[Paper Review] Status of the global electroweak fit of the Standard Model

A. Hoecker|arXiv (Cornell University)|Sep 7, 2009

Particle physics theoretical and experimental studies6 references3 citations

TL;DR

This paper presents a state-of-the-art global electroweak fit of the Standard Model using precision data from LEP, SLC, and the Tevatron, combined with direct Higgs searches, to constrain the Higgs boson mass and other parameters. It reports an upper limit of 153 GeV at 95% CL for the Higgs mass and provides the most precise determination of the strong coupling constant αₛ(M_Z²) = 0.1193 ± 0.0028 ± 0.0001, with implications for the stability of the electroweak vacuum up to the Planck scale.

ABSTRACT

Results from the global Standard Model fit to electroweak precision data, including newest Tevatron measurements, are reviewed and discussed. The complete fit using also the constraints from the direct Higgs boson searches yields an upper limit on the Higgs mass of 153 GeV at 95% CL. The top mass is indirectly determined to be (177.2 +10.5 -7.8) GeV and (179.5 +8.8 -5.2) GeV for fits including or not the constraints from the direct Higgs searches, respectively. Using the 3NLO perturbative prediction of the massless QCD Adler function, the strong coupling constant at the Z-mass scale is determined to be alpha_s(MZ)=0.1193 +- 0.0028 +- 0.0001, which is in excellent agreement with the 3NLO result from hadronic tau decays. The perspectives of the electroweak fit for forthcoming and proposed future collider projects are discussed. The available constraints on the Higgs mass are convolved with the high-scale behaviour of the Higgs quartic coupling to derive likelihoods for the survival of the Standard Model versus its cut-off scale evolved up to the Planck mass.

Motivation & Objective

• To update and refine the global electroweak fit of the Standard Model using the latest precision electroweak data from LEP, SLC, and the Tevatron.
• To incorporate constraints from direct Higgs boson searches to improve bounds on the Higgs mass and other parameters.
• To provide a modern, maintainable, and extensible framework for model testing in high-energy physics using the Gfitter package.
• To assess the viability of the Standard Model up to the Planck scale by combining Higgs mass constraints with the high-scale evolution of the Higgs quartic coupling.
• To evaluate the impact of future collider data—particularly from the LHC—on the stability and consistency of the Standard Model.

Proposed method

• The Gfitter package, implemented in C++ with ROOT, XML, and Python, is used to perform a multidimensional parameter fit to electroweak precision observables.
• The fit includes full two-loop corrections for the W boson mass and effective weak mixing angle, with higher-order corrections in m_t² and αα_s².
• The 3NLO perturbative calculation of the massless QCD Adler function is incorporated to improve the theoretical prediction of the Z hadronic width and α_s(M_Z²).
• Theoretical uncertainties, correlations, and inter-parameter dependencies are consistently handled using dynamic parameter caching to optimize computational efficiency.
• Vacuum stability and perturbativity bounds are evaluated by evolving the Higgs quartic coupling up to the Planck scale using the renormalization group equations.
• Pseudo-Monte Carlo sampling is used to derive confidence levels for the cut-off scale Λ, under the assumption of absolute vacuum stability.

Experimental results

Research questions

• RQ1 What is the most stringent upper limit on the Higgs boson mass based on global electroweak fits including direct Higgs search constraints?
• RQ2 How precisely can the strong coupling constant α_s(M_Z²) be determined using electroweak precision data and advanced QCD calculations?
• RQ3 To what extent can the Standard Model survive up to the Planck scale without new physics, given current Higgs mass constraints?
• RQ4 How do future LHC data, particularly from early Higgs searches, affect the confidence in the stability of the electroweak vacuum?
• RQ5 What is the impact of theoretical uncertainties on the derived upper bound for the cut-off scale Λ in the context of vacuum stability?

Key findings

• The global electroweak fit, including direct Higgs searches, yields an upper limit of 153 GeV at 95% confidence level for the Higgs boson mass.
• The top quark mass is indirectly determined to be 177.2⁺¹⁰.⁵₋₇.₈ GeV when Higgs search constraints are included, and 179.5⁺⁸.⁸₋₅.₂ GeV when excluded.
• The strong coupling constant is determined as α_s(M_Z²) = 0.1193 ± 0.0028 ± 0.0001, in excellent agreement with 3NLO results from hadronic τ decays.
• With current data, no confidence level above 68% can be achieved for the cut-off scale Λ to reach or exceed the Planck scale, indicating the SM is on the edge of instability.
• If a Higgs boson with mass 115 GeV is discovered and precisely measured, the 95% CL upper limit on the cut-off scale would be log₁₀(Λ/GeV) < 10.4, including theoretical uncertainties.
• The p-value for the SM to remain stable up to the Planck scale under the 115 GeV Higgs scenario is equivalent to a 5.3σ fluctuation, indicating extreme fine-tuning.