| The standard model of particle physics(SM)has been tested by various experiments,but there are also many physical problems within the SM need to be solved or further investigated.Es-pecially the study of quantum chromodynamics(QCD)which describes the strong interaction,is one of the frontiers of particle physics.In describing hadron involved high energy reactions,people use perturbative QCD(pQCD)to successfully calculate the hard scattering processes with large momenta trausfer,i.e.,the parton(quarks and gluons)level reactions.Howe.ve.r,how to handle the soft process such as hadron structure or parton hadronization etc.,is hitherto an unsolved problem.Parton distribution functions(PDFs)and fragmentation functions(FFs)are the physical quantities that describe hadron structure and hadronization process respectively.They are not only the important inputs for high energy reactions,but also the basis for doing many other new physics researches.They have prominent positions in current researches on particle physics.The concept of PDFs was first introduced by Feynman et al.PDFs describe the parton momenta distribution in a fast moving hadron.High energy lepton-nucleon scattering(DIS)is one of the major experimental method for studying PDFs.After many years of experimental and theoretical investigation,our knowledge about PDFs has transformed from the intuitive definition to the gauge invariant quantum field theoretical definition,from the unpolarized case to polarization dependent cases,also from one dimensional description to three dimensional(3D)description which involves transverse momentum dependence(TMD).Very similar to PDFs,FFs describe the momenta distribution of the final state hadrons from partons,so they must be studied in parallel with PDFs.However,due to the lack of enough experimental data,the study of FFs is not as detailed as PDFs,so it’s even more necessary to carry out the studies on FFs.In this context,we take the electron positron annihilation process,the best place to access FFs,as the main line of this thesis to give a systematic study of the TMD FFs in high energy reactions.First,after giving the intuitive definition of PDFs and FFs in high energy reactions,we start from the quantum field theory description,and by applying the collinear expansion technique,get the gauge invariant definition of FFs using quantum field operators,i.e.,the definition via the decomposition of parton correlators.From the definition of parton correlators,we,for the first time,make a complete Lorentz structure decomposition of quark-quark correlator for spin-1 hadron production.Through the decomposition,in total 72 TMD FFs are defined,among them,eight are unpolarized,24 are vector polarized,and 40 are tensor polarized FFs.We give some discussions on the properties of these FFs under time reversal.In addition,we also give a complete decomposition of the twist-3 TMD FFs from quark-gluon-quark correlator.By applying the QCD equation of motion,we get a unified relation between these FFs with those defined from quark-quark correlator.Second,among different high energy reactions,electron positron annihilation to vector and pseudo-scalar meson production(e＋e-→Z → VπX)is the simplest process to access these 3D FFs.We first carry out a general kinematic analysis of this process,i.e.,under the constraints of Hermiticity and current conservation,we construct the complete results of the basic Lorentz tensors for decomposing the hadronic tensor,and give the most general expression of the cross section in terms of structure functions.Based on this,we give the the results of some physical observables including hadron azimuthal asymmetries and polarizations,they are all expressed in terms of the structure functions.it’s usually very difficult to measure hadron azimuthal asym-metries and polarizations simultaneously,so,for hadron azimuthal asymmetries,we consider the case of summing over the polarizations or unpolarized hadron production,then there exist in total four asymmetries,i.e.,<cosφ>,<sinφ>,<cos2φ>and<sin2φ>;for hadron polarizations,we consider the results averaged over the azimuthal angle,it is shown that two longitudinal polar-izations and six transverse polarizations with respect to the lepton-hadron plane exist.These above results are all from general kinematic analysis and model independent,they are the basis for the further study of FFs in the reaction.The third,in the framework of QCD parton model,the above structure functions can all be expressed by the convolution of the FFs.Another work of this thesis is the calculation of e＋e-→VπX using parton model.In the framework of leading order perturbative QCD,we carry out the calculation of this process up to twist-3 level by considering the contributions from the quark-quark correlator and the quark-gluon-quark correlator,and get the cross section results in terms of the FFs.By comparing the cross section results in terms of the structure functions,we get the corresponding parton model results of the structure functions in terms of the convolution of the FFs.The calculation results show that,there are 27 structure functions contribute to leading twist level,among them,19 are parity conserved and the other 8 are parity violated.The number of structure functions which has twist-3 as the leading contribution is 36.For hadron azimuthal asymmetries,in the unpolarized case,there is only one<cos2φ)azimuthal asymmetry.It comes from the transverse polarization correlation of the quark and antiquark produced in the reaction,and the Collins effect in the fragmentation process.For the azimuthal asymmetries at twist-3,there is a parity conserved(cosφ)azimuthal asymmetry,and a parity violated(sinφ)azimuthal asymmetry.For hadron polarizations,at leading twist,there exist two longitudinal polarization components,i.e.,<λ>and(SLL).And they have very obvious differences,the former depends on the quark polarization and is parity violated,while the latter is independent of the quark polarization and is parity conserved,which means that it can also exist in the electromagnetic reaction process.For the transverse polarizations,at leading twist there are six polarizations with respect to the hadron-hadron plane,i.e.,<STn),(STt),<STt>,<SLTn>,<STTnn)and<SttNT>.At twist-3 level,there are also six transverse polarizations with respect to the lepton-hadron plane.These above physical observables results are all expressed by the convolution of the different components of the gauge invariant 3D FFs.Finally,in the parton model calculation,we found hadron polarizations at leading twist can be divided into two categories:one depends on the polarization of the fragmenting quark,and is parity violated;another one is independent of the quark polarization,and is parity conserved.Due to the polarization of the quark produced in electro-weak interaction has very strong energy dependence,we expect that,the above two kinds of hadron polarizations will have very different energy dependences.Inspired by this physical image,in the last part of this thesis,we carry out a numerical analysis on The hadron polarizations in the inclusive reaction process e+e-→λ*/Z→hX.We take the A hyperon longitudinal polarization PLA and K*vector meson spin alignmentρ00K as examples,and calculate their energy dependence.The former depends on the polarized fragmentation function G1L(z,Q2)and quark polarization Pq,while the latter is independeat of the quark polarization and depends on the tensor polarized fragmentation function DILL(2,Q2).We use the experimental data on LEP to make a parameterization of the polarized fragmentation functions,and also consider the QCD evolution of the fragmentation functions.The final results show clearly that,PLA has a very strong energy dependence,because the quark polarization has a strong energy dependence;while the energy dependence of ρ00K*is rather weak,and it’s energy dependence mainly comes from the QCD evolution of the fragmentation functions.We make a prediction that at the low energy electron positron annihilation experiments like BES or BELLE,the hyperon longitudinal polarization is negligible,while the spin alignment of the vector meson is still sizable.These studies will give us a better understanding of the spin effects in hadronization process and fragmentation functions. |
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