Asymptotic behavior of meson transition form factors

Understand

One of the open issues in evaluations of the contribution from hadronic light-by-light scattering to the anomalous magnetic moment of the muon $(g-2)_\mu$ concerns the role of heavier scalar, axial-vector, and tensor-meson intermediate states.

• The coupling of axial vectors to virtual photons is suppressed for small virtualities by the Landau-Yang theorem, but otherwise there are few rigorous constraints on the corresponding form factors.
• In this paper, we first derive the Lorentz decomposition of the two-photon matrix elements into scalar functions following the general recipe by Bardeen, Tung, and Tarrach.
• Based on this decomposition, we then calculate the asymptotic behavior of the meson transition form factors from a light-cone expansion in analogy to the asymptotic limits for the pseudoscalar transition form factor derived by Brodsky and Lepage.