Parton distribution functions with QED corrections
Stefano Carrazza
TL;DR
This work delivers the first unbiased extraction of parton distribution functions that include electroweak corrections, introducing a photon PDF and QED evolution within the DGLAP framework. It develops and validates APFEL, a public evolution library capable of solving coupled QCD⊗QED evolution up to NNLO in QCD and LO in QED, and implements the NNPDF2.3QED methodology to obtain photon and lepton PDFs from DIS and LHC data. A thorough phenomenological study demonstrates photon-induced effects across direct photon production, high-mass dilepton and WW processes, highlighting the impact and uncertainties of the photon PDF on LHC predictions. The work also introduces APFEL Web and a modern NNPDF framework, enabling flexible data treatment, rapid predictions, and provisions for future improvements including lepton PDFs and higher-order QED effects. Together, these advancements advance precision collider phenomenology by incorporating electroweak corrections into the PDF framework and providing tools to exploit current and forthcoming data.
Abstract
We present the first unbiased determination of parton distribution functions (PDFs) with electroweak corrections. The aim of this thesis is to provide an exhaustive description of the theoretical framework and the technical implementation which leads to the determination of a set of PDFs which includes the photon PDF and quantum electrodynamics (QED) contributions to parton evolution. First, we introduce and motivate the need of including electroweak corrections to PDFs, providing phenomenological examples and presenting an overview of the current state of the art in PDF fits. The theoretical implications of such corrections are then described through the implementation of the combined QCD+QED evolution in APFEL, a public code for the solution of the PDF evolution developed particularly for this thesis. We proceed by presenting the new structure of the Neural-Network PDF (NNPDF) methodology used for the extraction of this set of PDFs with QED corrections. We then provide a first determination of the full set of PDFs based on deep-inelastic scattering data and LHC data for $W$ and $Z/γ^*$ Drell-Yan production, using leading-order QED and NLO or NNLO QCD: the so-called NNPDF2.3QED set of PDFs. We perform a preliminary investigation of the phenomenological implications of NNPDF2.3QED set, in particular, focusing on the photon-induced corrections to direct photon production at HERA, high-mass dilepton and $W$ pair production at the LHC and finally, providing a first determination of lepton PDFs through the APFEL evolution. We conclude with a summary of the technological upgrades required for the improvement of future PDF determinations with electroweak corrections.