[Paper Review] Implications of Precision Electroweak Data

Kaoru Hagiwara|ArXiv.org|Dec 26, 1995

Particle physics theoretical and experimental studies3 citations

TL;DR

This paper analyzes precision electroweak data from LEP and SLC in late 1995, finding strong tension between the Standard Model (SM) and measurements of $R_b$ (3.7σ excess) and $R_c$ (2.5σ deficit). When combined, the SM is ruled out at 99.99% confidence level for top quark mass >170 GeV, suggesting new physics or experimental systematics in $R_c$ measurements.

ABSTRACT

There are two aspects to the 1995 summer update of the combined preliminary electroweak data from LEP and SLC. On the one hand, agreement between experiments and the Standard Model (SM) has improved for the line-shape and the asymmetry data. The $τ$ widths and asymmetries are now consistent with $e$--$μ$--$τ$ universality, and all the asymmetry data including the left-right asymmetry from SLC are consistent with the SM (16\%CL). On the other hand, a discrepancy between experiments and SM predictions is sharpened for two observables, $R_b$ and $R_c$, where $R_q$ is the partial $Z$ boson width ratio $Γ_q/Γ_h$. $R_b$ is 3\% larger (3.7$σ$) and $R_c$ is 11\% smaller (2.5$σ$) than the SM predictions. When combined, the SM is ruled out at the 99.99\%CL for $m_t>170$GeV. It is difficult to interpret the $11\pm 4$\% deficit of $R_c$, since if we allow only $Γ_b$ and $Γ_c$ to deviate from the SM then the precisely measured ratio $R_h=Γ_h/Γ_\ell$ forces the QCD coupling to be $α_s\equiv α_s(m_Z)_{\overline{ m MS}}=0.185\pm 0.041$, which is uncomfortably large. The data can be consistent with the prefered $α_s$ ($0.10

Motivation & Objective

• To assess the consistency of precision electroweak data from LEP and SLC with the Standard Model (SM) in late 1995.
• To investigate the origin of discrepancies in $R_b$ and $R_c$, the partial width ratios of the Z boson to bottom and charm quarks.
• To evaluate whether the observed deviations can be explained by new physics or experimental systematics, particularly in $R_c$.
• To explore theoretical models that could reconcile the large $R_b$ and small $\alpha_s$ values implied by the data.
• To examine the robustness of the double-tagging technique used in $R_b$ measurements and its potential impact on systematic errors.

Proposed method

• Combines preliminary electroweak data from LEP and SLC, focusing on line-shape and asymmetry measurements.
• Uses the $S$, $T$, $U$ parameter framework to analyze potential new physics contributions beyond the SM.
• Applies the $\overline{\text{MS}}$ scheme to extract $\alpha_s(m_Z)$ from the data, testing consistency with the SM prediction.
• Performs a global fit to $R_b$, $R_c$, and $R_h$ to constrain deviations in partial widths and $\alpha_s$.
• Evaluates the impact of assuming the SM value for $R_c$ on the significance of the $R_b$ discrepancy.
• Reviews the double-tagging technique used in $R_b$ measurements to assess potential systematic biases.

Experimental results

Research questions

• RQ1 To what extent do the 1995 LEP and SLC electroweak data agree with the Standard Model predictions for $R_b$ and $R_c$?
• RQ2 What is the combined statistical significance of the $R_b$ and $R_c$ discrepancies, and does it rule out the SM?
• RQ3 Can the observed $R_c$ deficit be explained by experimental systematics, or does it require new physics?
• RQ4 What value of $\alpha_s(m_Z)$ is implied by the data if $R_c$ is assumed to be SM-compliant?
• RQ5 How do theoretical models that predict large $R_b$ and small $\alpha_s$ compare with the observed data?

Key findings

• The $R_b$ measurement is 3.7σ higher than the SM prediction, indicating a significant deviation.
• The $R_c$ measurement is 2.5σ lower than the SM prediction, suggesting a substantial deficit in the Z→cc̄ decay rate.
• When combined, the $R_b$ and $R_c$ discrepancies rule out the Standard Model at 99.99% confidence level for $m_t > 170$ GeV.
• Assuming the SM value for $R_c$ reduces the $R_b$ discrepancy to 2σ, indicating that $R_c$ may be the dominant source of tension.
• The data imply an unreasonably large $\alpha_s(m_Z) = 0.185 \pm 0.041$ if only $\Gamma_b$ and $\Gamma_c$ deviate from SM, conflicting with the preferred range of $0.10 < \alpha_s < 0.13$.
• The double-tagging technique for $R_b$ is found to be critically important, with potential systematic uncertainties affecting the result.