Variations of Little Higgs Models and their Electroweak Constraints

TL;DR

Facing the naturalness tension of the Standard Model, the paper assesses whether tree-level electroweak precision data restricts a broad class of Little Higgs models. It performs a global fit to precision observables across variations of Littlest Higgs with SU(5)/SO(5), as well as SU(6)/Sp(6) and SU(4)^4/SU(3)^4 constructions. The results show that, in most parameter regions, the symmetry-breaking scale must lie at multi-TeV values, with explicit bounds such as $f>3.0\,\mathrm{TeV}$ for the minimal $SU(6)/Sp(6)$ and $f^2=f_1^2+f_2^2>(4.2\,\mathrm{TeV})^2$ for $SU(4)^4/SU(3)^4$. Notably, there exist parameter regions with $f$ as low as $1-2\,\mathrm{TeV}$ when heavy gauge boson mixing is small and heavy U(1) couplings to light fermions are suppressed, though the naturalness of these regions depends on the UV completion. Overall, the work informs model-building by delineating the viable parameter space and highlighting where precision data allow or constrain Little Higgs scenarios.

Abstract

We calculate the tree-level electroweak precision constraints on a wide class of little Higgs models including: variations of the Littlest Higgs SU(5)/SO(5), SU(6)/Sp(6), and SU(4)^4/SU(3)^4. By performing a global fit to the precision data we find that for generic regions of the parameter space the bound on the symmetry breaking scale f is several TeV, where we have kept the normalization of f constant in the different models. For example, the ``minimal'' implementation of SU(6)/Sp(6) is bounded by f>3.0 TeV throughout most of the parameter space, and SU(4)^4/SU(3)^4 is bounded by f^2 = f_1^2+f_2^2 > (4.2 TeV)^2. In certain models, such as SU(4)^4/SU(3)^4, a large f does not directly imply a large amount of fine tuning since the heavy fermion masses that contribute to the Higgs mass can be lowered below f for a carefully chosen set of parameters. We also find that for certain models (or variations) there exist regions of parameter space in which the bound on f can be lowered into the range 1-2 TeV. These regions are typically characterized by a small mixing between heavy and standard model gauge bosons, and a small (or vanishing) coupling between heavy U(1) gauge bosons and the light fermions. Whether such a region of parameter space is natural or not is ultimately contingent on the UV completion.