Accuracy and Precision in Collider Event Shapes

In this thesis, we discuss and investigate the use of Soft-Collinear Effective Theory (SCET) for high precision calculations. In the first part of the work, we present an extraction of the strong coupling, $α_s(m_Z)$ and the leading nonperturbative parameter $Ω_1$, using the event shape C-parameter. By comparing lepton collider data to the C-parameter cross section, we extract values $α_s(m_Z)=0.1123\pm 0.0015$ and $Ω_1=0.421\pm 0.063\,{\rm GeV}$ with $χ^2/\rm{dof}=0.988$ for $404$ bins of data. The later parts of this thesis are dedicated to using on-shell helicity methods to extend SCET beyond leading power. We present a complete set of scalar helicity building blocks and describe an interesting angular momentum selection rule that restricts how these building blocks can be assembled.

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