Axial-vector exchange contribution to the hadronic light-by-light piece of the muon anomalous magnetic moment

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 $a_{\mu}^{$\text{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.