FAITHFUL ESTIMATION OF UNCERTAINTIES IN MODERN PDF EXTRACTIONS

The primary focus of this Ph.D. thesis is the precise determination and validation of the uncertainties associated with parton distribution func- tions (PDFs). We introduce and implement the theory covariance method within the NNPDF4.0 framework, enabling the incorporation of theoretical uncertainties into the PDF determination process. Additionally, we revisit and expand upon the closure tests framework, which serves as a tool for val- idating the PDF extraction methodology in a controlled environment. This framework is applied to a dataset that has been deliberately constructed to be inconsistent, allowing for a rigorous assessment of the methodology’s ro- bustness. Furthermore, we utilize this framework to validate the extraction of the strong coupling constant using the correlated replica method. Finally, we present a novel theoretical pipeline, which introduces several technical advancements and underpins all the results discussed in this thesis.