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arXiv 2004.06451hep-ph
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真空极化对μ子$g-2$反问题的贡献

Vacuum polarization contribution to muon $g-2$ as an inverse problem

Hsiang-nan Li, Hiroyuki Umeeda

摘要:

利用色散关系分析了任意光子不变质量$q^2$下的电磁流相关器。将色散关系转化为一个反问题,通过该反问题,在大$q^2$时,微扰输入$Π(q^2)$,求解低$q^2$时的真空极化函数$Π(q^2)$。结果表明,$Π(q^2)$的结果,包括它的一阶导数$Π^\prime(q^2=0)$,与格点QCD的结果一致,它的虚部容纳了$e^+e^-$湮灭数据。相应的强子真空极化贡献$a^{\rm HVP}_μ= (641^{+65}_{-63})\times 10^{-10}$的μ子异常磁矩$g-2$,其中的不确定性来自微扰输入的变化,也同意在其他唯象和理论方法获得的。我们指出,我们的形式等价于对只依赖实验数据的唯象方法施加了解析性约束,并且可以提高标准模型中$a^{\rm HVP}_μ$确定的精度.

英文摘要:

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.

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