The experimental program at the Large Hadron Collider (LHC) at CERN has been very successful, leading to the discovery of a Higgs-like boson in 2012. However, the LHC experiments have so far not uncovered direct signals of new physics beyond that of the Standard Model. One may therefore anticipate an increased focus on precision measurements during the second run of the LHC, scheduled to start early 2015. This raises an acute need for increased theoretical precision in order to observe signals of new physics hiding in the QCD background. Owing to the large number of different processes and the complexity of evaluating their cross section, the traditional computational methods are not suited to meet the demands of the LHC. An accurate quantitative understanding of the QCD backgrounds therefore urgently requires the development of sophisticated new tools for their evaluation. Precision measurements call for next-to-next-to-leading order (NNLO) calculations. These calculations make use of two-loop scattering amplitudes as key ingredients.
This proposal aims to develop novel methods for computing two-loop scattering amplitudes. The methods will lay the foundation for automating the computation of two-loop amplitudes. This would allow the computation of currently unattainable processes needed for LHC phenomenology. The underlying framework is a two-loop extension of generalized unitarity techniques which have proven remarkably successful in the computation of one-loop amplitudes and subsequently been implemented in modern software libraries such as BlackHat, CutTools, HELAC-NLO, MadLoop, NGluon, Rocket, and SAMURAI. I anticipate that the computational techniques to be developed under this proposal will be implemented in the BlackHat software library, allowing it to become a tool for NNLO calculations serving searches for new physics during the next run of the LHC. This proposal will also develop cross-disciplinary links between particle physics and algebraic geometry.
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