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The goal of this study is to determine a set of diffractive partondistribution function (diffractive PDFs) from a QCD analysis of all availableand up-to-date diffractive deep inelastic scattering (diffractive DIS) datasets from HERA $ep$ collider, including the most recent H1 and ZUES combinedinclusive diffractive cross section measurements. This extraction ofdiffractive PDFs, referred to as {\tt HK19-DPDF}, is performed atnext-to-leading (NLO) and next-to-next-to-leading (NNLO) in perturbative QCD.This new determination of diffractive PDFs is based on the fracture functionsmethodology, a QCD framework designed to provide a statistically soundrepresentation of diffractive DIS processes. Heavy quark contributions to thediffractive DIS are considered within the framework of the FONLL general massvariable flavor number scheme (GM-VFNS) and the "Hessian approach" is used todetermine the uncertainties of diffractive PDFs. We discuss the novel aspectsof the approach used in the present analysis, namely an optimized and flexibleparametrization of the diffractive PDFs as well as a strategy based on thefully factorization theorem for diffractive hard processes. We then present thediffractive PDFs, and discuss the fit quality and the stability upon variationsof the kinematic cuts and the fitted data sets. We find that the systematicinclusion of higher-order QCD corrections could improves the description of thedata. We compare the extracted sets of diffractive PDFs based on the fracturefunctions approach to other recent sets of diffractive PDFs, finding in generalvery good agreements.

Phenomenology of diffractive DIS in the framework of fracture functions and determination of diffractive parton distribution functions