Electromagnetic structure of axial-vector mesons and implications for the muon <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>g</mml:mi> <mml:mo>−</mml:mo> <mml:mn>2</mml:mn> </mml:math>

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 (CI) model. This largely algebraic approach exposes the role of symmetries and their breaking in a transparent manner, and has proven successful in describing anomaly-sensitive processes, including pseudoscalar to two-photon TFFs, <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>γ</a:mi> <a:mo stretchy="false">→</a:mo> <a:mn>3</a:mn> <a:mi>π</a:mi> </a:math> , and vector-to-pseudoscalar radiative decays. Restricting our analysis to the lowest-lying axial-vector meson multiplet, <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"> <d:mrow> <d:mi mathvariant="normal">A</d:mi> <d:mo>=</d:mo> <d:mo stretchy="false">{</d:mo> <d:msub> <d:mrow> <d:mi>a</d:mi> </d:mrow> <d:mrow> <d:mn>1</d:mn> </d:mrow> </d:msub> <d:mo>,</d:mo> <d:msub> <d:mrow> <d:mi>f</d:mi> </d:mrow> <d:mrow> <d:mn>1</d:mn> </d:mrow> </d:msub> <d:mo>,</d:mo> <d:msubsup> <d:mrow> <d:mi>f</d:mi> </d:mrow> <d:mrow> <d:mn>1</d:mn> </d:mrow> <d:mrow> <d:mo>′</d:mo> </d:mrow> </d:msubsup> <d:mo stretchy="false">}</d:mo> </d:mrow> </d:math> , we also explore the corresponding light-by-light contribution to the muon anomalous magnetic moment. This contribution is underestimated in the CI model mainly due to the normalization of the TFFs. After applying a phenomenologically motivated rescaling to the TFFs, a process required given the limitations of the CI model, we obtain <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:mrow> <i:msubsup> <i:mrow> <i:mi>a</i:mi> </i:mrow> <i:mrow> <i:mi>μ</i:mi> </i:mrow> <i:mrow> <i:mi mathvariant="normal">A</i:mi> </i:mrow> </i:msubsup> <i:mo>=</i:mo> <i:mn>8.1</i:mn> <i:msubsup> <i:mrow> <i:mn>6</i:mn> </i:mrow> <i:mrow> <i:mo>−</i:mo> <i:mn>1.02</i:mn> </i:mrow> <i:mrow> <i:mo>+</i:mo> <i:mn>1.22</i:mn> </i:mrow> </i:msubsup> <i:mo>×</i:mo> <i:msup> <i:mrow> <i:mn>10</i:mn> </i:mrow> <i:mrow> <i:mo>−</i:mo> <i:mn>11</i:mn> </i:mrow> </i:msup> </i:mrow> </i:math> , consistent with contemporary assessments.