μ子衰变中的迹不变性与能量依赖纠缠
On trace invariance and energy-dependent entanglement in muon decay
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中文总结 AI 辅助
该研究重新审视μ子磁异常测量的一项修正，结合费米实验室g-2合作组数据，得到能量依赖修正，修正后结果与相关测定兼容，当前分箱数据无法在常数与能量依赖偏移间做决定性判别。
中文摘要 AI 辅助
我们重新审视了针对μ子磁异常测量的一项拟议修正，并将其与费米实验室g-2合作组报告的能量分箱扫描结果进行了比较。核心要点在于，从探测到的正电子集合推断出的相对论三体衰变中，相关中微子的偏迹定义在探测器处的渐近态，而非衰变顶点处的理想化态。由于拟合的正电子样本混合了不同衰变时间、飞行时间、能量和接收度的事件，对未观测到的中微子螺旋度求迹后，会在观测区域留下一个时间相关的混合态。利用角动量平衡，我们在正电子能量区间$E_p \in (1.5,2.9)$ GeV中得到了一个能量依赖的修正。修正后的μ子异常实验区间向基于BaBar和τ的测定结果靠拢，同时在1σ水平上与数据驱动及格点标准模型评估结果兼容。随后，我们对费米实验室第1至6轮运行的数字化公开$R(E_p)$扫描结果进行了拟合，采用两个单参数假设：常数偏移和受纠缠启发的能量依赖偏移。在数字化精度范围内，χ²差异仍较小，当前分箱数据无法在两者间做出决定性判别。
英文摘要
We revisit a proposed correction to the muon magnetic anomaly measurement and compare it with energy-binned scans reported by the Fermilab $g-2$ collaboration. The central point is that, for a relativistic three-body decay inferred from an ensemble of detected positrons, the relevant neutrino partial trace is defined on the asymptotic state at the detector, not on an idealised state at the decay vertex. Because the fitted positron sample mixes events with different decay times, flight times, energies and acceptances, tracing over the unobserved neutrino helicities leaves a time-dependent mixed state in the observed sector. Using angular-momentum balance, we obtain an energy-dependent correction in the positron energy interval $E_p \in (1.5,2.9)$ GeV. The corrected experimental interval for the muon anomaly moves towards the BaBar- and $τ$-based determinations, while remaining compatible at the $1σ$ level with both data-driven and lattice-based Standard Model evaluations. We then fit digitised public $R(E_p)$ scans for Fermilab's runs $1$ to $6$, with two one-parameter hypotheses: a constant shift and the entanglement-motivated energy-dependent shift. Within digitisation accuracy, the differences in $χ^2$ remain modest and the current binned data do not provide decisive discrimination between them.
