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Little-Higgs corrections to precision data after LEP2

Guido Marandella, Christian Schappacher, Alessandro Strumia

TL;DR

The paper reevaluates little-Higgs corrections to precision electroweak data across several global-symmetry models, showing that most corrections are universal and can be captured by the four oblique parameters $\\hat{S}$, $\\hat{T}$, $W$, and $Y$, with LEP2 data tightening the bounds. It introduces a practical method to compute these universal effects by integrating out heavy vector bosons and demonstrates it on multiple models, including the littlest Higgs variants, the SO(9) model, and SU(6)/Sp(6) constructions, while also treating non-universal Z' contributions via an approximate four-parameter encoding. The results yield lower bounds on the symmetry-breaking scale $f$ of typically a few TeV, highlighting a residual little-hierarchy problem and significant fine-tuning to reproduce the electroweak scale. The work also shows how non-universal Z' effects can be mapped onto the same parameter set using leptonic data, and discusses prospects for testing these scenarios with future precision measurements at e^+e^- colliders.

Abstract

We reconsider little-Higgs corrections to precision data. In five models with global symmetries SU(5), SU(6), SO(9) corrections are (although not explicitly) of `universal' type. We get simple expressions for the Shat, That, W, Y parameters, which summarize all effects. In all models Shat > (W+Y)/2 and That, W, Y\ge 0. Results differ from previous analyses, which are sometimes incomplete, sometimes incorrect, and because we add LEP2 e ebar --> f fbar cross sections to the data set. Depending on the model the constraint on f ranges between 2 and 20 TeV. We next study the `simplest' little-Higgs model (and propose a new related model) which is not `universal' and affects precision data due to the presence of an extra Z' vector. By restricting the data-set to the most accurate leptonic data we show how corrections to precision data generated by a generic Z' can be encoded in four effective Shat, That, W, Y parameters, giving their expressions.

Little-Higgs corrections to precision data after LEP2

TL;DR

The paper reevaluates little-Higgs corrections to precision electroweak data across several global-symmetry models, showing that most corrections are universal and can be captured by the four oblique parameters , , , and , with LEP2 data tightening the bounds. It introduces a practical method to compute these universal effects by integrating out heavy vector bosons and demonstrates it on multiple models, including the littlest Higgs variants, the SO(9) model, and SU(6)/Sp(6) constructions, while also treating non-universal Z' contributions via an approximate four-parameter encoding. The results yield lower bounds on the symmetry-breaking scale of typically a few TeV, highlighting a residual little-hierarchy problem and significant fine-tuning to reproduce the electroweak scale. The work also shows how non-universal Z' effects can be mapped onto the same parameter set using leptonic data, and discusses prospects for testing these scenarios with future precision measurements at e^+e^- colliders.

Abstract

We reconsider little-Higgs corrections to precision data. In five models with global symmetries SU(5), SU(6), SO(9) corrections are (although not explicitly) of `universal' type. We get simple expressions for the Shat, That, W, Y parameters, which summarize all effects. In all models Shat > (W+Y)/2 and That, W, Y\ge 0. Results differ from previous analyses, which are sometimes incomplete, sometimes incorrect, and because we add LEP2 e ebar --> f fbar cross sections to the data set. Depending on the model the constraint on f ranges between 2 and 20 TeV. We next study the `simplest' little-Higgs model (and propose a new related model) which is not `universal' and affects precision data due to the presence of an extra Z' vector. By restricting the data-set to the most accurate leptonic data we show how corrections to precision data generated by a generic Z' can be encoded in four effective Shat, That, W, Y parameters, giving their expressions.

Paper Structure

This paper contains 10 sections, 32 equations, 1 figure, 4 tables.

Table of Contents

  1. Introduction
  2. Experimental data
  3. Computing universal effects
  4. The SU(5)/SO(5) 'littlest' Higgs models
  5. The SO(9)/(SO(5) $\otimes$ SO(4)) model
  6. The SU(6)/Sp(6) models
  7. Models with generic $Z'$ vector bosons
  8. The 'simplest' little-Higgs
  9. The 'oldest' little-Higgs
  10. Conclusions

Figures (1)

  • Figure 1: Bound from precision data on the scale $f$ in TeV of little-Higgs models. The constraint is computed at $99\%$ C.L. for 1 dof, i.e. $\chi^2 = \chi^2_{\rm SM} +6.6$. As described in the text in each model the angles $\phi$ parameterize the gauge couplings of the extra gauge groups, which become strongly coupled at $\phi\to 0$ and/or $\phi\to \pi/2$. The dotted iso-lines show that the constraint on $f$ gets slightly relaxed in presence of arbitrary extra corrections to $\hat{T}$. We assumed a light higgs, $m_h\sim 115\,{\rm GeV}$.