Generalized parton distributions of the pion in chiral quark models and their QCD evolution

We evaluate generalized parton distributions of the pion in two chiral quark models: the spectral quark model and the Nambu–Jona-Lasinio model with a Pauli-Villars regularization. We proceed by the evaluation of double distributions through the use of a manifestly covariant calculation based on the α representation of propagators. As a result polynomiality is incorporated automatically and calculations become simple. In addition, positivity and normalization constraints, sum rules, and soft-pion theorems are fulfilled. We obtain explicit formulas, holding at the low-energy quark-model scale. The expressions exhibit no factorization in the t-dependence. The QCD evolution of those parton distributions is carried out to experimentally or lattice accessible scales. We argue for the need of evolution by comparing the parton distribution function and the parton distribution amplitude of the pion to the available experimental and lattice data, and confirm that the quark-model scale is low, about 320 MeV.