[Paper Review] Theoretical and Experimental Status of the Indirect Higgs Boson Mass Determination in the Standard Model

U. Baur, R. Clare+5 more|ArXiv.org|Nov 23, 2001

Particle physics theoretical and experimental studies21 references6 citations

TL;DR

This paper evaluates the indirect determination of the Higgs boson mass ($M_H$) in the Standard Model using electroweak precision observables, focusing on $M_W$ and $\sin^2\theta_{\mathrm{eff}}$. It estimates current theoretical uncertainties at $\delta M_W \approx 7$ MeV and $\delta\sin^2\theta_{\mathrm{eff}} \approx 7\times10^{-5}$, and projects that a Linear Collider with GigaZ capabilities could achieve a relative precision of ~8% in $M_H$ determination, with a current upper bound of $M_H < 196$ GeV at 95% CL.

ABSTRACT

The impact of theoretical and experimental uncertainties on the indirect determination of the Higgs boson mass, MH, in the Standard Model (SM) is discussed. Special emphasis is put on the electroweak precision observables MW (the W boson mass) and sin^2(theta_eff) (the effective leptonic mixing angle). The current uncertainties of the theoretical predictions for MW and sin^2(theta_eff) due to missing higher order corrections are conservatively estimated to delta MW \approx 7 MeV and delta sin^2(theta_eff) \approx 7 x 10^-5 . Expectations and necessary theoretical improvements for future colliders are explored. Results for the indirect MH determination are presented based on the present experimental and theoretical precisions as well as on improvements corresponding to the prospective situation at future colliders. The treatment of the different future colliders is done in a uniform way in order to allow for a direct comparison of the accuracies that can be reached. Taking all experimental, theoretical, and parametric uncertainties into account, a current upper bound on MH of \sim 200 GeV is obtained. Furthermore we find in a conservative approach that a Linear Collider with GigaZ capabilities can achieve a relative precision of about 8% (or better) in the indirect determination of MH.

Motivation & Objective

• To assess the current and future precision of indirect $M_H$ determination using electroweak precision observables in the Standard Model.
• To quantify the impact of theoretical uncertainties—particularly from missing higher-order corrections—on $M_W$ and $\sin^2\theta_{\mathrm{eff}}$.
• To project the achievable precision in $M_H$ determination at future colliders, including the Tevatron, LHC, and Linear Collider with GigaZ capabilities.
• To evaluate the interplay between experimental, theoretical, and parametric uncertainties in constraining $M_H$.

Proposed method

• A global fit to electroweak precision observables is performed, with $\Delta\chi^2$ as a function of $\log M_H$ used to derive confidence limits.
• Theoretical uncertainties in $M_W$ and $\sin^2\theta_{\mathrm{eff}}$ are estimated from missing higher-order corrections, conservatively set at $\delta M_W \approx 7$ MeV and $\delta\sin^2\theta_{\mathrm{eff}} \approx 7\times10^{-5}$.
• Future collider projections are modeled uniformly across colliders to allow direct comparison of precision reach.
• Parametric uncertainties from $\Delta\alpha(M_Z)$, $m_t$, and $\alpha_s(M_Z)$ are included, with $\delta\Delta\alpha(M_Z) = 7\times10^{-5}$ assumed for future estimates.
• Theoretical improvements are modeled as reduced uncertainties in two-loop corrections and improved hadronic vacuum polarization estimates.
• Cumulative uncertainties in $M_H$ are computed by adding experimental, theoretical, and parametric errors in quadrature.

Experimental results

Research questions

• RQ1 What is the current upper bound on the Higgs boson mass $M_H$ derived from indirect constraints using electroweak precision observables?
• RQ2 How do theoretical uncertainties in $M_W$ and $\sin^2\theta_{\mathrm{eff}}$ affect the indirect determination of $M_H$?
• RQ3 What precision in $M_H$ can be expected from future colliders, particularly the Linear Collider with GigaZ capabilities?
• RQ4 How do parametric uncertainties—especially from $\Delta\alpha(M_Z)$ and $m_t$—limit the precision of indirect $M_H$ determination?
• RQ5 What theoretical improvements are necessary to ensure that theoretical uncertainties do not dominate over experimental errors at future high-precision experiments?

Key findings

• A current 95% confidence level upper bound on the Higgs boson mass is $M_H < 196$ GeV, derived from a global fit to electroweak precision data.
• Theoretical uncertainties in $M_W$ and $\sin^2\theta_{\mathrm{eff}}$ due to missing higher-order corrections are conservatively estimated at $\delta M_W \approx 7$ MeV and $\delta\sin^2\theta_{\mathrm{eff}} \approx 7\times10^{-5}$, respectively.
• A Linear Collider with GigaZ capabilities is projected to achieve a relative precision of approximately 8% in the indirect determination of $M_H$, assuming improved theoretical and parametric uncertainties.
• The effective leptonic mixing angle $\sin^2\theta_{\mathrm{eff}}$ provides greater sensitivity to $M_H$ than $M_W$ for equal relative experimental precisions, with a sensitivity enhancement factor of 3.1 at $M_H \approx 115$ GeV.
• Future improvements in theoretical precision—particularly complete two-loop corrections and reduced uncertainties in $\Delta\alpha(M_Z)$—are essential to ensure theoretical uncertainties do not limit the precision of $M_H$ determination at GigaZ.
• With $\delta\Delta\alpha(M_Z) = 7\times10^{-5}$ and improved $\alpha_s(M_Z)$, the parametric uncertainty in $\sin^2\theta_{\mathrm{eff}}$ could be reduced to $2.5\times10^{-5}$, limiting its contribution to the overall $M_H$ uncertainty.