Verifiable Radiative Seesaw Mechanism of Neutrino Mass and Dark Matter

A minimal extension of the Standard Model is proposed, where the observed lefthanded neutrinos obtain naturally small Majorana masses from a one-loop radiative seesaw mechanism. This model has two candidates (one bosonic and one fermionic) for the dark matter of the Universe. It has a very simple structure and should be verifiable in forthcoming experiments at the Large Hadron Collider. In the well-known canonical seesaw mechanism [1], three heavy singlet Majorana neutrinos Ni (i = 1, 2, 3) are added to the Standard Model (SM) of elementary particles, so that M ν = −MDM N MTD, (1) where MD is the 3× 3 Dirac mass matrix linking the observed neutrinos να (α = e, μ, τ) to Ni, and MN is the Majorana mass matrix of Ni. More generally [2], Mν comes from the unique dimension-five operator LΛ = fij Λ (νiφ 0 − liφ)(νjφ − ljφ) +H.c., (2) where (νi, li) are the usual left-handed lepton doublets transforming as (2,−1/2) under the standard electroweak SU(2)L×U(1)Y gauge group and (φ, φ) ∼ (2, 1/2) is the usual Higgs doublet of the SM. There are three and only three tree-level realizations [3] of this operator, one of which is of course the canonical seesaw mechanism. There are also three generic mechanisms for obtaining this operator in one loop [3]. Whereas the new particles required in the three tree-level realizations are most likely too heavy to be observed experimentally in the near future, those involved in the one-loop realizations may in fact be light enough to be detected, in forthcoming experiments at the Large Hadron Collider (LHC) for example. Consider the following minimal extension of the SM. Under SU(2)L × U(1)Y × Z2, the particle content is given by (νi, li) ∼ (2,−1/2;+), l i ∼ (1, 1;+), Ni ∼ (1, 0;−), (3) (φ, φ) ∼ (2, 1/2;+), (η, η) ∼ (2, 1/2;−). (4) Note that the new particles, i.e. Ni and the scalar doublet (η , η), are odd under Z2. A previously proposed model [4] of neutrino mass shares the same particle content of this model, but the extra symmetry assumed there is global lepton number, which is broken explicitly but softly by the unique bilinear term μΦη +H.c. in the Higgs potential. Here, Z2 is an 2 exact symmetry, in analogy with the well-known R−parity of the Minimal Supersymmetric Standard Model (MSSM), hence this term is strictly forbidden. As a result, η has zero vacuum expectation value and there is no Dirac mass linking νi with Nj . Neutrinos remain massless at tree level as in the SM. The Yukawa interactions of this model are given by LY = fij(φνi + φ̄li)l j + hij(νiη − ljη)Nj +H.c. (5) In addition, the Majorana mass term 1 2 MiNiNi +H.c. and the quartic scalar term 1 2 λ5(Φ η) +H.c. are allowed. Hence the one-loop radiative generation of Mν is possible, as depicted in Fig. 1. This diagram was discussed in Ref. [3], but without recognizing the crucial role of the exact Z2 symmetry being considered here.