Fant\^omas: An analysis of parton distributions in a pion with B\'ezier parametrizations

TL;DR

This paper introduces Fantômas, a new Bézier curve-based method for parametrizing parton distribution functions, applied to pion PDFs, revealing significant correlations and uncertainties in the distributions.

Contribution

It presents a novel automated Bézier parametrization technique for PDFs, integrated into xFitter, to better quantify uncertainties in global QCD analyses.

Findings

Sea and gluon distributions in the pion are strongly correlated.

PDF solutions with zero gluon and large quark sea are experimentally plausible.

The method enhances understanding of parametrization dependence in PDFs.

Abstract

We systematically explore the parametrization dependence of the Parton Distribution Functions (PDFs) to better quantify the true uncertainty from global QCD analyses. To achieve this, we employ a novel technique that automates the generation of polynomial parametrizations for PDFs using B\'ezier curves. This technique is implemented in a C++ module, named Fant\^omas, which is now included within the xFitter program. As an example, we examine the charged pion PDF. Our analysis reveals that the sea and gluon distributions in the pion are strongly correlated, and PDF solutions featuring a vanishing gluon and a large quark sea are still experimentally allowed.