A Little Higgs model of neutrino masses

Little Higgs models are formulated as effective theories with a cut-off of up to 100 times the electroweak scale. Neutrino masses are then a puzzle, since the usual see-saw mechanism involves a much higher scale that would introduce quadratic corrections to the Higgs mass parameter. We propose a model that can naturally accommodate the observed neutrino masses and mixings in Little Higgs scenarios. Our framework does not involve any large scale or suppressed Yukawa couplings, and it implies the presence of three extra (Dirac) neutrinos at the TeV scale. The masses of the light neutrinos are induced radiatively, they are proportional to small (≈ keV) mass parameters that break lepton number and are suppressed by the Little Higgs cut-off. Introduction. The stability of the electroweak (EW) scale at the loop level has been the main motivation to search for physics beyond the standard model (SM) during the past 30 years. Namely, SM loops introduce quadratic corrections to the EW scale. If this scale is natural, consistent with the dynamics and not the result of an accidental cancellation between higher scales, then new physics must compensate the SM quadratic contributions. In particular, top quark corrections to the Higgs mass squared become of order (500 GeV) for a cutoff ≈ 2 TeV, what would suggest new contributions (from supersymmetry, extra dimensions,...) of the same order at the reach of the LHC. Little Higgs (LH) ideas [1, 2, 3] provide another very interesting framework with a scalar sector free of unsuppressed loop corrections. New symmetries protect the EW scale and define consistent models with a cutoff as high as Λ ≈ 10 TeV. Therefore, these models could describe all the physics to be explored in the next generation of accelerators. More precisely, in LH models the scalar sector has a (tree-level) global symmetry G that is broken spontaneously at a scale f ≈ 1 TeV. The SM Higgses are then Goldstone bosons (GBs) of the broken symmetry, and remain massless and with a flat potential at that scale. Yukawa and gauge interactions break explicitly the global symmetry. However, the models are built in such a way that the loop diagrams giving non-symmetric contributions must contain at least two different couplings. This collective breaking keeps the Higgs sector free of quadratic top-quark and gauge contributions. At the same time, loops (and/or explicit non-symmetric terms in the scalar potential) give mass and quartic couplings to the Higgs, both necessary to break the SM symmetry (see [4] for a recent review). The inclusion of neutrino masses in this framework looks problematic. In the SM these masses require a new scale much larger than the EW one, Leff = 1 2Λν h†h†LL+ h.c. , (1) where h = (h h−) and L = (ν e) are, respectively, the SM Higgs and lepton doublets. At the EW phase transition 〈h0〉 = v and the neutrinos get their mass mν = v/Λν ≈ 0.1 eV, what implies Λν ≈ 10 GeV. This effective (low-energy) scenario is simply realised using the see-saw mechanism [5]. A SM singlet per family, n, is introduced with a large Majorana mass M and sizeable Yukawa couplings λν with the lepton doublets: Lν = λνhLn + 1 2 Mnn + h.c. (2) (the fields denote two-component left-handed spinors and family indices are omitted). The spectrum is then three (Majorana) fields of mass ≈ M plus the observed low-energy neutrinos with mass mν ≈ λνv/M . 2 This scenario looks inconsistent in LH models, since the EW scale is not stable at the quantum level. In particular, the diagram in Fig. 1 gives a large contribution to the Higgs mass proportional to M: ∆mh ≈ − λν 8π2 (