Numerical Solution Of The DGLAP Evolution Equation For Parton Distribution Functions And Its Evolution With The Energy Scale

In1969, the charged lepton nucleon deep inelastic scattering (DIS) experiments make people aware of the fact for the first time that nucleon is composed of many point-like particles which are known as partons. On this basis, Feynman proposed the parton model. In deep-inelastic scattering (DIS) and "hard" proton-proton (or proton-antiproton) high-energy collisions, the scattering proceeds via the parton constituents of hadrons. To predict the rates of various processes, we need to determine a series of universal parton distribution functions (PDFs). These distributions are best determined by global fits to all the available DIS and related hard scattering data. The fits can be performed at leading-order (LO), next-to-leading order (NLO) or at next-to-next-to-leading order (NNLO) in the strong coupling asFirstly, we give an introduction to the related theoretical background for PDFs, giving their concepts via the structure functions of proton in DIS. With the perturbative corrections, the PDFs depend on the factorization energy scale and their evolutions are described by DGLAP equation. We summarize the DGLAP equation and its numerical solutions in chapter3. Our works are summarized in chapter4. Based on the PDFs at some scale given by various collaborations via global fits, we evolve the PDFs by using the QCDNUM program at the NNLO and give the results at different energy scales. Concretely, we give the PDFs of dv uv, d, u, s, s, c, g at the energy scale μ2=1GeV2,μ2=10GeV2, μ2=100GeV2and μ2=104GeV2with brief analysis and comparisons. It is easily seen that the light PDFs vary more rapidly than heavy ones when the energy scale is fixed. The results given by this thesis may have some significance for exclusive processes involving PDFs.