  In this work we study the axial contributions to the hadronic light-by-light
piece of the muon anomalous magnetic moment using the framework of resonance
chiral theory. As a result, we obtain $a_{\mu}^{\textrm{HLbL};A} =
\left(0.8^{+3.5}_{-0.1}\right)\cdot 10^{-11}$, that might suggest a smaller
value than most recent calculations, underlining the need of future work along
this direction. In particular, we find that our results depend critically on
the asymptotic behavior of the form factors, and as such, emphasizes the
relevance of future experiments for large photon virtualities. In addition, we
present general results regarding the involved axial form factors description,
comprehensively examining (and relating) the current approaches, that shall be
of general interest.
