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.
Highlights
Standard Model (SM) particles are T-even and the new particles are T-odd and pair-produced
In this work we propose an economic cure to these problems which consists in enlarging minimally the global group, introducing a new pattern for the spontaneous symmetry breaking (SSB) and adding extra fermionic degrees of freedom
The original Littlest Higgs model with T-parity (LHT) allows for masses of SM and mirror leptons through Yukawa interactions but, in order to be consistent with gauge and T-parity invariance, the right-handed components of mirror leptons must share a complete SO(5) quintuplet ΨR with T-odd mirror-partner leptons (l−c )R and a singlet (χ+)R that must be T-even according to Eq (71)
Summary
SM particles are T-even and (most of) the new particles are T-odd and pair-produced. A subgroup [SU(2) × U(1)]2 of the full global symmetry group SU(5) is gauged and gets broken spontaneously to the diagonal subgroup SU(2) × U(1), leading to a set of T-odd massive vector bosons with masses of order f after eating up the rest of Goldstone scalar fields. Otherwise there would still remain an unbroken global symmetry that is sufficient to ensure the Goldstone nature of the Higgs boson When those couplings are not set to zero the model predicts a divergence in the Higgs mass sensitive to just the logarithm of the cut-off, solving the problems of quadratic divergences and fine-tuning of the SM. In the last section we present our conclusions and outlook
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