The purpose of parameterization in PDFs (Parton Distribution Functions) and FFs (Fragmentation Functions) is to describe the distributions of partons (PDFs) and hadrons (FFs) within a proton or other hadron. This allows for the calculation of cross sections and other observables in high-energy collisions.
PDFs are primarily determined through global fits to a wide range of experimental data from particle colliders, deep inelastic scattering experiments, and other processes. FFs, on the other hand, are mainly determined through data from e+e- annihilation and semi-inclusive deep inelastic scattering experiments.
The uncertainties in PDFs and FFs represent our limited knowledge and understanding of the distributions of partons and hadrons within a proton. These uncertainties can have a significant impact on the predictions of high-energy collision processes and must be taken into account in any analysis.
PDFs and FFs are scale-dependent, which means that their values change as the energy scale of the collision changes. This is due to the effects of QCD (Quantum Chromodynamics) evolution, which describes how the distributions of partons and hadrons change as the energy scale of the collision increases.
Yes, PDFs and FFs provide valuable information about the internal structure of the proton, such as the distribution of quarks and gluons within it. By studying the behavior of PDFs and FFs at different energy scales, we can learn more about the fundamental properties of the proton and the strong force that binds it together.