Parton Distribution Functions (PDFs) and Transverse-Momentum-Dependent PDFs (TMDs) encode our knowledge of the nucleon internal structure in terms of their elementary constituents, quarks and gluons. They are determined by means of global analyses of experimental data which require the development of suitable fitting methodologies. PDFs and TMDs represent an important input for precision studies at current and future accelerator facilities. The development of reliable fitting methodologies and their subsequent validation, in order to ensure the soundness of the corresponding results, is therefore a crucial problem in high-energy physics.
Thanks to the wealth of new data and fitting methodologies, the accuracy to which PDFs and TMDs are known is rapidly improving. With the reduction of the uncertainties, an increasing tension has been observed among results from different groups, making the discussion around the determination of faithful uncertainties all the more urgent.
This research proposal, Bayesian tools for one-dimensional and three-dimensional hadron structure (Bayhadron), develops a new methodology based on Bayesian inference and a set of statistical validation tools for PDF and TMD determination. The main goals of Bayhadron are two. 1) The development of a fully Bayesian methodology for PDF determination, providing a valid alternative to the methodologies based on parametric regression currently used within the community, and the release of a first PDF set based on it. 2) The application of validation tools developed within the PDF community to validate the fitting methodologies currently used for TMD determinations and their possible improvement by means of a Bayesian approach. Both goals of Bayhadron concur to a faithful determination of PDF and TMD errors, introducing a set of innovative statistical tools in the field and making the proposal particularly timely in light of current and future experimental and phenomenological efforts.