Quark decay functions as measured in electron positron annihilation and semi-inclusive process in electron proton collisions

The modern theory describing the strong interaction, which holds the quarks together in the hadrons, is quantum chromodynamics (QCD), in which the interaction is mediated by the exchange of spin 1 particles called gluons. Today good qualitative agreement between the theory and experimental results has been found in the investigation of the interactions in which there is a large momentum transfer. This situation has prompted us to look for other detailed tests of the theory. We study the order αs measurement of the MS parton decay functions, which play an important role in the application of high order perturbative QCD calculations. We calculate the hard scattering cross section for e+ + e- → parton + anything. Then, by carefully analyzing the electron positron annihilation data, we obtain the order αs MS quark decay function. We also study the gluon bremsstrahlung effects predicted by QCD in a semi-inclusive process at the future HERA electron proton collider, p + e- → h + e- + X. In analogy to studies of Drell-Yan process we study the transverse momentum distribution and angular distribution of the final state hadrons, which are sensitive to the gluon bremsstrahlung effects. Then we investigate the general structure of the hadronic tensor, which appears in the formula for the cross section, including both the parity conserving and parity violating terms. Using the soft gluon resummation technique, the singular and the nonsingular structure functions are all calculated for the process p + e- → γ → h + e- + X