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

TL;DR

This paper studies the radially excited pion's electromagnetic form factor and its contribution to the muon's g-2 using a non-perturbative framework, providing new insights into excited meson effects on fundamental magnetic moment calculations.

Contribution

It introduces a combined Schwinger-Dyson and Bethe-Salpeter approach to accurately describe the first radial excitation of the pion without reparametrizing interaction kernels, extending previous work.

Findings

Calculated the mass and decay constant of the excited pion.

Derived the electromagnetic form factor of the excited pion.

Estimated the excited pion's box contribution to muon g-2 as approximately -2.02 x 10^-13.

Abstract

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 $a_{\mu}$.