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

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.