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Curing the Ills of Higgsless Models: the S Parameter and Unitarity

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Giacomo Cacciapaglia, Csaba Csaki, Christophe Grojean, John Terning

High Energy Physics - Phenomenology · Submitted 13 Sep 2004

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim At the same time the experimental bounds on such Z' and W' gauge bosons become very weak, and their masses can be lowered to make sure that perturbative unitarity is not violated in this theory before reaching energies of several TeV.

how it is stated · asserted 0.87 read the record →

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arXiv IDhep-ph/0409126 (version 2)
Pith IDZBGB5LKN, Pith's permanent record of this paper and its review
CitationChristophe Grojean, Csaba Csaki, Giacomo Cacciapaglia, John Terning. "Curing the Ills of Higgsless Models: the S Parameter and Unitarity." arXiv:hep-ph/0409126 (2004). https://pith.science/paper/ZBGB5LKN
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The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 5,811 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.83 · human participants 0.01 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.23 · compares with prior results 0.21 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

We consider various constraints on Higgsless models of electroweak symmetry breaking based on a bulk SU(2)_L x SU(2)_R x U(1)_{B-L} gauge group in warped space. First we show that the S parameter which is positive if fermions are localized on the Planck brane can be lowered (or made vanishing) by changing the localization of the light fermions. If the wave function of the light fermions is almost flat their coupling to the gauge boson KK modes will be close to vanishing, and therefore contributions to the S parameter will be suppressed. At the same time the experimental bounds on such Z' and W' gauge bosons become very weak, and their masses can be lowered to make sure that perturbative unitarity is not violated in this theory before reaching energies of several TeV. The biggest difficulty of these models is to incorporate a heavy top quark mass without violating any of the experimental bounds on bottom quark gauge couplings. In the simplest models of fermion masses a sufficiently heavy top quark also implies an unacceptably large correction to the Zb\bar{b} vertex and a large splitting between the KK modes of the top and bottom quarks, yielding large loop corrections to the T-parameter. We present possible directions for model building where perhaps these constraints could be obeyed as well.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We consider various constraints on Higgsless models of electroweak symmetry breaking based on a bulk SU(2)_L x SU(2)_R x U(1)_{B-L} gauge group in warped space. contribution 0.58 0.49 0.04 asserted 0.57
s1 First we show that the S parameter which is positive if fermions are localized on the Planck brane can be lowered (or made vanishing) by changing the localization of the light fermions. result 0.90 0.89 0.25 asserted 0.99
s2 If the wave function of the light fermions is almost flat their coupling to the gauge boson KK modes will be close to vanishing, and therefore contributions to the S parameter will be suppressed. interpretation 0.74 0.55 0.11 asserted 0.68
s3 At the same time the experimental bounds on such Z' and W' gauge bosons become very weak, and their masses can be lowered to make sure that perturbative unitarity is not violated in this theory before reaching energies of several TeV. result 0.72 0.66 0.30 asserted 0.87
s4 The biggest difficulty of these models is to incorporate a heavy top quark mass without violating any of the experimental bounds on bottom quark gauge couplings. limitation 0.88 0.27 0.07 asserted 1.00
s5 In the simplest models of fermion masses a sufficiently heavy top quark also implies an unacceptably large correction to the Zb\bar{b} vertex and a large splitting between the KK modes of the top and bottom quarks, yielding large loop corrections to the T-parameter. limitation 0.51 0.19 0.05 asserted 0.99
s6 We present possible directions for model building where perhaps these constraints could be obeyed as well. future work 0.84 0.59 0.15 hedged possibility 0.96

What kind of paper the classifier reports this is: theoretical result 0.98 · evidence from proof or derivation 0.77.

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sources read
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not examined
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  • figures and tables
  • references and citing sentences
  • relations to other papers
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  • P abstract
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  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

We consider various constraints on Higgsless models of electroweak symmetry breaking based on a bulk SU(2)_L x SU(2)_R x U(1)_{B-L} gauge group in warped space. First we show that the S parameter which is positive if fermions are localized on the Planck brane can be lowered (or made vanishing) by changing the localization of the light fermions. If the wave function of the light fermions is almost flat their coupling to the gauge boson KK modes will be close to vanishing, and therefore contributions to the S parameter will be suppressed. At the same time the experimental bounds on such Z' and W' gauge bosons become very weak, and their masses can be lowered to make sure that perturbative unitarity is not violated in this theory before reaching energies of several TeV. The biggest difficulty of these models is to incorporate a heavy top quark mass without violating any of the experimental bounds on bottom quark gauge couplings. In the simplest models of fermion masses a sufficiently heavy top quark also implies an unacceptably large correction to the Zb\bar{b} vertex and a large splitting between the KK modes of the top and bottom quarks, yielding large loop corrections to the T-parameter. We present possible directions for model building where perhaps these constraints could be obeyed as well.

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References
How later papers used it

51 later papers cite it

Evidence: substantial. 44 of the citing papers share no author with it, and 5 of those carry a confident label from Pith's citation classifier.

Pith read 17 of the 93 citing sentences, choosing only those whose citation markers point at this paper alone, and wrote the paraphrases from them. The summary, the counts, the evidence level, the links and the quotes come from code; the summary counts the papers listed below. A later paper is listed under a label when Pith's citation classifier gives one of its sentences that label at probability 0.8 or more (0.95 for support), Pith's reading finds that the citing paper itself did it, and a second check confirms the paraphrase against the sentence. This section lists uses only. It does not list criticism or disagreement, so their absence here says nothing about how the paper has been received. Papers that share an author with this one are listed apart, under "By the same authors". A quote is the citing authors' own sentence, shown when their paper's licence is CC BY, CC BY-SA or CC0. JSON

Uses its method or tool 1 paper
How the literature uses it

47 arXiv papers cite this in 89 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers whose main result relates to this one's

Found among the papers closest to this one by title and main claim. Pith's classifier compared each pair's main results and a second model family confirmed the relation; checked against two further families, shown conflicts agreed 118 times in 120 and shown same results 218 times in 239. The quoted sentence is the other paper's main claim.

States a conflicting result 1 paper

Papers citing it · 73 sentences without a confident label

Uses its method or tool 1 paper
Compares with it 1 paper
Cites it as support 3 papers
  • As we demonstrate in the Appendix, this amount of delocalization insures the equality of the tree-level three-site model couplings to those of the standard model, up to corrections of order $x^4$ [ref] and the absence of large tree-level corrections to precision electroweak measurements [ref] .

    The Flavor Structure of the Three-Site Higgsless Model · Gauge-Boson Couplings at Tree-Level · 0.96

  • The visible excess over the SM estimate at high values of $m_W^+W^-$ results from a residual logarithmic growth of the $VVW^+W^-$ sub-amplitude at invariant masses large compared to the first Kaluza-Klein resonance [ref] .

    QCD Corrections to Vector-Boson Fusion Processes in Warped Higgsless Models · Impact of the fermion sector · 0.96

  • If the light fermion profiles are almost flat $(c≃1/2)$ then their coupling to the gauge boson Kaluza-Klein modes is vanishingly small thereby suppressing the contributions to the $S$ parameter [ref] .

    TASI Lectures on a Holographic View of Beyond the Standard Model Physics · The warped Higgsless model · 0.96

Cites it as background 10 papers
  • Higgsless models [ref] of electroweak symmetry breaking provide effective low-energy theories of a strongly-interacting symmetry breaking sector [ref] which, in the case of “delocalized" fermions [ref] , can be consistent with electroweak precision measurements [ref] .

    Z to b bbar and Chiral Currents in Higgsless Models · Introduction · 0.98

  • In Higgsless models [ref] , the first two neutral resonances are nearly degenerate, and they correspond to the first KK excitation of the $Z$ and of the photon.

    Nearby resonances beyond the Breit-Wigner approximation · Numerical example: $Z'$ and $A'$ in Higgsless models · 0.87

  • Inspired by the idea that one could maintain perturbative unitarity in extra-dimensional models through heavy vector resonance exchanges in lieu of a Higgs [ref] , Higgsless models were intially introduced in an extra-dimensional context as $SU(2)×SU(2)×U(1)$ gauge theories living in a slice of $AdS_5$, with symmetry breaking codified in the boundary condition of the gauge fields [ref] .

    Top-Higgs and Top-pion phenomenology in the Top Triangle Moose model · Introduction · 0.96

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