A Study Of Fragmentations Functions In Electron Positron Annihilation At High Energies

As is well known, fragmentation functions (FFs) and parton distribution functions (PDFs) are the two impor-tant quantities in the description of high energy reactions and in studying the properties of non-perturbative QCD.Recently, people are now very interested in the three dimensional information of hadron structure, i.e., the transverse momentum dependent (TMD) PDFs, since it contains much more interesting physics comparing with the one-dimensional PDFs. Fragmentation functions are more complicated than PDFs and hence are more interesting. During my research on this Ph.D. thesis, I concentrated on the fragmentation functions. Since there is no hadron involved in the initial state, electron positron annihilation is most suitable to study fragmentation functions among all different high energy reactions.Higher twist terms may have very important contributions to azimuthal asymmetries and spin asymmetries, which are usually measured in experiments to study the properties of fragmentation functions and parton dis-tribution functions. By applying collinear expansion to both inclusive and semi-inclusive electron positron annihilation processes, we have constructed a framework to systematically calculate the leading twist and higher twist contributions for hadrons with different spins at leading order pQCD. With this framework, we have made a complete calculation for the azimuthal asymmetries and polarizations of hadrons in terms of corresponding fragmentation functions, defined from quark-gluon correlation functions.1. We started our research from the inclusive e+e- annihilation process, e+e- �' h+X. With the framework mentioned above, we calculated the cross sections for hadrons with different spins up to twist-3. We found that there are many interesting features.(I) For spin-1/2 hadrons, there exist two twist-3 transverse polarizations, besides the leading twist lon-gitudinal polarization. One of the transverse-polarization-dependent fragmentation functions, DT(z), is very interesting. It is a T-odd fragmentation function. Unlike the parton distribution functions, gauge link is not the only source of T-odd effects. Hence, in one dimensional case, such T-odd frag-mentation functions are not forbidden by time reversal invariance. This T-odd fragmentation function also contributes in electromagnetic process, e++e- �' γ* �' h+X. Hence we can also extract its information from low energy electron positron experiments.(II) For spin-1 hadrons, there is a spin alignment (ρoo≠ 1/3) for spin-1 hadrons at leading twist. This has been confirmed by LEP experiments. The spin alignment does not dependent on the polarization of initial quark or antiquark. This means that the vector mesons are tensor polarized in both weak and electromagnetic processes. Hence, we predict that this tensor polarization can also be measured in low energy electron positron annihilation experiments, such as BES. 2. As a second step, we applied collinear expansion to the semi-inclusive e+e- annihilation process, e+e- �' h+q+X. Similarly, we used the same gauge invariant formulism to calculate the leading twist and twist-3 contributions. We found that there are two azimuthal asymmetries at twist-3 for spin-0 hadrons. We also calcu-lated the longitudinal polarization and two transverse polarizations for spin-1/2 hadrons and all five tensor polarizations for spin-1 hadrons up to twist-3. These polarization parameters correspond to different fragmentation functions. The most suitable directions to study the transverse polarizations and the corresponding fragmentation functions are that in and perpendicular to the hadron production plane. Our work provides a foundation to study the fragmentation functions from electron positron experiments.Our research provides a basis to study the fragmentation functions in electron positron experiments. For ex-ample, the spin-alignment-related fragmentation function, D1LL(z), can be parameterized by measuring the spin alignment of vector mesons. The data from LEP experiment provide us some hints on the z-dependence. However, the data are still far from enough to limit its precise form. There is almost no parameterization for the TMD fragmentation functions even at leading twist.We should mention here, the collinear expansion can only be applied to the light quark case (u, d, s). How to calculate the leading and higher twist contributions from heavy quark production and annihilation processes is still waiting to be studied.