Subtraction schemes at next-to-next-to-leading order with applications to top-quark and jet physics

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Progress in Elementary Particle Physics is tightly related to the success of the Large Hadron Collider. This experiment has already provided one fundamental discovery: a new particle that fits the profile of the Higgs boson, a scalar resonance predicted by the mass generation mechanism of the Standard Model (SM). In order to substantiate the claim for detection, experimentalists performing the analysis have used tremendously advanced theoretical tools: next-to-next-to-leading order (NNLO) perturbative expansions of the signal cross sections in the strong coupling constant and next-to-leading order results including multiple particle emission, known as parton showering, for backgrounds. At present, there is no evidence for further resonances, and it is clear that there is high demand for a precise theoretical understanding of possible SM foreground and background processes together with the assessment of the accuracy of the predictions. The required effort might prove crucial in making further discoveries. It is the purpose of the proposed project to contribute to the theoretical studies needed for the future success of the LHC. The concept is to analyse two processes, top-quark pair production and di-jet production, at the next-to-next-to-leading order of perturbative QCD and develop general tools for a high precision evaluation of the respective differential cross sections. The link between the two processes is established by the need to perform Monte Carlo simulations of the contribution of real radiation with up to two emissions of massless partons. This can be done in great generality, and we plan to develop methods and implement them in software that will be publicly available and applicable to arbitrary collider processes. On the phenomenological side, the relevance of the selected process of top-quark pair production lies in the fact that it allows for the determination of the top-quark mass, the strong coupling, and the gluon distribution function inside the proton. Furthermore, it constitutes an important background for new physics searches and may hide new physics effects, as speculated in the case of the well-known asymmetry anomaly measured at the Tevatron. On the other hand, a precise knowledge of the differential cross section for di-jet production is crucial in the determination of the gluon distribution function.