Implications of Precision Electroweak Data

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 $α_s\equiv α_s(m_Z)_{\overline{\rm MS}}=0.185\pm 0.041$, which is uncomfortably large. The data can be consistent with the prefered $α_s$ ($0.10<α_s<0.13$) only if the sum $Γ_h=Σ_q Γ_q$ does not deviate significantly from the SM prediction. Possible experimental causes for the under-estimation of $R_c$ are discussed. By assuming the SM value for $R_c$, the discrepancy in $R_b$ decreases to 2\% (3$σ$). The double tagging technique used for the $R_b$ measurements is critically reviewed. A few theoretical models that can explain large $R_b$ and small $α_s$ ($= 0.104\pm 0.008$) are discussed. If the QCD coupling $α_s$ is allowed to be fitted by the data, the standard $S$, $T$, $U$ analysis for a new physics