Fantômas4QCD: pion PDFs with epistemic uncertainties

In these proceedings, we reiterate and extend the discussion of the Next-to-Leading Order (NLO) QCD analysis of the charged pion Parton Distribution Function (PDF) obtained within the Fant\^omas4QCD framework. The goal of the Fant\^omas analysis is to quantify the dependence on the parametrization form in global QCD analyses, with a first application to the pion PDFs. We highlight the anti-correlation between the experimentally allowed gluon and sea distributions in the pion, as made apparent by the sampling over parametrization forms. This result, for the sea and gluon sector, illustrates the importance of accounting for epistemic uncertainties in data-driven QCD analyses. In that regard, we further discuss the meaning of the sampling uncertainty and why it is key in phenomenological studies of hadron structure.