  We study the transition form factors (TFFs) of axial-vector mesons in the
context of currently available experimental data, including new constraints
from $e^+ e^- \to f_1(1285) \pi^+ \pi^-$ that imply stringent limits on the
high-energy behavior and, for the first time, allow us to provide an
unambiguous determination of the couplings corresponding to the two
antisymmetric TFFs. We discuss how these constraints can be implemented in a
vector-meson-dominance picture, and, in combination with contributions from the
light-cone expansion, construct TFFs as input for the evaluation of
axial-vector contributions to hadronic light-by-light scattering in the
anomalous magnetic moment of the muon.
