标题： 轻子电偶极算符在缪子$(g-2)_μ$的背景下具有$Γ_2$模块不变性 显示英文标题

标题： Leptonic dipole operator with $Γ_2$ modular invariance in light of Muon $(g-2)_μ$

摘要： 我们研究了与μ子异常磁矩的最新数据相关的轻子电弱偶极矩和轻子味非守恒衰变，$(g-2)_{\mu}$在轻子偶极子算符中。 我们采用了Meloni-Parriciatu成功的$\Gamma_2$模块不变模型作为轻子的味对称性。 假设$(g-2)_{\mu}$，$\Delta a_{\mu}$的异常为新物理（NP）的证据，我们将它与电子的异常磁矩$\Delta a_e$，电子电弱偶极矩$d_e$和$\mu\to e \gamma$衰变相关联。 我们发现NP对$\Delta a_{e(\mu)}$的贡献与轻子质量平方成正比，同样如朴素标度$\Delta a_\ell \propto m^2_\ell$所示。 在我们的框架中，$|d_e|$的实验约束比分支比$\mathcal{B} (\mu \to e \gamma)$的约束要严格得多。 假设我们模型参数$\delta_{\alpha}$对于电子的相位为一阶量，我们估计了$\mathcal{B}(\mu \to e \gamma)$的上限，该上限最多为$10^{-21}-10^{-20}$。 如果某些模型参数为实数，轻子电偶极矩（EDM）将消失，因为由于模形式$\tau$的模量导致的 CP 相位不贡献于 EDM。 然而，在特定情况下，我们可以得到$\mathcal{B} (\mu \to e \gamma)\simeq 10^{-13}$，其中$d_e$不为零。 参数的虚部可能导致在次领先项中出现$d_e$。 预测的电子 EDM 低于$10^{-32}$e cm，而$\mathcal{B} (\mu \to e \gamma)$接近实验上限。 $\tau\to e\gamma$和$\tau\to \mu\gamma$的分支比也进行了讨论。 显示英文摘要

摘要： We have studied the leptonic EDM and the LFV decays relating with the recent data of anomalous magnetic moment of muon, $(g-2)_{\mu}$ in the leptonic dipole operator. We have adopted the successful $\Gamma_2$ modular invariant model by Meloni-Parriciatu as the flavor symmetry of leptons. Suppose the anomaly of $(g-2)_{\mu}$, $\Delta a_{\mu}$ to be evidence of New Physics (NP), we have related it with the anomalous magnetic moment of the electron $\Delta a_e$, the electron EDM $d_e$ and the $\mu\to e \gamma$ decay. We found that the NP contributions to $\Delta a_{e(\mu)}$ are proportional to the lepton masses squared likewise the naive scaling $\Delta a_\ell \propto m^2_\ell$. The experimental constraint of $|d_e|$ is much tight compared with the one from the branching ratio $\mathcal{B} (\mu \to e \gamma)$ in our framework. Supposing the phase of our model parameter $\delta_{\alpha}$ for the electron to be of order one, we have estimated the upper-bound of $\mathcal{B}(\mu \to e \gamma)$, which is at most $10^{-21}-10^{-20}$. If some model parameters are real, leptonic EDMs vanish since the CP phase of the modular form due to modulus $\tau$ does not contribute to the EDM. However, we can obtain $\mathcal{B} (\mu \to e \gamma)\simeq 10^{-13}$ with non-vanishing $d_e$ in a specific case. The imaginary part of a parameter can lead to $d_e$ in the next-to-leading contribution. The predicted electron EDM is below $10^{-32}$e\,cm, while $\mathcal{B} (\mu \to e \gamma)$ is close to the experimental upper-bound. The branching ratios of $\tau\to e\gamma$ and $\tau\to \mu\gamma$ are also discussed.