Transverse Momentum Dependent Parton Density Functions and a Self-similarity based Model of Proton Structure Function F2(x,Q2) at Large and Small x

TL;DR

This paper explores a self-similarity based model of the proton structure function F2(x,Q2), extending it to large x, modifying uPDFs for theoretical consistency, and discussing saturation of the Froissart bound in QCD.

Contribution

It introduces modifications to a self-similarity based model of proton structure functions to ensure compatibility with large x behavior and discusses saturation phenomena within this framework.

Findings

Modified uPDFs align with theoretical expectations at large x

The model's potential saturation of Froissart bound is analyzed

Reanalysis of PDFs using TMDPDF relations confirms model consistency

Abstract

Unintegrated parton density functions (uPDFs) of Quantum Chromodynamics (QCD), also known as TMDPDFs, are generally used to study details of hadronic final states in high energy lepton-hadron and hadron-hadron collisions; while the integrated parton density functions (PDFs) are used for conventional deep inelastic inclusive processes. The self-similarity based Model of proton structure function $ F_{2}(x,Q^{2}) $ suggested in recent years are however based on specific uPDFs with self-similarity at small \textit{x}. In this work, we study large \textit{x} limit of such a Model and modify the defining uPDFs to make them compatible with theoretical expectations in such limit. Possibility of saturation of Froissart bound in this Model is discussed. We also reanalyze the PDFs in this approach using its conventional relation with TMDPDFs.