标题： 径向激发的π介子：电磁形式因子和μ子的$g-2$盒图贡献 显示英文标题

标题： Radially excited pion: electromagnetic form factor and the box contribution to the muon's $g-2$

摘要： 我们研究了径向激发带电π介子的性质，重点关注其电磁形式因子（EFF）及其对μ子反常磁矩的盒图贡献，记为$a_{\mu}$。利用结合施温格-狄拉克和贝特-萨尔彼得方程的耦合非微扰框架，我们首先计算了π介子第一径向激发的质量和弱衰变常数。首先提供了彩虹梯子（RL）近似的初步结果，随后进行了扩展的超越RL（BRL）分析，该分析纳入了介子云效应。基于我们的先前工作，这项分析表明，无需重新参数化相互作用核即可准确描述第一径向激发。在证明截断方案的有效性后，我们继续计算相应的EFF，并由此得出π介子第一径向激发对μ子反常磁矩的HLbL分量的贡献，得到$a_{\mu}^{\pi_1-\text{box}}(\text{RL}) = -(2.03 \pm 0.12) \times 10 ^{-13}$和$a_{\mu}^{\pi_1-\text{box}}(\text{BRL}) = -(2.02 \pm 0.10) \times 10 ^{-13}$。我们的计算也为计算相关极点贡献奠定了基础，这些贡献来自激发赝标介子到$a_{\mu}$的贡献。 显示英文摘要

摘要： We investigate the properties of the radially excited charged pion, with a specific focus on its electromagnetic form factor (EFF) and its box contribution to the hadronic light-by-light (HLbL) component of the muon's anomalous magnetic moment, $a_{\mu}$. Utilizing a coupled non-perturbative framework combining Schwinger-Dyson and Bethe-Salpeter equations, we first compute the mass and weak decay constant of the pion's first radial excitation. Initial results are provided for the Rainbow-Ladder (RL) approximation, followed by an extended beyond RL (BRL) analysis that incorporates meson cloud effects. Building on our previous work, this analysis demonstrates that an accurate description of the first radial excitation can be achieved without the need for a reparametrization of the interaction kernels. Having demonstrated the effectiveness of the truncation scheme, we proceed to calculate the corresponding EFF, from which we derive the contribution of the pion's first radial excitation to the HLbL component of the muon's anomalous magnetic moment, producing $a_{\mu}^{\pi_1-\text{box}}(\text{RL}) = -(2.03 \pm 0.12) \times 10 ^{-13}$, $a_{\mu}^{\pi_1-\text{box}}(\text{BRL}) = -(2.02 \pm 0.10) \times 10 ^{-13}$. Our computation also sets the groundwork for calculating related pole contributions of excited pseudoscalar mesons to $a_{\mu}$.