Executive Summary : | Quarks and gluons (Collectively called partons) are fundamental constituent particles of matter and the knowledge of their momentum distributions help us understand about the structure of the nucleons which are the building blocks of matter. Parton Distribution Functions (PDF) are also essential ingredients in calculation of hadronic cross-sections and in predictions of standard model processes at the Accelerators such as Large Hadron Collider (LHC) and Relativistic Heavy Ion Collider (RHIC). Many high precision cross-section measurements of hadronic processes at these Accelerators are sensitive to PDF uncertainties. PDF has played important role in the discovery of the Higgs boson. Incomplete knowledge on PDFs is one of the main limitations in searches of new physics. However, within the scope of Quantum Chromodynamics (QCD), the determination of PDFs is mainly performed via parameterization and fitting of the experimental data of structure functions in the framework of linear DGLAP (Dokshitzer-Gribov-Lipatov-Altarelli-Parisi) QCD evolution equation. But, in the kinematic region of small momentum fraction x (Bjorken variable), this linear DGLAP equation predicts sharp rise of gluon distribution function. This unusual rise of gluons towards small-x lead to violation of Froissart bound and unitarity of the physical cross-sections. Therefore, there must be a mechanism to tame down the unusual rising of gluons at the high dense regime and correspondingly some nonlinear corrections needed in the DGLAP evolution equation. Gluon recombination is believed to be the mechanism that controls the growth of gluons towards small-x. Zhu, Ruan and Shen, considering the recombination effect re derived the DGLAP equation in a Time-Ordered-Perturbation-Theory (TOPT) framework which led to some modifications in the DGLAP equation. This new equation is known as the Modified DGLAP (MD-DGLAP) equation which contains the nonlinear terms due to the gluon recombination. This project is about phenomenological study of the evolution of PDFs and the deep inelastic scattering (DIS) structure functions of proton and some heavy nuclei in the framework of modified DGLAP (MD-DGLAP) equation. We intend to study and analyze the higher order QCD effects (i.e., beyond leading orders) on the PDFs and structure functions at small Bjorken x (≤10^-2). MD-DGLAP equation is a nonlinear evolution equation where gluon recombination probabilities are included, and its solutions facilitate us in understanding the nonlinear effects of shadowing and antishadowing on structure functions. To test compatibility our results will be compared with the global PDF data. |