| Nucleon structure is an important topic of modern physics. With the boost from theory and experiments, for the last 30 years the research on nucleon structure have made great progress, evolving from the leading twist parton distribution functions to higher twist parton correlation functions (givingΛ/Q power suppressed contributions), from transverse-momentum-integrated one dimensional parton distribution/correlation functions q(x) to transverse-momentum-dependent three dimensional parton distribu-tion/correlation functions q(x, k⊥). High energy deep inelastic lepton-nucleon scatter-ing(DIS) is an important tool of research on nucleon structure, and the semi-inclusive DIS process with one final state jet(hadron) observed probe more information on nu-cleon structure. The azimuthal asymmetries of final state particles in SIDIS process are one important kind of observables, and measurements of azimuthal asymmetries are important goals of large international experimental collaborations such as HERMES, COMPASS, JLab. In intermediate and small transverse momentum region, higher twist contributions to azimuthal asymmetries are not negligible, and it is important to calcu-late higher twist contributions with systematic methods.The standard method of calculating higher twist contributions is collnear expan-sion technique developed by Ellis, Furmanski, Petronzio, Jian-Wei Qiu and Sterman et.al. The procedures of collinear expansion technique are as follows:first, perform a Taylor expansion of the parton hard scattering process over parton momentum near their collinear to the nucleon momentum direction k=xp, in the mean time decom-pose the gluon field into a collinear component and non-collinear components; second, employ Ward identities to relate parton scattering matrices of different orders to each other; third, add all terms together and recombine them, then we obtain many gauge invariant parton correlation matrices; finally, expand parton correlation matrices withγ-matrices, take trace and simplify the final results with QCD equation of motion. With above collinear expansion technique they obtained the twist-4 contributions to deep inelastic scattering process. Members of our group, Zuo-tang Liang and Xin-Nian Wang, extended the previous collinear expansion technique to semi-inclusive DIS process eN→eqX. They found that, if the jet production process which is simpler with respect to hadron production is considered, the only difference between semi-inclusive DIS and inclusive DIS is that the former contains an extra kinematic factorδ2(k⊥'-k⊥), which will not affect the application of the collinear expansion technique, while this kinematic factor will render the extracted parton distribution/correlation func-tions transverse-momentum-dependent. With this discovery, they obtained twist-3 con-tributions to the cross section and (cos 0) azimuthal asymmetry with unpolarized lepton and transversely polarized nucleon.The first work of current thesis is to calculate the cross section and azimuthal asym-metries of the process eN eN→eqX with lepton and nucleon taking any polarization combinations, and furthur extend collinear expansion to unpolarized semi-inclusive DIS process eN→eqX at twist-4 level, obtaining the cross section and (cos 20) azimuthal asymmetry. The result indicates that (cos 20) azimuthal asymmetry is propotional to the ratio of higher twist parton correaltion functions to leading twist parton distribu-tion functions, both of which are gauge invariant physical quantities. Measurement of the azimuthal asymmetries (cos 0) and (cos 20) of jet production is an effective way of studying higher twist parton correlation functions.Studing the nuclear dependence of azimuthal asymmetries is another work of cur-rent thesis. In recent years our group members proposed a model which describes the effects of nuclear environment on parton distribution functions. The model states that gluon lines that produce gauge link can connect to different nucleons in a large nucleus, thus the gauge link contains the information of nucleon distribution in a large nucleus. Under "Maximal Two-Gluon Correlation Apprximation" they find a simple gaussian kT broadening, while furthur analysis showed that it generate a clear nuclear suppression effect on (cos 0) azimuthal asymmetry. Current thesis also employ this model to study even higher order azimuthal asymmetries, and find that (cos 20) azimuthal asymmetry show a stronger nuclear suppression effect. The final physical conclusion is:nuclear environment have such an effect on the parton transverse momentum distribution that it makes it more fat (transverse momentum broadening effect) and more round (suppres-sion effect of azimuthal asymmetries).Developing the method to extract the parameterization form of higher twist parton correlation functions from experimental data, is the third work of current thesis. Higher twist parton correlation functions, like leading twist parton distribution functions, are physical quantities decided by non-perturbative QCD dynamics, whose analytical forms are not currently obtainable from ab initio calculations. The only way to them is to extract their parameterization from experimental data. Current thesis review the exper-iments on azimuthal asymmetries in SIDIS and how the theorist deal with higher twist contributions to azimuthal asymmetries, and stress that parameterization of higher twist correlation functions is also very important to the extraction of Boer-Mulders functions. The thesis just take contributions from higher twist parton correaltion functions into account, and convulute them with leading twist fragmentation functions. The author independently developed Fortran code employing differential evolution algorithm, and give a fast way of obtaining uncertainties of parameters according to the charactoristics of differential evolution. With data from ZEUS and EMC collaborations, current the-sis perform an preliminary fit to the parameterization form of higher twist correlation functions. The results are of some reference value.
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