Parametrization sampling and the pion PDF in a phenomenological analysis

In these proceedings, we extend the discussion of the pion PDF obtained by NLO QCD analysis in the Fant\^omas4QCD framework. Our pion analysis uses a state-of-the-art statistical methodology that accounts for the epistemic uncertainty. Fantômas4QCD, designed to handle multiple functional forms for solving the inverse problem, systematically explores a variety of solutions for PDFs, thereby improving estimates of epistemic uncertainty. Through this novel approach, we interpret our results for the valence sector, considering various non-perturbative methods available for predicting the pion PDF. We emphasize the distinctions between (global) QCD analyses and QFT-based calculations.