The HTL Resummation In The Light Cone Gauge And The Evolution Equation Of The Medium Modified Parton Fragmentation Functions

In the modem physical theory,within millionths of a second of the birth of the universe,there was one matter which is called Quark-Gluon plasma.Scientists hope to solve the puzzle of the universe formation with mini-universe bang,i.e.heavy ion collision.Experimentally,two nuclei are accelerated to collide with light velocity,and that gives rise to the high temperature environment.The temperature was 100 thousand times of the temperature of the star core,which was in millionths of a second.after the big bang thirteen point seven billion years ago.Study the expansion and freeze process of the QGP,and observe it how to form the particles,which make up the matter in the universe.Due to deconfinement phase transition in the heavy ion collisions,the QGP generated in the heavy ion collision has free and energetic quark and gluon,i.e.partons.The partons scatters with the medium several times,they radiate gluon until escaping the the hot and dense medium,and finally fragment in the vacuum.By jet reconstruction,understand the interaction mechanism between jet and medium.Recently there was several mechanisms to escribe the the energy loss of the parton in the medium,such as HT,GLV,AMY and BDMPS.Jet quenching describes the the energy loss of the generated parton in the heavy in collision escaping the QGP,including the collision energy loss and radiation energy loss.Experimentally,compared to that in proton-proton collisions,there is a large suppression of the single inclusive hadron yield at high transverse momentum.In order to quantify such nuclear modification effect,people define the nuclear modification factor RAA.Jet quenching is a good probe to study the property of the QGP.For the light quark,radiation energy loss is dominant,and the collision energy loss is secondary but can not be ignored.For heavy quark,in the low energy and intermediate energy,collision energy loss is dominant.But in the high energy,the radiation energy loss is dominant.Thanks to the asymptotic freedom of QCD,many high-energy scattering processes can be analyzed using perturbation theory.In most case such analyses are in the form of factorization theorem,which separate the perturbatively calculable part of the cross section from the non-perturbative part.If specific particles are identified in the final state,parton fragmentation func-tion(FFs)appear frequently as non-perturbatively ingredient of QCD factorization formulas..Generally,FFs describe how the color-carrying quarks and gluons transform into color-neutral particles such hadrons or photons.Comparing the FFs in the heavy ion collision to the FFs in vacuum,people can quantify interaction of the parton and the medium,and the energy loss of the parton through the medium.FFs is non-perturbatively physical quantity,and can only be extracted by experiment.Scientists extract the information of the parton fragmentation function in the vacuum via sibgle inclusive annihilation,deep inelastic scattering,proton-proton collision.Inversely,the jet influence the hot and dense medium.Recently,simulate the evolution of the medium with Boltzmann equation and the model of the jet plus fluid.In this thesis,we derive the HTL resummed gluon propagator in the light cone gauge,and then calculate the longitudinal and transverse part of the gluon HTL self energy.We get the same dispersion relation of the boson in the Coulomb gauge and the light cone gauge.Although the expression of tensor of the HTL resumed propagators in the two gauges are different,the same result of the hard quark and gluon can be given in the two different gauge,which prove that the HTL resummed gluon propagator in the light cone gauge is gauge independent.In the second part,we introduce the fragmentation function.Due to the hard process,we use the bare propagator in the light cone gauge to calculate the leading order contribution which has the infrared divergence and collinear divergence.The infrared divergence can be cancelled by the virtual correction.the coll inear divergence is absorbed by redefining the fragmentation,the fragmentation function become the scale Q dependent.By summing all the contribution of the radiation and annihilation we get the evolution equation of the fragmentation function.Above are the correction of the hard process for the medium modified parton fragmentation function.With the HTL resummed propagators in the light cone gauge,we calculate the medium modified fragmentation function with soft process.Compared with the multiple incoherent s-cattering,in the multiple coherent scattering the LPM effect suppresses the gluon radiation rate.The LPM effect is positively related to the length of the medium which the partons go through.Due to the correction from the soft process and the LPM effect,we get the evolution equation of the medium modified parton fragmentation function.