arXiv 2006.126662020-06hep-phhep-ex

μ子$g$-2与$Δα$的联系

The muon $g$-2 and $Δα$ connection

Alexander Keshavarzi, William J. Marciano, Massimo Passera, Alberto Sirlin

备注：: 33 pages, 16 figures
发表信息：: Phys. Rev. D 102, 033002 (2020)
DOI：: 10.1103/PhysRevD.102.033002

摘要：

标准模型理论和μ子磁矩异常（$a_μ=\left(g_μ-2\right)/2$）的实验测量之间的差异与精确的电弱（EW）预测有关，它们共同依赖于强子真空极化效应。总$e^+e^- \rightarrow \text{hadrons}$截面的相同数据$σ_{\rm had}(s)$被用作色散关系的输入，以估计强子真空极化贡献$a_μ^{\rm had,\,VP}$，以及五味强子对$Z$极处运行的QED耦合的贡献$Δα_{\rm had}^{(5)}(M_{Z}^2)$，其进入自然关系和全球EW拟合。$Δα_{\rm had}^{(5)}(M_{Z}^2) = 0.02722(41)$的EW拟合预测与从色散关系方法获得的$Δα_{\rm had}^{(5)}(M_{Z}^2) = 0.02761(11)$吻合良好，但表现出较小的中心值，表明$Δa_μ=a_μ^{\rm exp} - a_μ^{\rm SM}$的差异大于目前的预期。假设$Δa_μ$的差异可能是由于缺少$σ_{\rm had}(s)$的贡献，影响$M_W$，$\sin^2 \! θ^{\rm lep}_{\rm eff}$和$M_H$从全球EW拟合。发现在95%CL下，在$\sqrt{s} \gtrsim 0.7$ GeV以上排除了桥接$Δa_μ$所需的$σ_{\rm had}(s)$中的位移。此外，考虑到所需的横截面增加，认为$Δa_μ$起源于该能量以下的前景是不可能的。强子数据的这种假设变化也被发现会影响其他相关的观测量，如电子异常，$a_e^{\rm SM}$，比率$R_{e/μ} = (m_μ/m_e)^2 (a_{e}^{\rm had,\,LO\,VP}/a_μ^{\rm had,\,LO\,VP})$和弱混合角在低能量下的运行，尽管这些后果目前限制较少。

英文摘要：

The discrepancy between the Standard Model theory and experimental measurement of the muon magnetic moment anomaly, $a_μ=\left(g_μ-2\right)/2$, is connected to precision electroweak (EW) predictions via their common dependence on hadronic vacuum polarization effects. The same data for the total $e^+e^- \rightarrow \text{hadrons}$ cross section, $σ_{\rm had}(s)$, are used as input into dispersion relations to estimate the hadronic vacuum polarization contributions, $a_μ^{\rm had,\,VP}$, as well as the five-flavor hadronic contribution to the running QED coupling at the $Z$-pole, $Δα_{\rm had}^{(5)}(M_{Z}^2)$, which enters natural relations and global EW fits. The EW fit prediction of $Δα_{\rm had}^{(5)}(M_{Z}^2) = 0.02722(41)$ agrees well with $Δα_{\rm had}^{(5)}(M_{Z}^2) = 0.02761(11)$ obtained from the dispersion relation approach, but exhibits a smaller central value suggestive of a larger discrepancy $Δa_μ=a_μ^{\rm exp} - a_μ^{\rm SM}$ than currently expected. Postulating that the $Δa_μ$ difference may be due to missing $σ_{\rm had}(s)$ contributions, implications for $M_W$, $\sin^2 \! θ^{\rm lep}_{\rm eff}$ and $M_H$ obtained from global EW fits are investigated. Shifts in $σ_{\rm had}(s)$ needed to bridge $Δa_μ$ are found to be excluded above $\sqrt{s} \gtrsim 0.7$ GeV at the 95\%CL. Moreover, prospects for $Δa_μ$ originating below that energy are deemed improbable given the required increases in the cross section. Such hypothetical changes to the hadronic data are also found to affect other related observables, such as the electron anomaly, $a_e^{\rm SM}$, the ratio $R_{e/μ} = (m_μ/m_e)^2 (a_{e}^{\rm had,\,LO\,VP}/a_μ^{\rm had,\,LO\,VP})$ and the running of the weak mixing angle at low energies, although the consequences of these are currently less constraining.

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