated at the two-loop level. Another very interesting model is the Zee model [17] which adds a new scalar doublet and a complex scalar singlet (6 new degrees of freedom), however, the simplest version of the model gives a too sharp bimaximal prediction for neutrino mixing and has already been excluded [24,25,26]. Therefore, we will only consider here the Zee-Babu model.…”

New Weinberg operator for neutrino mass and its seesaw origin

“…The Weinberg operator discussed above can be straightforwardly generalised to the case of multi-Higgs doublet models [23], to the operators of the form H a H b L i L j , for Higgs doublets H a,b , where a, b = 1, · · · , N can be taken to have the same hypercharge, opposite to that of L i . The question of which Weinberg operators arise will depend on the details of the particular multi-Higgs doublet model, such as the symmetries controlling the Higgs and fermion sectors, the seesaw origin of the Weinberg operators and so on 1 .…”

“…. However in[24] the authors do not explicitly mention the multi-Higgs doublet generalisation in[23] which is relevant here.…”

Discriminating between lepton number violating scalars using events with four and three charged leptons at the LHC

“…5 Typically a heavier triplet coupling to the LH lepton bilinear, with a small VEV or/and with scalar couplings softly breaking LN. 6 We can also write the Weinberg operator but with one of the Higgs doublets replaced by a new heavy doublet of hypercharge 1/2, [21] but this does not contain a doubly-charged component and cannot resonate in same-sign di-lepton channels. Moreover, there is only one combination of the lepton doublets that gives a triplet involving the same-sign charged lepton bilinear; any other possible invariant operator of that type must be related.…”