A Study Of Spin-dependent Fragmentation Functions In High Energy E~+e~-Annihilation Process

Parton distribution functions(PDFs)and fragmentation functions(FFs)are two important quantities in describing the high energy reactions.Both of them are long dis-tance non-perturbative quantities which cannot be calculated with perturbative theory,they are mainly calculated by phenomenological models and parametrized by experi-ment data.When three-dimensional,i.e.,the transverse momentum dependent(TMD)PDFs and FFs are considered,the sensitive quantities studied in experiments are of-ten different azimuthal asymmetries.Measuring these azimuthal asymmetries,we can extract the TMD PDFs and FFs.Because the parton transverse momentum is one of the origins of higher twist contributions,to study the TMD PDFs and FFs one should consider the higher twist contributions at the same time.The higher twist calculations benefit very much from the collinear expansion.It provides not only the correct formal-ism where the differential cross sections or the hadronic tensors are given in terms of gauge invariant PDFs and FFs but also very simplified expressions so that even twist-4 contributions can be calculated.The collinear expansion has been first introduced in inclusive deeply inelastic scattering(DIS)process.It has been shown that it can also be applied to the semi-inclusive DIS process and recently also to inclusive and semi-inclusive electron positron annihilation(EPA)processes.Comparing to the semi-inclusive DIS process(l+ p T l'+ h + X)and the proton proton collision process(p+p ? ?+X)y without the effects of the initial hadron(s),EPA process(e++e-?h(+jet/h)+ X)is regarded as the best place to study the FFs.In the inclusive EPA process(e+ + e-? h+X),without the definition of the transverse direction,one cannot calculate the azimuthal asymmetries which originate from the parton transverse momentum.In other words,only 1-dimensional FFs can be studied in inclusive EPA process.However,in semi-inclusive EPA process(e++e-?h+jet+X)the transverse direction can be defined by the jet transverse momentum,in this case the azimuthal asymmetries can be studied,so as the 3-dimensional FFs.As we know the transverse momenta are not only the origin of the azimuthal asymmetries but also one of the origin of the higher twist contributions.To study the transverse momentum dependent FFs,one has to study the higher twist contributions at the same time.The higher twist contributions includes two aspects,one is that higher twists contribute to the unique azimuthal asymmetries,the other is that higher twist contributions can be seen as the corrections to the leading twist contributions.If the weak interaction is taken into consideration in the annihilation process,one finds that the quarks produced in the EPA process are naturally polarized.Because in standard model,the lefted-handed and right-handed fermions belongs to the different symmetry groups,they have different quantum numbers,the interactions with Z0 are also different,so quarks are meant to be polarized.In high energy EPA process,we "believe" that the quark polarization can be transferred to the hadrons and makes the hadrons polarized,which provides us opportunities to study the spin-dependent FFs.In this dissertation,we calculate the complete twist-4 results with collinear expan-sion in EPA process.To study the(transverse momentum dependent)FFs we calculate the structure functions,hadron polarizations and azimuthal asymmetries.We first cal-culate them in the inclusive process and then extend to the semi-inclusive process.We also present the phenomenological studies in this dissertation.The main topics in this dissertation are as follows.1,we present a complete set of kinematics analysis methods for studying high en-ergy reaction.This method can be applied into the one hadron involved process as well as the two hadrons involved process.In this dissertation we apply it into both the inclu-sive and semi-inclusive EPA processes and calculate the complete structure functions in both of them.We obtain 19 structure functions in the inclusive annihilation process in which 6 structure functions have leading twist contributions,8 structure functions have twist-3 contributions and 5 structure functions have twist-4 contributions.Simi-larly we have 81 structure functions in semi-inclusive annihilation process in which 18 structure functions have leading twist contributions,36 structure functions have twist-3 contributions and 27 structure functions have twist-4 contributions.2,for the first time we calculate the EPA process at the twist-4 level.Not only the quark-gluon-gluon-quark correlation functions,but also the 4-quark correlation func-tions should be taken into consideration at twist-4 level.After calculation we find that the contributions from the 4-quark correlation functions have the same forms at ones from the quark-gluon-gluon-quark correlation functions.We should sum them over to obtain the complete results at twist-4 level.3,in the inclusive EPA process we calculate the hadron polarizations,including<<STx,y>>,<<STx,y>>and<<STTxx,xy>>.We find that<<STx,y>>and<?STx,y>>only have twist-3 contributions while<<STTxx,xy>>only have twist-4 contributions.We calculate the az-imuthal asymmetries in semi-inclusive annihilation process as well as the hadron po-larizations.We find that<cos?>U and<sin?>U only have twist-3 contributions while(cos 2?)U and(sin 2?)U only have twist-4 contributions.For the longitudinal polariza-tions<<?h>>and<<SLL>>,they have both the leading twist and twist-4 contributions.In hadron-jet frame,the transverse polarizations<<STn,t>>,<<SLTn,t>>and<<STTnn,nt>>al-so have both the leading twist and twist-4 contributions.In the lepton-hadron frame,<<STx,y>>and<<STx,y>>only have twist-3 contributions while<<STTxx,xy>>only have twist-4 contributions.4,we present a new method to estimate the twist-4 contributions.In this method we neglect the multi-gluon scattering contributions and only take the parton transverse momentum contributions into consideration in higher twist calculations.After calcula-tions,we relate the twist-4 FFs to the leading twist FFs and then simplify the twist-4 correction factors.We find that the twist-4 contributions are significant.5,we also present a simple model to calculate the unpolarized FF.We also cal-culate the energy-dependence of the hadron polarizations,and find those polarizations which depend on the quark polarization have a strong energy-dependence while those polarizations which do not depend on the quark polarization are less sensitive to the energy.