Pion radiative weak decay from the instanton vacuum

We investigate the vector and axial-vector form factors for the pion radiative weak decays $\pi^+\to e^+\nu_e \gamma$ and $\pi^+\to e^+\nu_e e^+ e^-$, based on the gauged effective chiral action from the instanton vacuum in the large $N_c$ limit. The nonlocal contributions, which arise from the gauging of the action, enhance the vector form factor by about $20\,\%$, whereas the axial-vector form factor is reduced by almost $30\,\%$. Both the results for the vector and axial-vector form factors at the zero momentum transfer are in good agreement with the experimental data. The dependence of the form factors on the momentum transfer is also studied. The slope parameters are computed and compared with other works.