Precision determination of the strong coupling constant

Abstract

In this thesis we study the event shapes variable thrust. Event shape variables are observables that characterize the shape of the distribution of the final state particles of a reaction. We take advantage of the formalism of Soft Collinear Effective Theory (SCET), an effective theory of the strong interactions appropriate for describing energetic jets. We give a factorization theorem for the process e+e- to hadrons, valid in the whole range of thrust values. This factorization theorem resums large logarithms at the N3LL accuracy and contains the full O(a) result for the fixed order cross section. In order to be able to describe the whole range of thrust values, we define the profile functions, which are thrust-dependent factorization scales which smoothly interpolate between regions where resummation of large logarithms is important and where it is not. To determine non perturbative effects, we fit renormalon-free nonperturbative matrix elements of operators defined in field theory, Q1. We perform a global analysis to all available thrust data in the tail region, where a two parameter fit to a,(mz) and the first power correction Q1 suffices. We find cr(mz) = 0.1135 i (0.0002)expt ± (0.0005)hadr ± (0.0009)pert, with X2 /dof(= 485) = 0.91, where the displayed 1-sigma errors are the total experimental error, the hadronization uncertainty, and the perturbative theory uncertainty, respectively. Furthermore, we perform a global analysis to all available data on the first moment of the thrust distribution. This analysis is a partially independent check of the tail fit, in fact it probes different regions of the thrust distribution and the analysis of experimental systematic uncertainties was conducted independently with respect to the data for the distribution. We find a,(mz) = 0.1141 i (0.0004)exp ± (0.0014)hadr ± (0.0007)pert with X2/dof(= 45) = 1.33. We also consider pp collisions, in particular the Drell-Yan process. Here we calculate analytically the beam thrust logarithms of the relevant beam functions and of the coefficient function at O(a2). This is a necessary ingredient for the calculation of the nonsingular terms in resummed predictions.