论文标题
真空两极分化对MUON $ G-2 $作为反问题
Vacuum polarization contribution to muon $g-2$ as an inverse problem
论文作者
论文摘要
我们通过利用其相关的分散关系，以任意光子不变的质量$ q^2 $分析电磁电流相关器。分散关系变成了一个反问题，通过该问题，在低$ q^2 $下，涉及的真空极化函数$π（q^2）$在大$ q^2 $下以$π（q^2）$的扰动输入来解决。发现$π（q^2）$的结果，包括其第一个衍生$π^\ prime（q^2 = 0）$，与lattice qCD的结果一致，其虚构零件可容纳$ e^+e^+e^ - $ nihihilation数据。相应的望态真空极化贡献$ a^{\ rm hvp}_μ=（641^{+65} _ { - 63}）\ times 10^{ - 10^{ - 10} $ to muon Anomaloles $ g-2 $，同时出现了这些不确定的磁性差异，并在其中出现了其他危险的现象，并在此期间出现了其他现有的现象，并在这种情况下进行了这种现象，并在这种情况下进行了效果，并在此中呈现出来的其他现象。方法。我们指出，我们的形式主义等同于仅依靠实验数据的现象学方法的分析性约束，并且可以提高标准模型中$ a^{\ rm HVP}_μ$确定的精度。
We analyze the electromagnetic current correlator at an arbitrary photon invariant mass $q^2$ by exploiting its associated dispersion relation. The dispersion relation is turned into an inverse problem, via which the involved vacuum polarization function $Π(q^2)$ at low $q^2$ is solved with the perturbative input of $Π(q^2)$ at large $q^2$. It is found that the result for $Π(q^2)$, including its first derivative $Π^\prime(q^2=0)$, agrees with those from lattice QCD, and its imaginary part accommodates the $e^+e^-$ annihilation data. The corresponding hadronic vacuum polarization contribution $a^{\rm HVP}_μ= (641^{+65}_{-63})\times 10^{-10}$ to the muon anomalous magnetic moment $g-2$, where the uncertainty arises from the variation of the perturbative input, also agrees with those obtained in other phenomenological and theoretical approaches. We point out that our formalism is equivalent to imposing the analyticity constraint to the phenomenological approach solely relying on experimental data, and can improve the precision of the $a^{\rm HVP}_μ$ determination in the Standard Model.
