Comparison of analytical and parton-shower approaches to soft-gluon resummation at NLL accuracy

This thesis presents a systematic study of the differences between analytic soft gluon resummation at next-to-leading logarithmic accuracy and parton shower algorithms. First, the necessary formalisms are briefly reviewed. A Markovian Monte-Carlo algo- rithm for resummation of additive three-jet observables in electron-positron annihilation to hadrons is constructed and tuned to exactly reproduce the analytic calculation in the CAESAR formalism. The correctness is verified by comparison to analytic results and by explicit investigation of the infrared limit. Three observables, thrust, a BKS observable and a fractional energy correlation, are considered as specific examples. Approximations intrinsic to resummation are then removed, in order to obtain a tradi- tional, momentum and probability conserving parton shower. The impact of each of the different approximations is studied, and an overall comparison is made between parton shower and pure resummation of leading and next-to-leading logarithms. Finally, differences in comparison to modern parton shower algorithms formulated in terms of color dipoles are analysed.