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Perturbative, Non-Supersymmetric Completions of the Little Higgs
High Energy Physics - Phenomenology · Submitted 20 Dec 2004
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim 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.
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The abstract, sentence by sentence
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.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | The little Higgs mechanism produces a light 100 GeV Higgs while raising the natural cutoff from 1 TeV to 10 TeV. | background 1.00 | 0.10 | 0.06 | asserted 1.00 |
| s1 | 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. | contribution 0.90 | 0.76 | 0.07 | asserted 0.35 |
| s2 | 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. | result 0.85 | 0.67 | 0.11 | asserted 1.00 |
| s3 | 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. | limitation 0.60 | 0.73 | 0.18 | asserted 0.99 |
| s4 | Top loops, for example, produce an expansion parameter of not 1/(4 pi) but 1/5. | result 0.79 | 0.72 | 0.04 | asserted 1.00 |
| s5 | The geometric increase in the number of fields at higher energies simply exacerbates this problem. | interpretation 0.52 | 0.40 | 0.06 | asserted 1.00 |
| s6 | 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. | contribution 0.77 | 0.96 | 0.22 | asserted 1.00 |
| s7 | 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. | contribution 0.90 | 0.92 | 0.05 | hedged possibility 0.62 |
| s8 | 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. | result 0.98 | 0.94 | 0.52 | hedged possibility 0.94 |
| s9 | The fine-tuning is not completely eliminated, but evidence suggests that this result is model dependent. | limitation 0.59 | 0.86 | 0.25 | hedged possibility 0.92 |
| s10 | 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. | future work 1.00 | 0.33 | 0.04 | speculative 1.00 |
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The paper
Original 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.
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5 arXiv papers cite this in 5 sentences
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NC also thanks Nima Arkani-Hamed for reminding him of [ref] in the first place, and Tim Cohen for enlightening conversations about TMNTs in general.
Twin Turtles · Conclusions · 0.89
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