arXiv 2109.097222021-09-29hep-phhep-ex

关于μ子反常磁矩的测量

On the measurement of the muon anomalous magnetic moment

Ara Ioannisian

备注：: minor changes in the text, statistics is corrected

摘要：

文中提出的思想和公式将有助于把μ子反常磁矩的理论预言和"μ子g-2"实验的结果结合起来。在这样做时，我们只在标准模型中讨论新的效应。在量子物理学中，自旋垂直于磁场的状态可以表示为自旋平行于磁场和反平行于磁场的能量本征态的叠加：所产生的自旋进动是由于两个本征态之间的能量差。如果这种状态像μ子一样是不稳定的，并且可以衰变，那么它将具有自然的能量扩散。结果，自旋进动的频率可以变化。对于恒定磁场，所测量的自旋进动速度将根据具有宽度$\left(γτ\right)^{-1}$、洛伦兹伽马因子$γ=E/ m$和粒子寿命$τ$的洛伦兹分布而扩展。虽然洛伦兹分布的真实均值和方差是不确定的，但后者可以通过最大似然法估计为${2 \over N (γτ)^2}$，是正态分布的两倍。因此，实际上异常磁矩的统计误差应该比实验的$χ^2$分析更宽。

英文摘要：

The ideas and formulas presented in the article will help to bring together the theoretical predictions for the anomalous magnetic moment of muon and the results of the "Muon g-2" experiment. In doing so, we are discussing the new effect exclusively within the Standard Model. In quantum physics a state with spin perpendicular to a magnetic field can be expressed as a superposition of energy eigenstates with spins parallel and antiparallel to the field: the resultant spin precession is due to the energy difference between the two eigenstates. If the state, like the muon, is unstable and can decay, it will have a natural energy spread. As a result the frequency of the spin precession can vary. For a constant magnetic field the measured spin precession velocity will be spread according to the Lorentzian distribution with width $\left(γτ\right)^{-1}$, for Lorentz gamma factor $γ=E/ m$, and particle lifetime $τ$. Although the true mean and variance of a Lorentzian distribution is undefined, the latter can be estimated by the maximum likelihood method to be ${2 \over N (γτ)^2}$, twice that of a normal distribution. Thus, the statistical error on the anomalous magnetic moment in reality should turn out to be wider than with $χ^2$ analysis of the experiment.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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英文摘要：

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