Soft Gluon Exponentiation and Resummation

TL;DR

The work develops a cohesive, field-theoretic framework for resumming large logarithms in semi-inclusive QCD processes by exploiting factorization into hard, jet, and soft (eikonal) components. It establishes nonabelian eikonal exponentiation to simplify higher-order soft radiation, and demonstrates explicit calculations of A-coefficients governing threshold and jet-related singularities using LCOPT. The thesis applies these tools to thrust and generalized dijet event shapes, deriving NLL (and partial NNLL) resummations, plus insights into power corrections and non-global logarithms. It further connects PDF renormalization and web exponentiation to high-precision predictions, enabling refined determinations of parton dynamics and strong coupling through jet observables, with extensions to hadronic initial states via color-space formalisms. Overall, it provides both methodological advances in resummation and concrete results for key observables in jet and energy flow physics.

Abstract

In calculations of (semi-) inclusive events within perturbative Quantum Chromodynamics, large logarithmic corrections arise from certain kinematic regions of interest which need to be resummed. When resumming soft gluon effects one encounters quantities built out of eikonal or Wilson lines (path ordered exponentials). In this thesis we develop a simplified method to calculate higher orders of the singular coefficients of parton distribution functions which is based on the exponentiation of cross sections built out of eikonal lines. As an illustration of the method we determine the previously uncalculated fermionic contribution to the three-loop coefficient A^(3). The knowledge of these coefficients is not only important for the study of the parton distribution functions themselves, but also for the resummation of large logarithmic effects due to soft radiation in a variety of cross sections. In the second part of this thesis we study the energy flow pattern of this soft radiation in jet events. We develop the concept of event shape-energy flow correlations that suppress radiation from unobserved "minijets" outside the region of interest and are sensitive primarily to radiation from the highest-energy jets. We give analytical and numerical results at next-to-leading logarithmic order for shape/flow correlations in e+e- dijet events. We conclude by illustrating the application of our formalism to events with hadrons in the initial state, where the shape/flow correlations can be described via matrices in the space of color exchanges.

Figures (38)

• Figure 1: Outline of the thesis. The boxes denote various intermediate stages in factorization and resummation procedures, the ovals describe the necessary tools. The items in the dashed boxes correspond to the sections of this thesis where corresponding descriptions and examples can be found.
• Figure 2: The electromagnetic form factor: a) 1-loop correction, b) graphical representation of the solutions to the Landau equations, Eqs. (\ref{['Landau']}), in Feynman gauge, c) general reduced diagram.
• Figure 3: a) Ward identity for a scalar polarized gluon. b) Identity for a single longitudinally polarized gluon attaching to an eikonal line. c) Resulting identity after iterative application of Figs. a) and b). Repeated gauge-group indices are summed over.
• Figure 4: Illustration of momentum flow for two jet-configurations: a) a final-state jet in $e^+e^-$ annihilation, b) a jet which radiates into initial and final states in the Drell-Yan process. The reduced diagrams in cut-diagram notation for the two processes are shown on the left, the jet-configurations which we study as examples are shown in the boxes. The vertical line (cut) represents the final state.
• Figure 5: Pole structure of configuration Fig. \ref{['Glaubfig']} b) in the complex plane, according to Eq. (\ref{['DYpole']}) for small and larger $k^+$. The scale is arbitrary.