The interplay of transverse degrees of freedom and axial-vector mesons with short-distance constraints in g-2

We revisit well-known short-distance constraints relating the hadronic light-by light Greens function to the $langle VVA rangle$ one. As a novelty, we identify a previously unnoticed relation among the longitudinal and transverse degrees of freedom that is enforced by the axial anomaly. Such relation allows, among other things, to overcome the problem of basis ambiguities when describing axial-vector mesons transition form factors. It also helps elucidating some caveats of previous models used to describe the short-distance behavior. The new results here presented are model independent and should help paving the way for a better understanding of the, so far, controversial interplay among short-distance constraints and transverse degrees of freedom such as axial-vector mesons.