TOWARDS A GENERALIZATION OF THE NESTED SOFT-COLLINEAR SUBTRACTION SCHEME FOR NNLO INFRA-RED DIVERGENCES IN QCD

Our understanding of nature at its most fundamental level is guided by experiments at particle colliders, the largest and most energetic being the Large Hadron Collider (LHC). Proton-proton collisions at the LHC led to the Higgs boson's discovery in 2012 and continue to probe Standard Model (SM) particles with remarkable precision while searching for new physics. Theoretical predictions for these processes rely on quantum field theories, most importantly perturbative Quantum Chromodynamics (pQCD). Consequently, the development of theoretical techniques capable of providing predictions at progressively higher orders of perturbation theory has emerged as one of the most vibrant and engaging areas in theoretical particle physics over the last decade. High-precision physics requires various computational tools to match experimental data, including parton distribution functions, resummation, parton showers, hadronization modeling, and fixed-order calculations. In fixed-order calculations, one of the major challenges consists of constructing infra-red (IR) regularization schemes: this thesis focuses on the latter area. It is well-known that IR singularities arise separately in virtual and real corrections and cancel when these contributions are summed. The important question, therefore, is how to organize this cancellation in a process-independent manner and how to obtain finite remainders that are suitable for numerical evaluation. This issue was fully resolved at next-to-leading order (NLO) in pQCD many years ago, but extending this to next-to-next-to-leading order (NNLO) and beyond has proven to be very challenging. Numerous NNLO subtraction and slicing schemes have been proposed and used for many impressive computations at this perturbative order, but it is fair to state that the level of generality attained at NLO remains elusive at NNLO. This thesis focuses on addressing this problem within the framework of the Nested Soft-Collinear (NSC) subtraction scheme,and it represents a significant step toward this goal. We present the application of the NSC method to the computation of the NNLO QCD corrections for a hadron-hadron scattering process that produces an arbitrary number of partons and a colorless object in the final state, where we assume that one of these final-state partons is a quark, and all additional radiated partons are gluons. The main result of this thesis is a formula that enables the calculation of NNLO QCD corrections for the above process using the NSC subtraction scheme. Importantly, we show that the complex cancellation of IR singularities for this process can be achieved for any multiplicity in a relatively straightforward way.