arXiv 2106.112912021-06hep-ph

μ子反常磁矩的单圈贡献

General Remarks on the One-loop Contributions to the Muon Anomalous Magnetic Moment

Bingrong Yu, Shun Zhou

备注：: 36 pages, 10 figures, 2 tables, more discussions and references added, version accepted by Nucl.Phys.B
发表信息：: Nucl.Phys.B 975 (2022) 115674
DOI：: 10.1016/j.nuclphysb.2022.115674

摘要：

费米实验室对μ子反常磁矩$a^{}_μ \equiv (g^{}_μ- 2)/2$的最新测量发现了一个与标准模型（SM）的理论预测不一致的$4.2\,σ$。出于这一令人兴奋的进展，我们调查在本文件中的一般单循环的贡献$a^{}_μ$内SM和超越。首先，与以往的工作不同的是，现在的解析公式的相关回路函数积分后，推出，并把紧凑的形式与Passarino-Veltman函数的帮助下。其次，考虑到μ子与新粒子在环中的相互作用，我们澄清了当一个环对$a^{}_μ$的贡献可以按照需要取正确的正号时。第三，可能的分歧在零和无限质量的限制进行检查，并在计算中没有任何分歧导致一些一致性条件的紫外线完整的模型建设。我们的一般公式的应用，如SM，跷跷板模型，$Z^\prime$和leptoquark模型，也进行了讨论。

英文摘要：

The latest measurement of the muon anomalous magnetic moment $a^{}_μ \equiv (g^{}_μ- 2)/2$ at the Fermi Laboratory has found a $4.2\,σ$ discrepancy with the theoretical prediction of the Standard Model (SM). Motivated by this exciting progress, we investigate in the present paper the general one-loop contributions to $a^{}_μ$ within the SM and beyond. First, different from previous works, the analytical formulae of relevant loop functions after integration are now derived and put into compact forms with the help of the Passarino-Veltman functions. Second, given the interactions of muon with new particles running in the loop, we clarify when the one-loop contribution to $a^{}_μ$ could take the correct positive sign as desired. Third, possible divergences in the zero- and infinite-mass limits are examined, and the absence of any divergences in the calculations leads to some consistency conditions for the construction of ultraviolet complete models. Applications of our general formulae to specific models, such as the SM, seesaw models, $Z^\prime$ and leptoquark models, are also discussed.

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