Generic modelling of non-perturbative quantities and a description of hard exclusive $\pi^+$ electroproduction

Based on Regge-inspired arguments and counting rules, we formulate empirical models for zero-skewness generalized parton distributions (GPDs) ${\widetilde H}^{(3)}$ and ${\widetilde E}^{(3)}$ in the iso-vector sector. If a hypothetical $a_1/\rho_2$ master trajectory is taken into account, we find that the polarized deep inelastic structure function $g_1^{(3)}$, axial-vector form factor, pseudoscalar form factor, and lattice data are well described. Thereby, we use a symmetric valence scenario in which the `spin puzzle' in the iso-vector sector is trivially resolved. Utilizing a minimalist `holographic' GPD principle, tying the $t$-channel angular momentum and collinear conformal spin together, we build skewness dependent GPD models. Confronting these models with HERMES and JLAB measurements of hard exclusive $\pi^+$ electroproduction within the collinear factorization approach, we might conclude that minimalist GPD models are disfavored at leading order. We provide then a set of GPDs on the cross-over line that fairly describes both HERMES and JLAB measurements.