Heavy Quark-Pair Production in Electron Positron Collisions at Next-to-Next-to-Leading Order QCD

Abstract

Standard Model high-precision computations of observables relatedto heavy quark physics are very important, both for testing the consistency of Standard Model and for providing a precision tool for data analysis in the context of searches for new physics. The calculation of differential cross sections and (exclusive) observables at higher order perturbation theory in Quantum Chromodynamics (QCD) requires a method for handling the soft and collinear singular configurations that arise from the radiation of massless partons and appear in individual contributions.In this thesis, we present a set-up, within the antenna subtraction framework, for computing the production of a massive quark-antiquark pair in electron positron collisions at next-to-next-to-leading order in the coupling $\alpha_s$ of QCD at the differential level. Our set-up applies to the calculation of any infrared-safe observable.We apply this formalism to the production of top-quark pair $(\ttbar)$ production in the continuum and also to bottom-pair $(\bbbar)$ production at the Z resonance. We compute the respective production cross sections and several distributions. We determine, in particular, the forward-backward asymmetries $A_{\rm FB}^Q$of these heavy quarks at order $\alpha_s^2$, which are important observables for electroweak precision tests and for determining the neutral-current couplingsof these quarks. The order $\as^2$ corrections turn out to be significant.In the top quark case we compute $A_{\rm FB}^t$ for several center-of-mass energies above the $\ttbar$ production threshold. For $\bbbar$ production at the $Z$ peak, we compute $A_{\rm FB}^b$ both for the $b$-quark axis and the oriented thrust axis definition of the asymmetry. We find thatif one takes into account the complete massive order $\as^2$ corrections to the leading-order asymmetry, which is a new result, then the magnitude of the QCD correctionsincreases slightly compared to previously known results.This reduces the well-known tension between the experimentally determinedbare $b$-quark asymmetry and the value obtained by a global fit from $2.5\sigma$ to $2.2\sigma$.