论文标题
附录：对粘液异常磁矩贡献的平时和间距的内核函数（2022 J.Phys。G：Nucl。part。phys。49055001）
Addendum: Timelike and spacelike kernel functions for the hadronic vacuum polarization contribution to the muon anomalous magnetic moment (2022 J. Phys. G: Nucl. Part. Phys. 49 055001)
论文作者
论文摘要
该附录为[J.中获得的结果提供了互补的结果。物理。 G49，055001（2022）]。具体而言，获得了一种等同的关系形式，该形式将“间距”内核结合在一起，用于对哑光的真空极化对MUON异常磁矩$ a^{\ text {hvp}}_μ$的贡献。结果表明，“空间式”和“时间型”内核函数的红外限制值，它们输入涉及Adler函数的$ a^{\ text {hvp}}_μ$的表示形式与$ r $ -ratio涉及$ r $ -ratio相同，与对相应的QED贡献了对Muon Anomal Anomal Anomal Anomal Anomal Anomal Anomal Anomal Anomal Anomal Anomal Anomal Anomal Anomal Anomal Anomal Anomal Anomal Anomal Anomal Anomal Anomal Anomal Anomal Anomal Anomal a anomal anmal anmal anmal anmal anmal and ance的效力相同。近代领先的订单贡献$ a^{\ text {hvp}（3b）}_μ$（包括Leptonic和Hadroonic插入）和$ a^{\ text {hvp}（3c）} _μ$（其中包括双重HADRONIC INSTRIEN），均已进行研究。 $ a^{\ text {hvp}（3b）}_μ$出现的三个内核函数，其中涉及辐射真空极化函数，adler函数和$ r $ -RATIO，用于电子和$τ$ - $ -CH $ -Lepton loop loop intersertions。
This addendum provides results complementary to those obtained in [J. Phys. G49, 055001 (2022)]. Specifically, an equivalent form of the relation, which binds together the "spacelike" kernel functions for the hadronic vacuum polarization contribution to the muon anomalous magnetic moment $a^{\text{HVP}}_μ$, is obtained. It is shown that the infrared limiting value of the "spacelike" and "timelike" kernel functions, which enter the representations for $a^{\text{HVP}}_μ$ involving the Adler function and the $R$-ratio, is identical to the corresponding QED contribution to the muon anomalous magnetic moment of the preceding order in the electromagnetic coupling. The next-to-leading order contributions $a^{\text{HVP}(3b)}_μ$ (which includes the leptonic and hadronic insertions) and $a^{\text{HVP}(3c)}_μ$ (which includes the double hadronic insertion), are studied. The three kernel functions appearing in the representations for $a^{\text{HVP}(3b)}_μ$, which involve the hadronic vacuum polarization function, Adler function, and the $R$-ratio, are presented for the cases of the electron and $τ$-lepton loop insertions.
