UC Berkeley

Matrix-element calculations and parton shower programs are both crucial tools in the analysis of data at modern particle physics experiments at colliders. Finding the most effective ways to combine these complementary, but sometimes conflicting, approaches to simulating physical events has been the subject of much work in the recent decade. This thesis investigates state-of-the-art ways in which the precision of the matrix elements can be extended in combination with the parton shower. We identify three dimensions along which precision can be improved and describe how progress can be made along each one.

First, we present a general method to match fully differential next-to-next-to-leading-order (NNLO) calculations to parton shower (PS) programs, which represents an extension of the successful LO+PS (leading order) and NLO+PS (next-to-leading order) frameworks to NNLO+PS. We discuss in detail the perturbative accuracy criteria a complete NNLO+PS matching has to satisfy, and we give an explicit and general construction of the input "Monte Carlo cross sections" satisfying all required criteria.

Next, we describe how augmenting an NLO calculation with higher-order resummation of large Sudakov logarithms allows one to extend the lowest-order matching of tree-level matrix elements with parton showers to give a complete description at the next higher perturbative accuracy in α_s, at both small and large jet resolutions. As a byproduct, this combination naturally leads to a smooth connection of the NLO calculations for different jet multiplicities. We focus on the general construction of our method and present results of an implementation in the GENEVA Monte Carlo framework. For leptonic collisions, we apply our construction to e⁺e^- → jets and obtain good agreement with LEP data for a variety of 2-jet observables. For hadronic collisions, we look at Drell-Yan production.