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The `LEP paradox'

Riccardo Barbieri, Alessandro Strumia

TL;DR

Barbieri and Strumia address the LEP paradox: precision electroweak data favor a light Higgs $m_h$ (roughly $100$–$200$ GeV) while indicating a high new-physics scale $\Lambda$ ( $\Lambda \gtrsim 5$ TeV), which together imply a sizable top-quark loop contribution to $m_h^2$. They frame the Standard Model as an effective theory below $\Lambda$ with higher-dimension operators $\mathcal{O}_i^{(4+p)}$, and show that EWPT prefer a light Higgs within this EFT context, though certain operators could mimic a heavier Higgs. Supersymmetry offers a natural resolution by canceling the dangerous top-loop contribution with stop loops, effectively replacing $k_{\max}^2$ by $m_{\tilde t}^2 \ln(k_{\max}^2/m_{\tilde t}^2)$ and keeping $m_h$ under control for $m_{\tilde t}$ at the weak scale. The paper further discusses how $m_h$ in SUSY depends on the RG scale $Q$ and $m_{\tilde t}$, suggesting near-term SUSY signatures (e.g., NatSUSY with $m_{\tilde t}\sim 400$ GeV) and arguing that resolving the LEP paradox likely requires new physics at the weak scale. Overall, the authors contend that SUSY remains the most plausible solution to the LEP paradox, while acknowledging that cancellations in EWPT could, in principle, hide a heavier Higgs and calling for focused theoretical attention on this tension.

Abstract

Is there a Higgs? Where is it? Is supersymmetry there? Where is it? By discussing these questions, we call attention to the `LEP paradox', which is how we see the naturalness problem of the Fermi scale after a decade of electroweak precision measurements, mostly done at LEP.

The `LEP paradox'

TL;DR

Barbieri and Strumia address the LEP paradox: precision electroweak data favor a light Higgs (roughly – GeV) while indicating a high new-physics scale ( TeV), which together imply a sizable top-quark loop contribution to . They frame the Standard Model as an effective theory below with higher-dimension operators , and show that EWPT prefer a light Higgs within this EFT context, though certain operators could mimic a heavier Higgs. Supersymmetry offers a natural resolution by canceling the dangerous top-loop contribution with stop loops, effectively replacing by and keeping under control for at the weak scale. The paper further discusses how in SUSY depends on the RG scale and , suggesting near-term SUSY signatures (e.g., NatSUSY with GeV) and arguing that resolving the LEP paradox likely requires new physics at the weak scale. Overall, the authors contend that SUSY remains the most plausible solution to the LEP paradox, while acknowledging that cancellations in EWPT could, in principle, hide a heavier Higgs and calling for focused theoretical attention on this tension.

Abstract

Is there a Higgs? Where is it? Is supersymmetry there? Where is it? By discussing these questions, we call attention to the `LEP paradox', which is how we see the naturalness problem of the Fermi scale after a decade of electroweak precision measurements, mostly done at LEP.

Paper Structure

This paper contains 6 sections, 6 equations, 4 figures, 1 table.

Table of Contents

  1. Is there a Higgs?
  2. Where is the Higgs?
  3. Is supersymmetry there?
  4. Where is supersymmetry?
  5. Conclusion
  6. Acknowledgments

Figures (4)

  • Figure 1: Level curves at $\{68\%,90\%,99\%,99.9\%\}{\rm CL}$ of $\epsilon_1$ and $\epsilon_3$ compared with the SM prediction for $m_h=100,300,600,1000\,{\rm GeV}$, from right to left.
  • Figure 2: Level curves of $\Delta \chi^2=\{1,2.7,6.6,10.8\}$ that correspond to $\{68\%,90\%,99\%,99.9\%\}{\rm CL}$ for the first 2 operators in table 1 (${\cal O}_{WB}$ and ${\cal O}_{H}$) and $c_i=-1$.
  • Figure 3: Correlation between the stop mass and the RGE scale $Q$ at which $m_h(Q)$ vanishes.
  • Figure 4: Correlation between the chargino and the Higgs mass in GeV. Sampling spectra excluded (allowed) by accelerator bounds are drawn in light red (dark green).