Fant\^omas: epistemic and nuclear uncertainties for the parton distributions of the pion

We present Fanto10, a new ensemble of NLO error parton distribution functions (PDFs) in a charged pion that provides the most detailed estimate of uncertainties from experimental, theoretical, and methodological sources in order to enable faithful comparisons against upcoming precision experiments and ab initio QCD predictions. For the first time, the Fanto10 PDFs quantify two important types of uncertainties, arising from in-depth exploration of feasible functional forms of pion PDFs and from the nuclear PDFs describing the internal composition of the tungsten target in the key E615 data set for pion-nuclear Drell-Yan process. Accounting for these uncertainties modifies physics conclusions of more restrictive analyses about the pion's gluon and quark sea composition. These advancements are made by employing the recently developed C++ framework Fant\^omas for systematic exploration of epistemic sources of PDF uncertainties, such as those arising from the choice of the PDF functional forms and sampling over methodological choices and third-party inputs, e.g., the nuclear PDF uncertainty in the presented case. The framework employs polynomial universal approximators (B\'ezier curves) to parametrize diverse PDF functional forms and reduce biases associated with the PDF parametrization choice. Its other component combines PDF ensembles from multiple preliminary fits into a single published ensemble of Hessian error PDFs. We review key steps of the Fant\^omas methodology, properties of Fanto10 PDFs, and implications for future studies.