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Electroweak symmetry breaking after LEP1 and LEP2

Riccardo Barbieri, Alex Pomarol, Riccardo Rattazzi, Alessandro Strumia

TL;DR

This paper develops a model-independent, four-parameter framework for electroweak symmetry breaking in universal theories, where heavy new physics affects low-energy observables through vector-boson self-energies encoded in $\widehat S$, $\widehat T$, $W$, and $Y$. By combining LEP1 EWPT with LEP2 differential cross-section data, it shows that all four form factors are tightly constrained to be at the level of $\mathcal{O}(10^{-3})$, effectively favoring SM-like behavior in the presence of a light Higgs. The authors apply the formalism to several classes of models—gauge fields in extra dimensions, Little Higgs, and Higgsless 5D theories—finding that Higgsless 5D scenarios, if calculable, generally fail to describe EWSB within their full parameter space. The approach provides a robust, universal-testing ground for new physics scenarios and highlights where experimental data place the strongest constraints on such theories.

Abstract

In a generic 'universal' theory of electroweak symmetry breaking, non fine-tuned heavy new physics affects the low-energy data through four parameters, which include and properly extend the generally insufficient S and T. Only by adding the LEP2 data to the global electroweak fit, can all these four form factors be determined and deviations from the SM be strongly constrained. Several of the recently proposed models (little Higgs, gauge bosons in extra dimensions or Higgsless models in 5D) are recognized to be 'universal' in a straightforward way after a proper definition of the effective vector boson fields. Among various applications, we show that proposed Higgsless models in 5D, when calculable, do not provide a viable description of electroweak symmetry breaking in their full range of parameters.

Electroweak symmetry breaking after LEP1 and LEP2

TL;DR

This paper develops a model-independent, four-parameter framework for electroweak symmetry breaking in universal theories, where heavy new physics affects low-energy observables through vector-boson self-energies encoded in , , , and . By combining LEP1 EWPT with LEP2 differential cross-section data, it shows that all four form factors are tightly constrained to be at the level of , effectively favoring SM-like behavior in the presence of a light Higgs. The authors apply the formalism to several classes of models—gauge fields in extra dimensions, Little Higgs, and Higgsless 5D theories—finding that Higgsless 5D scenarios, if calculable, generally fail to describe EWSB within their full parameter space. The approach provides a robust, universal-testing ground for new physics scenarios and highlights where experimental data place the strongest constraints on such theories.

Abstract

In a generic 'universal' theory of electroweak symmetry breaking, non fine-tuned heavy new physics affects the low-energy data through four parameters, which include and properly extend the generally insufficient S and T. Only by adding the LEP2 data to the global electroweak fit, can all these four form factors be determined and deviations from the SM be strongly constrained. Several of the recently proposed models (little Higgs, gauge bosons in extra dimensions or Higgsless models in 5D) are recognized to be 'universal' in a straightforward way after a proper definition of the effective vector boson fields. Among various applications, we show that proposed Higgsless models in 5D, when calculable, do not provide a viable description of electroweak symmetry breaking in their full range of parameters.

Paper Structure

This paper contains 11 sections, 36 equations, 3 figures, 3 tables.

Table of Contents

  1. Introduction and statement of the problem
  2. Electroweak precision observables before LEP2
  3. Constraints from LEP2 measurements
  4. Global constraints on $\widehat{S}$, $\widehat{T}$, $Y$ and $W$
  5. Examples of "universal" theories of EWSB and their predictions
  6. Gauge bosons in 5 dimensions
  7. Gauge bosons and Higgs in 5 dimensions
  8. Little Higgs models
  9. Higgsless models
  10. Conclusions
  11. Acknowledgments

Figures (3)

  • Figure 1: Allowed values at $90,99\%$ C.L. of $(\widehat{S},\widehat{T})$ (for generic $W,Y$) and of $(W,Y)$ (for generic $\widehat{S},\widehat{T}$) with $m_h = 115$ GeV. The dashed lines show the weaker constraints obtained by the EWPT alone.
  • Figure 2: Constraints on the form factors $Y$ and $W$ in models where these are the only new physics effects. We separately show the impact of EWPT and of LEP2.
  • Figure 4: $\chi^2(\widehat{S})$ for $m_h = 115\,{\rm GeV}$ (dotted), $800\,{\rm GeV}$ (dashed). The $n$-$\sigma$ range for $\widehat{S}$ corresponds to $\chi^2 < \chi^2_{\rm min} +n^2$. Higgsless models that predict $\widehat{S}\approx + \hbox{\rm few} \cdot 10^{-3}$ and $X,Y,W>0$ are excluded.