Little Higgs Models: New Approaches to the Hierarchy Problem

The experimental results of the past decade indicate that the chiral Lagrangian describing EWSB works to one loop accuracy and irrelevant operators (such as |Dω|, where ω are the Goldstone bosons eaten by W and Z) are suppressed by a scale Λ ≫ 1 TeV. This strongly indicates perturbative physics at 1 TeV and a physical Higgs boson H = (h + v)ω. However, this linear sigma model is unstable to quantum corrections leading to the hierarchy problem, meaning that the Standard Model is in an incomplete description of physics parametrically above the weak scale. To date, only the MSSM provides a solution to the hierarchy problem and weakly coupled physics at 1 TeV. In this note we review models where the Higgs is a pseudo-Goldstone boson, Σ = e [1], for early attempts see [2]. Approximate global symmetries, Σ → LΣR keep the Higgs vev small relative to the cut-off, Λ ∼ 4πf . The global symmetries are broken by couplings, however, the structure of the symmetry breaking prevents large corrections to the Higgs vev. At 100 GeV the model is a two Higgs doublet model with a Higgs potential identical to the MSSM. There is a minidesert up to 1-3 TeV where new particles emerge that cancel the quadratic divergences of the Standard Model. The novelty of this set of models is that particles of the same spin cancel the respective quadratic divergences. Above the TeV scale there is another mini-desert until the 10-30 TeV