Perturbative, Non-Supersymmetric Completions of the Little Higgs

TL;DR

The paper investigates a perturbative, non-supersymmetric approach to solving the little hierarchy problem by stacking little-Higgs sectors into a tower that extends to about 100 TeV. It introduces explicit linear-sigma-model completions at 10 and 100 TeV, analyzes loop corrections, and demonstrates how higher-scale physics can remain insensitive to the electroweak scale through collective breaking and U(1) spurions, while acknowledging residual tuning from large field content. A non-linear sigma-model step is proposed to address bottom-quark Yukawa challenges and maintain perturbativity, with a preliminary large-N toy model suggesting a viable, though model-dependent, path to an exponentially large cutoff. The work highlights both the potential and the significant tuning and UV-completion hurdles involved in realizing a full tower of non-supersymmetric, perturbative Little Higgs theories.

Abstract

The little Higgs mechanism produces a light 100 GeV Higgs while raising the natural cutoff from 1 TeV to 10 TeV. We attempt an iterative little Higgs mechanism to produce multiple factors of 10 between the cutoff and the 100 GeV Higgs mass in a perturbative theory. In the renormalizable sector of the theory, all quantum corrections to the Higgs mass proportional to mass scales greater than 1 TeV are absent -- this includes quadratically divergent, log-divergent, and finite loops at all orders. However, even loops proportional to scales just a factor of 10 above the Higgs (or any other scalar) mass come with large numerical factors that reintroduce fine-tuning. Top loops, for example, produce an expansion parameter of not 1/(4 pi) but 1/5. The geometric increase in the number of fields at higher energies simply exacerbates this problem. We build a complete two-stage model up to 100 TeV, show that direct sensitivity of the electroweak scale to the cutoff is erased, and estimate the tuning due to large numerical factors. We then discuss the possibility, in a toy model with only scalar and gauge fields, of generating a tower of little Higgs theories and show that the theory quickly becomes a large-N gauge theory with ~ N fundamental scalars. We find evidence that at least this toy model could successfully generate light scalars with an exponentially large cutoff in the absence of supersymmetry or strong dynamics. The fine-tuning is not completely eliminated, but evidence suggests that this result is model dependent. We then speculate as to how one might marry a working tower of fields of this type at high scales to a realistic theory at the weak scale.