论文标题
三环QED对带有两个内部费米昂循环和一类KampédeFériet系列的$ G-2 $的$ G-2 $贡献
The three-loop QED contributions to the $g-2$ of charged leptons with two internal fermion loops and a class of Kampé de Fériet series
论文作者
论文摘要
带有两个内部封闭费用环的每个带电钩子的$ g-2 $的三环QED质量依赖的贡献，有时称为$ a^{（6）} _ 3 \ left（\ frac {m_1} {m_1} {m_2} {m_2}，\ frac {m_1} Mellin-Barnes（MB）表示技术。 Muon和$τ$ Lepton异常磁矩$ a^{（6）} _ {3，μ} $和$ a^{（6）} _ {3，τ} $的结果，它们仅在前几个项中是Lepton Mass Baties的串联质量比例，仅是其确切的表达方式。对电子$ a^{（6）} _ {3，E} $的异常磁矩的贡献也明确以封闭形式给出。除此之外，我们还表明，从MB表示的不同串联表示形式共同收敛于所有可能的质量值。这种出乎意料的行为与以下事实有关：这些系列将属于KampédeFériet系列的播放双几何系列播放，我们证明它们具有与Appell $ f_1 $双重高几何系列相同的简单收敛性和分析延续性。
The three-loop QED mass-dependent contributions to the $g-2$ of each of the charged leptons with two internal closed fermion loops, sometimes called $A^{(6)}_3\left(\frac{m_1}{m_2}, \frac{m_1}{m_3}\right)$ in the $g-2$ literature, is revisited using the Mellin-Barnes (MB) representation technique. Results for the muon and $τ$ lepton anomalous magnetic moments $A^{(6)}_{3,μ}$ and $A^{(6)}_{3,τ}$, which were known as series expansions in the lepton mass ratios up to the first few terms only, are extended to their exact expressions. The contribution to the anomalous magnetic moment of the electron $A^{(6)}_{3,e}$ is also explicitly given in closed form. In addition to this, we show that the different series representations derived from the MB representation collectively converge for all possible values of the masses. Such unexpected behavior is related to the fact that these series bring into play double hypergeometric series that belong to a class of Kampé de Fériet series which we prove to have the same simple convergence and analytic continuation properties as the Appell $F_1$ double hypergeometric series.
