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

The calculation of hard scattering processes containing hadrons in the final state wouldinvolve the parton fragmentation functions (FFs). The parton FFs describe the fragmentationprocess of parton to hadron. The parton FFs are nonperturbative quantities and need to bedetermined via a global fit of the relevant experimental data (such as the e e annihilation，lepton-hadron and hadron-hadron scattering and so on). Including the perturbative QCDcorrections, the parton FFs have scaling violations, which can be described by the DGLAPequations.Firstly, we review the theoretical background of the parton FFs. We introduce theconcept of parton FFs via the cross section of semi-inclusivee e annihilation and give ananalysis for scaling violations and the characteristics of different parton FFs (light quark,gluon and heavy quark). At present, there are many methods to solve the DGLAP equations,such as the Mellin transformation, Laguerre expansion and grid method. We introduce theQCDNUM17program which is based on the grid method and devoted to solve the DGLAPequations numerically, including its basic algorithm and implementation.To give the evolution of parton FFs by solving the DGLAP equations via QCDNMprogram, we need the parton FFs at an initial energy scale as inputs which need to bedetermined via a global fit of the relevant experimental data. Now, many sets of parton FFs atsome energy scale are available and we summarize those given by AKK、HKN and SKMAcollaborations. On this basis, we choose the parton FFs given by MSK as inputs and evolvethem to other energy scales by solving the DFGLAP equations via QCDNUM17. Finally, wegive the parton FFs as functions of fractional momentum x at different energy scales and abref analysis for them as results.