Stopping Distance for High Energy Jets in Weakly-Coupled Quark-Gluon Plasmas

Quark-gluon plasmas (QGPs) are hot dense media created in relativistic heavy ion collisions, and jet quenching makes it possible to study the properties of QGP medium, through observing changes in the jet fragmentation functions as compared to the unquenched case. Therefore, it has long been of interest to study the jet energy loss and stopping processes in relativistic QCD media. In weakly-coupled quark-gluon plasmas, a high energy parton's energy loss is dominated by medium induced gluon bremsstrahlung and pair production. However, the calculation of gluon bremsstrahlung is complicated by the Landau-PomeranchukMigdal (LPM) effect, in which the gluon formation time becomes longer than the mean free path between scatterings and successive scattering cannot be treated as independent. Arnold, Moore, and Yaffe (AMY) proposed a formalism to solve the LPM effect in uniform, infinite QCD mediums. In this thesis, gluon emission rates in the AMY formalism are reviewed, and the transport coefficient ˆq, which characterizes the scattering power of the medium, is calculated to the leading order in the weak coupling limit, and then is used to generalize the previous analytic results on the gluon bremsstrahlung and pair production rates at next-to-leading logarithmic order in weakly-coupled QGP. Stopping distance is a moregeneral idea, forunlike thebremsstrahlung rate, it can begeneralizedtostrongly-coupledsituations, inwhichwecannottalkaboutindividual ii partons. Inthisthesis, stoppingdistancesaredefined, andbyusingthegluonemission rates studied earlier, the analytic expressions for high energy jet's stopping distance is calculated in weak coupling, we will see that the stopping distance has a E 1/2 / √ lnE dependence on the initial parton's energy E in the high energy limit.

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