Soft Gluon Exponentiation and Resummation

TL;DR

This thesis introduces a simplified method for calculating higher-order soft gluon effects in QCD, including uncalculated three-loop coefficients, and explores energy flow patterns in jet events to improve understanding of soft radiation.

Contribution

Develops a new simplified approach to compute higher-order singular coefficients in soft gluon resummation using eikonal lines, and analyzes energy flow correlations in jet events.

Findings

Calculated the fermionic contribution to the three-loop coefficient A^(3).

Derived analytical and numerical results for shape/flow correlations at next-to-leading logarithmic order.

Applied formalism to initial state hadron events with color exchange matrices.

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.