Fluctuations with small numbers: Developing the perturbative paradigm for jet physics in the QGP at RHIC and LHC

Many novel results have emerged from the experimental heavy ion program at the Relativistic Heavy Ion Collider. For some, these necessitate a new paradigm, a jump into the extra dimension of strongly coupled physics and AdS/CFT. This thesis takes the opposite view.;Asymptotic weakly coupled arguments are of course inapplicable. Purely parametric relations are not sufficient as the temperatures are not hot enough, the jet energies not high enough, the lengths not long enough. However, perturbative techniques provide a strong foundation on which to build our explanations of data from RHIC and the upcoming LHC. This thesis presents the first detailed study of both collisional and radiative energy losses, applied to both light and heavy partonic jets at RHIC and LHC. The primary motivation is the heavy quark puzzle, observed through the surprisingly strong quenching of high momentum single non-photonic electrons at RHIC.;Collisional energy loss is likely a non-negligible component of the energy loss of jets. It also provides a calculation in which to examine our assumptions about jet-medium interactions. For the quantities of interest, the soft interactions o, q << T are not dominant; the rarer, moderately hard collisions are more important. This impacts the choice of one collision calculation---a simple, first term in a hard thermal loop calculation does not include the necessary medium recoil kinematics---and of the multiple collision convolution---a simple, drag-diffusion scheme is insufficient for the short lengths of interest.;This also motivates an opacity expansion evaluation of the radiative energy loss. This expansion is equivalent to Schrodinger-like equations used in some radiative models, and provides a suitable method of numerical solution to that equation. Presented here is a Monte Carlo numerical integration that can give results to ninth order in opacity and beyond. The results confirm that, for the lengths of interest at RHIC and LHC, the first order is most important and orders beyond third have very little impact on R AA(pT).;These all provide important developments in the perturbative paradigm of jet quenching. While simultaneous explanations of both light and heavy jet results are not yet achieved, both are well within the range of these calculations. This gives strong hope that further developments in the theory and modeling will be able to fit jet results at RHIC and LHC. And then we can move into the era of quantitative jet tomography.