Asymptoticity of QCD and massive, oriented event-shapes

TL;DR

This thesis advances the understanding of perturbative QCD by analyzing large-order behavior, renormalons, and non-perturbative corrections, while also computing event-shape distributions including quark mass effects at NLO.

Contribution

It introduces a formalism for large-$eta_0$ QCD series and applies it to various schemes and functions, alongside new NLO calculations of event-shape distributions with quark mass effects.

Findings

Development of a formalism for large-$eta_0$ QCD series

Calculation of $e^+e^-$ event-shape distributions at NLO with quark mass effects

Analysis of the FOPT-CIPT difference in tau decays

Abstract

This is a doctoral thesis dissertation developed in the frame of theoretical QCD predictions, with focus on two main topics. On the one hand, the large-order bahavior of perturbative QCD series is discussed. By reviewing the main literature, a cohesive discussion is made that includes the topics of large-order divergencies in QCD, renormalons, summation methods for asymptotic series and non-perturbative power corrections. A formalism for perturbative QCD series in the large-$\beta_0$ is presented, which allows for (1) the computation of the series, its renormalization factor and anomalous dimension, (2) the sum of all these quantities, (3) the study of the renormalon structure of the series and (4), the ambiguity in the sum due to IR renormalons, which is associated with the size of non-power corrections. Original and published work has been made to develop this formalism for both series without and with cusp-anomalous dimension. A large number of applications of our formalism are also presented, covering the short-distance mass schemes $\bar{\rm MS}$ and MSR, the QCD-to-SCET and SCET-to-bHQET matching coeficients and the SCET and bHQET jet functions. On the other hand, original and also published work in fixed-order perturbation theory is also carried out in the field of event shapes. The event-shape distribution for $e^+e^-$ to hadrons is computed to NLO differential with respect to the angle between the initial beam and the thrust axis of the event. The relevant finding is the presence of the quark mass already at $\cal{O}(\alpha_s^0)$ for the vector current. Finally, the dissertation also contains a brief study on the FOPT-CIPT difference in the context of tau decays.