[Paper Review] Global Fits of the electroweak Standard Model and beyond with Gfitter

Martin Goebel|arXiv (Cornell University)|May 15, 2009

Particle physics theoretical and experimental studies13 references3 citations

TL;DR

This paper presents a global fit of the electroweak Standard Model and extensions using the Gfitter framework, incorporating precision electroweak data, top and W boson masses, and direct Higgs searches. It reports a Higgs boson mass estimate of $ M_H = 116.3^{+15.6}_{-1.3} \, \text{GeV} $, a strong coupling constant of $ \alpha_S(M_Z^2) = 0.1193 \pm 0.0028_{\text{exp}} \pm 0.0001_{\text{theo}} $, and constraints on new physics via oblique parameters, including exclusion limits for the Littlest Higgs Model with T-parity and a Two Higgs Doublet Model.

ABSTRACT

In the global fit of the Standard Model using Gfitter, electroweak precision observables as well as constraints from direct Higgs searches have been compared with state-of-the-art electroweak predictions. We use the most recent results for direct Higgs searches at LEP and Tevatron and the latest measurements of m_t and M_W. Example results are an estimation of the mass of the Higgs boson (M_H=116.3 +15.6 -1.3 GeV) and a forth-order result for the strong coupling constant (alpha_S(M_Z^2)=0.1193 +-0.0028(exp) +-0.0001(theo)). A fit of the oblique parameters (STU) to the electroweak data is performed, in order to constrain physics beyond the Standard Model. For instance, the parameter space of the Littlest Higgs Model with T-parity can be restricted via the oblique parameters. In addition, fit results for a model with an extended Higgs sector (2HDM) using mainly observables from the B and K physics are presented.

Motivation & Objective

• To perform a global fit of the Standard Model using state-of-the-art electroweak precision data and direct Higgs search constraints.
• To constrain physics beyond the Standard Model using oblique parameters (S, T, U), particularly in the Littlest Higgs Model with T-parity.
• To test a Two Higgs Doublet Model (2HDM) using observables from B and K physics, including branching ratios and rare decays.
• To provide a modern, maintainable fitting framework (Gfitter) with consistent treatment of statistical, systematic, and theoretical uncertainties.

Proposed method

• Implementation of a C++-based, ROOT-integrated fitting package (Gfitter) with modular handling of theoretical and experimental errors.
• Use of one-mass-shell scheme with full two-loop and leading beyond-two-loop corrections for $ M_W $ and $ \sin^2\theta^{\text{eff}}_l $.
• Incorporation of NNNLO QCD corrections to the Adler function for accurate $ Z $-boson hadronic width predictions.
• Inclusion of direct Higgs search results from LEP and Tevatron via a Gaussian approximation of log-likelihood ratios to compute $ \chi^2 $ contributions.
• Fitting of oblique parameters (S, T, U) to constrain the Littlest Higgs Model with T-parity, using floating parameters $ f $, $ s_\lambda $, and $ \delta_c $.
• Global 2HDM fit using observables from $ R_b^0 $, $ B \to X_s\gamma $, leptonic decays ($ B\to\tau\nu $, $ K\to\mu\nu $), and $ B\to D\tau\nu $, with toy Monte Carlo tests for CL calculation.

Experimental results

Research questions

• RQ1 What is the best-fit value and uncertainty for the Higgs boson mass within the global electroweak fit, including direct search constraints?
• RQ2 How precisely can the strong coupling constant $ \alpha_S(M_Z^2) $ be determined from electroweak precision data?
• RQ3 To what extent do electroweak precision observables constrain the parameter space of the Littlest Higgs Model with T-parity?
• RQ4 What are the combined exclusion limits on the charged Higgs mass and $ \tan\beta $ in a Type-II Two Higgs Doublet Model from B and K physics?
• RQ5 How does the inclusion of direct Higgs searches affect the global fit and Higgs mass determination?

Key findings

• The global fit yields a Higgs boson mass estimate of $ M_H = 116.3^{+15.6}_{-1.3} \, \text{GeV} $, with the complete fit achieving $ \chi^2_{\text{min}} = 17.9 $ for 14 degrees of freedom.
• The strong coupling constant is determined as $ \alpha_S(M_Z^2) = 0.1193 \pm 0.0028_{\text{exp}} \pm 0.0001_{\text{theo}} $, reflecting high theoretical accuracy from NNNLO QCD corrections.
• The Littlest Higgs Model with T-parity is constrained in the $ (M_H, f) $-plane, with larger Higgs masses preferred due to reduced fine-tuning, as quantified by the $ F $-parameter.
• The 2HDM global fit excludes a charged Higgs boson with mass below $ 240\,\text{GeV} $ at 95% CL, independent of $ \tan\beta $, with stronger limits for larger $ \tan\beta $, such as $ M_{H^\pm} < 780\,\text{GeV} $ for $ \tan\beta = 70 $.
• The oblique parameter fit shows that $ M_W $ and $ m_t $ measurements are consistent with the SM, and the $ (T,S) $-plane contours exclude certain regions of the Littlest Higgs parameter space.
• The Gfitter framework successfully integrates modern theoretical calculations with experimental data, enabling robust, error-corrected global fits with full uncertainty propagation.