Improved phenomenology of $\pi N$ transition distribution amplitudes

To study cross sections and polarization asymmetries for the processes $e p \to e n \pi^+$ and $e p \to e p \pi^0$ in the backward region, we develop a flexible phenomenological model for nucleon-to-pion transition distribution amplitudes ($\pi N$ TDAs), which are used in the QCD collinear factorization description of the scattering amplitudes. Our model is based on the two-component factorized Ansatz for the corresponding spectral densities, quadruple distribution. It takes into account the constraints for $\pi N$ TDAs arising from the threshold pion production theorem and also includes a forward limit contribution that can be fitted to experimental data. We examine the sensitivity of observable predictions to various modelling assumptions.