Heavy quark masses from jets with effective field theory methods

The consideration of heavy quark masses is of crucial importance in many phenomenological applications in quantum chromodynamics, either because they represent important corrections in precision calculations or because they introduce additional conceptual complications. In this thesis, I tackle a wide range of aspects related to quark masses in the theory of strong interactions, including technical calculations as well as theory innovations. Essentially, this work is centered around four main results: The first is a general formula for NLO massive event-shape cross sections. This formula enables the computation of the NLO cross section with respect to any massive event shape by providing simple analytic formulas for the distributional terms and a general instruction for the algorithmic computation of the non-distributional terms. This represents a big improvement compared to previous approaches, where calculations were performed from the ground up, one type of event shape at a time, and mostly with only numerical results, even for distributional terms. The second result is the two-loop massive quark SCET jet function. This challenging-to-compute quantity was the last missing piece to perform N3LL resummation for some event shapes with massive quarks, including 2-jettiness. Third, the MSR mass renormalization scheme is introduced, a low-scale generalization of the MS-bar mass with variable intrinsic scale. Together with R-evolution, its associated renormalization group evolution, the MSR mass enables the systematic investigation of issues related to the pole-mass renormalon and the resummation of potentially large logarithms of mass-intrinsic scale ratios. Such logarithms are relevant in the conversion between short-distance mass renormalization schemes and for the comparison of mass values that were extracted at widely separated scales. Additionally, the MSR mass can be extended to include the effects of lighter massive quark flavors, resulting in a systematic and consistent matching and running procedure. That procedure can be used to decouple the momentum modes in the pole-MS-bar mass relation, which allows to systematically study the pole-mass renormalon and its flavor-number dependence. Both the resummation of logarithms of intrinsic scales and the systematic treatment of light massive flavors are unique to the MSR mass scheme. The fourth main result of this thesis is REvolver, a C++ library with additional Mathematica and Python interfaces. REvolver implements the MSR mass, R-evolution, and the related concepts in a user-friendly way, and is aimed both at theorists and experimentalists. The provided functionalities include exact renormalization group running of the MS-bar and MSR masses as well as the strong coupling, conversions between various mass renormalization schemes (with or without log-resummation via R-evolution), and the extraction of parameters that are related to the pole-mass renormalon such as the pole-mass ambiguity. The interaction with the library is based on the creation of so-called Core objects that encode a physical scenario, and the extraction of values from them. This makes the use of REvolver especially intuitive and streamlined. REvolver is the only public code that fully exploits the features of the MSR mass and R-evolution in mass-scheme and renormalon-related computations. All results presented in this thesis represent essential contributions to the investigation of quark mass effects, either by providing mass corrections for precision calculations or by introducing new concepts, methods, and tools that lead to a better understanding or facilitate computations. (author)