Fantômas unconfined: global QCD fits with Bézier parameterizations

Fantômas is a C++ toolkit for exploring the parametrization dependence of parton distribution functions (PDFs) and other correlator functions in quantum chromodynamics (QCD). Fantômas facilitates the generation of adaptable polynomial parametrizations for PDFs, called metamorphs, to find best-fit PDF solutions and quantify the epistemic uncertainty associated with the parametrizations during their fitting. The method employs Bézier curves as universal approximators for a variety of PDF shapes. Integrated into the xFitter framework for the global QCD analysis, Fantômas provides a foundation for general models of PDFs, while reducing the computational time compared to the approaches utilizing traditional polynomial parametrizations as well as providing an interpretable alternative to neural-network-based models. This paper outlines the structure and practical usage of the Fantômas toolkit, including its inputs, outputs, and implementation within xFitter . It also provides a practical example of using Fantômas for uncertainty quantification as well as the combination of PDF fits into a single ensemble. PROGRAM SUMMARY Program Title: Fantômas CPC Library link to program files: https://doi.org/10.17632/fngjh3p2y4.1 Developer’s repository link: https://gitlab.com/cteq-tea/public/fantomas4qcd https://gitlab.cern.ch/fitters/xfitter/ in the Fantomas branch. Licensing provisions: GPLv3 Programming language: C++ Nature of problem: Dependence on functional forms of parton distribution functions (PDFs) in a hadron introduces a significant uncertainty in precision predictions for many high-energy scattering processes. A new generation of global analyses of PDFs requires streamlined, fast generation of diverse functional forms satisfying number and momentum sum rules consistent with QCD, asymptotic limits, integrability of PDFs, and positivity of the resulting cross sections. Other approaches to approximate a variety of PDFs may lack parsimony and interpretability attributed to explicit functional forms. Solution method: The Fantômas toolkit provides a framework to construct families of increasingly flexible parametrizations for PDFs using Bézier curves. These polynomial functions are universal approximators that are computed from the values of the function itself at user-specified control points. Fantômas provides a method to cast many existing PDF parametrizations into an internal format (a metamorph) that simplifies raising the degree of the polynomial solely by adding new control points, without refitting all PDF parameters from scratch. The Fantômas approach systematizes exploration of the multidimensional parameter landscape of PDFs while potentially reducing human involvement and computing time compared to traditional realizations. Preprint numbers: ANL-197925, MSUHEP-25-016