Gauge Link Derivation In Drell-yan Process

The study of nucleon internal structure is the frontier of current high-energy nuclear physics.Protons and neutrons are the basic units of our world,while the internal structure is of great significance.The main interaction within the nucleons is strong interaction,which could be described by quantum chromodynamics(QCD).Therefore,the study of nucleon structure also provides an ideal place for testing QCD,studying the strong interaction,and developing theoretical tools for QCD.As QCD is non-perturbative at low energy,it is extremely difficult to solve it.So,people cannot analytically calculate out the wave function of the internal part of the nucleon,while we get the wave function of the hydrogen atom by solving the Schrodinger equation in QED.Till now,there are two methods to study the internal structure of nucleons:one is using lattice QCD with numerical simulation;Another is to use the perturbation QCD factorization th eorem to combine the cross section with the parton distribution function(PDF)which could be extracted in the experiment.Due to its great physical significance,nucleon structure has been a hot frontier for many years in the field.It is the core goal of the US Jefferson National Laboratory,the European Nuclear Center's COMPASS and the electron-ion collider(EIC)(the next generation).At the same time,the high-energy polarized proton-proton collision on the RHIC of Brookhaven National Laboratory is mainly used to study the polarization structure of protons.In the framework of perturbative QCD factorization,the nucleon structure is described by the PDF.In the early parton model,the nucleon moving almost as the speed of light was approximately regarded as a bunch of parallel moving partons.The probability distribution of a parton with certain longitudinal momentum is given by the collinear PDF.But the PDF can only describe one-dimensional nucleon structure.With the development of theoretical and experimental research,people have further introduced the naive parton model,that is,the transverse momentum dependent parton distribution function(TMD)and the generalized parton distribution function(GPD),etc.The TMD describes the distribution of partons in the three-dimensional momentum space,while GPD describes the distribution of partons in the two-dimensional coordinate space and the one-dimensional longitudinal momentum space.This paper mainly studies the TMD.In the experiment,the TMD PDF would be extracted mainly through the electron deep inelastic scattering(DIS)process and Drell-Yan process.The theoretical basis for extracting TMD PDF through high-energy scattering experiments is the pQCD factorization theorem.Only under the premise of the factorization theorem,can we decompose the high-energy scattering cross section into the perturbable hard part and the universal soft part,that is,the TMD PDFs.Finally,the TMD PDF could be linked to the experimental observables.However,people recently discovered that TMD factorization fails during the production of double jets in proton-proton collisions.What's more serious is that due to the so-called color entanglement effect,even the TMD factorization is also not applicable.The key step in the proving of TMD factorization is to absorb the collinear gluon exchange between the parton and the rest of the target into the gauge link of the TMD PDF,so as to ensure its gauge invariance.Since the final state involves complex color flow in the process of di-jet production,the remaining parts from different nucleons will influence each other,resulting in the contributions cannot be absorbed into the gauge link of the TMD function,thus destroying the TMD factorization.That is the color entanglement effect,which is the special effect of non-Abelian field theory.Then,M.Buffing and P.J.Mulders analyzed all the gluon exchange diagram in the Drell-Yan process,and found that there is also a color entanglement effect in the Drell-Yan process.Since the Drell-Yan process is a relatively well-studied high-energy scattering process,the discovery really caused considerable confusion in the field.This paper re-analyzed all gluon exchange diagrams in the Drell-Yan process,and found that M.Buffing and PJ Mulder's analysis of three gluons vertex diagrams was incorrect.After correctly calculating the contribution of the Feynman diagrams,It is found that the color entanglement term cancels accurately.Therefore,it is confirmed that TMD factorization is still valid in the Drell-Yan process.The detailed derivation of this calculation is given in Chapter 3 of this thesis.The introduction briefly introduces the Standard Model and QCD.Chapter 2 introduces the parton model and the improvement of pQCD to this model,that is,the DGLAP scaling evolution;Then we introduce the deep inelastic scattering process and give the specific derivation process of the cross section of this process.The first section of Chapter 3 introduces the TMD PDF;The second section gives the derivation of the TMD PDF;The third section gives the derivation of the gauge link in the order of two gluons exchanges,where it is found that the color entanglement term canceled out by three gluons exchange.Chapter 4 summarizes the full thesis,and discusses the impact of the research and related expansions.