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

## TL;DR

This paper presents a comprehensive QCD analysis to determine diffractive parton distribution functions from HERA diffractive DIS data, incorporating higher-order corrections and fracture functions methodology for improved accuracy.

## Contribution

It introduces a novel fracture functions-based framework for extracting diffractive PDFs at NLO and NNLO, with optimized parametrization and uncertainty estimation.

## Key findings

- Diffractive PDFs are successfully extracted with good fit quality.
- Higher-order QCD corrections improve data description.
- The new PDFs agree well with recent sets from other analyses.

## Abstract

The goal of this study is to determine a set of diffractive parton distribution function (diffractive PDFs) from a QCD analysis of all available and up-to-date diffractive deep inelastic scattering (diffractive DIS) data sets from HERA $ep$ collider, including the most recent H1 and ZUES combined inclusive diffractive cross section measurements. This extraction of diffractive PDFs, referred to as {\tt HK19-DPDF}, is performed at next-to-leading (NLO) and next-to-next-to-leading (NNLO) in perturbative QCD. This new determination of diffractive PDFs is based on the fracture functions methodology, a QCD framework designed to provide a statistically sound representation of diffractive DIS processes. Heavy quark contributions to the diffractive DIS are considered within the framework of the FONLL general mass variable flavor number scheme (GM-VFNS) and the "Hessian approach" is used to determine the uncertainties of diffractive PDFs. We discuss the novel aspects of the approach used in the present analysis, namely an optimized and flexible parametrization of the diffractive PDFs as well as a strategy based on the fully factorization theorem for diffractive hard processes. We then present the diffractive PDFs, and discuss the fit quality and the stability upon variations of the kinematic cuts and the fitted data sets. We find that the systematic inclusion of higher-order QCD corrections could improves the description of the data. We compare the extracted sets of diffractive PDFs based on the fracture functions approach to other recent sets of diffractive PDFs, finding in general very good agreements.