Electromagnetic structure of axial-vector mesons and implications for the muon $g-2$

Abstract

The electromagnetic structure of axial-vector mesons is investigated via elastic and two-photon transition form factors (TFFs). To this end, we employ a framework based on the Dyson-Schwinger and Bethe-Salpeter equations within a contact interaction model. This largely algebraic approach transparently exposes the role of symmetries and their breaking, and has proven successful in describing anomaly-sensitive processes, including pseudoscalar to two-photon TFFs, $\gamma \to 3\pi$, and vector-to-pseudoscalar radiative decays. Restricting our analysis to the lowest-lying states, $\text{A}=\{a_1,f_1,f_1^{\prime }\}$, we also evaluate the corresponding light-by-light contribution to the muon anomalous magnetic moment, and obtain $a_{\mu }^{\text{A}}=11.30(4.71)\times 10^{-11}$, consistent with contemporary estimates.

Comments: 14 pages, 4 figures