Resummation In Quantum Chromodynamics

Saturation physics deals with the high energy QCD theory which can describe the dense partons,in particular,the gluons inside hadrons.We usually encounter soft or collinear gluon radiation when treating some QCD processes.It has long been known that the emission of soft and collinear gluons causes large corrections in perturbation theory,limiting its range of applicability.Calculations beyond the NLO can be important also in processes which involve large logaritms when different significant scales appear.This is,for example,often the case at LHC where the Higgs boson product.ion has to be distinguished from the background.A computation beyond t,he NLO is needed when the NLO corrections are large and higher-order calculation permit,us to test the convergence of the perturbative expansion.Therefore the NLO pQCD computation turns out not to be enough and we have to perform all order soft gluon resummation to make reliable prediction.In chapter one,as we all known that the history of physics is nothing but the biography of great physicists.Firstly,we review the history from QED to QCD.Including the gauge invariance,Lagrangian of QCD and how to construct it.And a remarkable property of QCD,known as asymptotic freedom,is also shown.Then we give a brief review of light cone perturbation theory and deep inelastic scattering.Saturation physics will be shown in the end.The production of large-transverse-momentum photons has been recognized as excellent processes for studying the dynamics of hard-scattering processes.The advantages of studying such direct photons are both numerous and well known.Firstly,the process is rather simple.At leading order only two subprocesses con-tribute:gq??q and qq??g.Experimentally,photons are easier to reconstruct in a detector than jets.Theoretically,the photon's coupling makes it much easier to perform next-to-leading-order calculations which are necessary for precise tests of QCD.Finally the dominance of the gq??q subprocess in kinematical regions is useful for determining the gluon distribution within the proton.In chapter two,through one-loop calculation,Sudakov type logarithms we utilized when the pro-duced isolated-photon and jet are almost back-to-back.A method for calculating the production of direct photons plus a jet up to NLO accuracy has also been applied,utilizing a combination of perturbative QCD and Sudakov resuammation formalism.The method is described and examples are given,including comparison with experi-mental data for the photon-plus-jet azimuthal angular correlation and the transverse momentum imbalance.We also calculated the enhancement of the momentum im-balance distribution for AA as compared to pp collisions and make predictions for the future unfolded experimental data by introducing energy-loss into the system.Furthermore we distinguish quark jets from gluon jets in order to extract the jet transport coefficient more precisely.Higgs boson discovery at the CERN LHC has stimulated new area of high energy physics research at the colliders,where the precision Higgs physics is at the frontier.This includes Higgs production and decays to investigate the coupling between the Higgs boson and other fundamental particles.Threshold logarithms become domi-nant in partonic cross sections when the selected final state forces gluon radiation to be soft or collinear.This leads to the resummation of threshold logarithms.In Chapter three,we study the resummation of large corrections to the partonic cross sections relevant for the process p+A?H +X.These corrections arise near the threshold for the partonic reaction and are associated with soft-gluon emission.We perform the resummation to next-to-leading logarithmic accuracy.Using the Higgs production in forward rapidity region in pA collisions as an example,we construct a systematic formalism for the threshold resummation for forward rapidity particle productions in saturation formalism.And we find that distribution function satisfies the corresponding renormalization group equation.Through solving these kind of equations we can resumme the contribution of soft gluon emission automatically.In chapter four,employing the framework we developed before,we also study the threshold resummation to NLO QCD corrections for the process p+A?h+X when the single hadron is produced at high transverse momentum in the forward rapidity region.The aim is to solve the issue of the large negative next-to-leading cross section for single inclusive hadron production in pA collision in the saturation formalism.The resummation of the soft-gluon contributions is carried out in Mellin-N moment space,where the convolutions between parton distributions,fragmentation functions,and subprocess cross sections factorize into ordinary products.They both satisfy the corresponding RGE.The solution of RGE automatically contains the corresponding resummation.Only the theoretical calculation is done here,and the numerical calculation needs to be completed in the future.In the end,we have a conclusion and provide a outlook.