A new and gauge-invariant littlest Higgs model with T-parity

Abstract

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.

Lepton flavor violation in the Littlest Higgs Model with T parity realizing an inverse seesaw

“…8 We postpone to future work the complete analysis within the LHT keeping the O(v 2 /f 2 ) contributions to the form factors. This shall be necessary, since the heavy Majorana neutrinos have to have O(TeV) masses, as the T-odd particles, within a gauge invariant theory [46]. We will also need to study first semileptonic LFV tau decays within the LHT (following refs.…”

“…As a result, direct and indirect constraints on the LHT are significantly relaxed [21,22]. Thus, the LHT remains phenomenologically viable and well-motivated [23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][39][40][41][42][43][44][45][46].…”

Lepton flavour violation in hadron decays of the tau lepton within the littlest Higgs model with T-parity

“…Varied aspects of its phenomenology have been studied in refs. [23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39], in particular lepton flavor violating processes have been analyzed in refs. [32,[40][41][42][43][44][45][46][47][48][49][50][51].…”

Phenomenological implications of the new Littlest Higgs model with T-parity

“…However, the LHT has been shown to suffer from pathologies in the fermionic sector. The fermion content breaks explicitly the gauge invariance of the LHT [54,55]. In this model, the left-handed components of the SM and the mirror fermions come in incomplete SU (5) multiplets whereas their right-handed counterparts come in a multiplet of SO (5) [33,34,36,39,40,[56][57][58].…”

“…However, this setup breaks gauge invariance because the SO(5) multiplets transform non linearly. In fact, it has been shown [55] that a gauge transformation involves all the SO(5) generators, not only those associated to the gauge group, which implies that any SO (5) multiplet should be complete because in general a gauge transformation will mix all its components. As a consequence, all the right-handed fermions transforming in a SO (5) representation must have the same mass.…”