We show that the inverse see-saw is the most natural way of implementing neutrino masses in the Littlest Higgs model with T-parity. The three extra quasi-Dirac neutrinos are needed to cancel the quadratically divergent contributions of the mirror leptons to the Higgs mass. If the T-parity of the heavy neutrino singlets is chosen to be even, their contributions to lepton flavor violating transitions are one-loop finite. The most stringent limits on this scenario result from the non-observation of these transitions. Constraints on neutrino mixing imply an upper bound on the mass of the T-odd mirror leptons at the reach of the LHC and/or future colliders.

We inspect the Littlest Higgs model with T-parity, based on a global symmetry SU(5) spontaneously broken to SO(5), in order to elucidate the pathologies it presents due to the non-trivial interplay between the gauge invariance associated to the heavy modes and the discrete T-parity symmetry. In particular, the usual Yukawa Lagrangian responsible for providing masses to the heavy ‘mirror’ fermions is not gauge invariant. This is because it contains an SO(5) quintuplet of right-handed fermions that transforms nonlinearly under SU(5), hence involving in general all SO(5) generators when a gauge transformation is performed and not only those associated to its gauge subgroup. Part of the solution to this problem consists of completing the right-handed fermion quintuplet with T-odd ‘mirror partners’ and a gauge singlet, what has been previously suggested for other purposes. Furthermore, we find that the singlet must be T-even, the global symmetry group must be enlarged, an additional nonlinear sigma field should be introduced to parametrize the spontaneous symmetry breaking and new extra fermionic degrees of freedom are required to give a mass to all fermions in an economic way while preserving gauge invariance. Finally, we derive the Coleman–Weinberg potential for the Goldstone fields using the background field method.

The little Higgs model with T-parity, compatible with electroweak precision constraints, introduces new flavor-mixing sources some of which had been ignored until recently. They are reviewed here, showing that their influence does not only enrich the phenomenology of flavor-changing processes but is also needed to render finite one-loop amplitudes.

We investigate the parameter space of the new Littlest Higgs model with T-parity (NLHT) recently introduced to cure some pathologies of the original LHT. The model requires extra fermion content and additional pseudo-Goldstone bosons. While the heavy top quark sector is similar, there are both T-odd and T-even heavy quarks and leptons with masses proportional to just two sets of Yukawa matrices in flavor space, one more than in the LHT. The new scalars are a singlet and real triplet, T-odd, with masses controlled by gauge and Yukawa couplings, independent of the spontaneous symmetry breaking scale f, and hence potentially light. Imposing that no mass exceeds the cutoff scale, applying current lower bounds on vector-like quarks and assuming a simplified model with mass degenerate heavy fermions compatible with the heavy photon as dark matter constituent, we find that f gets constrained within the interval between 2 and 3 TeV, the common Yukawa coupling of heavy leptons gets fixed and the Yukawa coupling of heavy quarks becomes greatly correlated to the top quark Yukawa couplings. The particle spectrum is then bounded from below and above, with the (lightest) heavy photon at about 0.5 TeV, not far from the heavy leptons, the new scalars below 1 TeV, the usual complex scalar triplet close to the heavy weak bosons at about 1.5 to 2.5 TeV, and the heavy quarks and top quark partners between 2 and 5 TeV. The new scalars decay predominantly to a standard and a T-odd lepton and have a width comparable to that of the Higgs.