Automation of jet function calculations in Soft-Collinear Effective theory

The occurrence of large Sudakov logarithms, associated with soft and collinear radiation, in the calculation of cross sections in Quantum Chromodynamics (QCD) spoils the perturbative expansion in the strong coupling constant. This breakdown of perturbative QCD is a bottleneck for achieving precise predictions for a large class of observables at the Large Hadron Collider (LHC). Therefore, these logarithms must be resummed to all orders to preserve the predictive power of perturbation theory. A convenient way to achieve this resummation uses methods from effective field theory. Currently, most observables are calculated analytically case-by-case, but for some observables a numerical approach is the only feasible way.
This thesis is focused on developing a formalism that automates the calculation of two-loop jet functions, which are an essential ingredient for the resummation of Sudakov logarithms to next-to-next-to-leading logarithmic (NNLL) accuracy in Soft-Collinear Effective Theory (SCET). In particular, we developed a systematic strategy based on sector decomposition, selector functions, non-linear transformations, and suitable phase-space parametrisations to evaluate the quark and gluon jet functions to next-to-next-to-leading order (NNLO) in perturbation theory. The strategy allows one to completely factorise all the phase-space singularities associated with the jet functions in terms of master formulae. We furthermore transformed the master formulae into a computational parametrisation to improve the convergence of the numerical routines and to obtain reliable uncertainty estimates. The master formulae were finally implemented into the publicly available code pySecDec, which performs the expansion in the dimensional and rapidity regulators and which provides an interface to the CUBA library for the numerical integrations. The novel framework allows us to compute two-loop results for quark and gluon jet function for a broad class of collider observables. We have verified our framework against the known results for thrust and obtained new results for several e+e− event-shape variables both for SCETI and SCETII . This thesis represents the next step towards a complete automatic resummation tool for generic collider observables to NNLL accuracy in SCET.