Axial-vector Form Factors for $K_{\mathrm{\ell }2\gamma }$ and ${\pi }_{\mathrm{\ell }2\gamma }$ at $O(p^6)$ in Chiral Perturbation Theory

We present two-loop calculations on the axial-vector form factors $F_A$ of semileptonic radiative kaon and pion decays in chiral perturbation theory. The relevant dimension-6 terms of the lagrangian are evaluated from the resonance contribution and the results of the irreducible two-loop graphs of the sunset topology are given in detail. We also explicitly show that the divergent parts in $F_A$ are cancelled exactly as required.