Modern aspects of scattering amplitudes in quantum chromodynamics and gravity

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Abstract

Gauge-theory scattering amplitudes are a necessary ingredient to describe collision experiments. The method based on Feynman diagrams becomes computationally difficult to use in practice when the number of particles involved increase or when more precision is required. The search for new methods of computation of scattering amplitudes for gauge theories involves several ideas, which lead to improvement of the current techniques and to establish new ones. The new techniques and concepts lead to a better understanding of perturbative quantum field theory. In this thesis, the Cachazo-He-Yuan (CHY) formalism based on the scattering equations and the Bern-Carrasco-Johansson (BCJ) duality are used to compute amplitudes in Quantum Chromodynamics (QCD) at tree-level. These formalisms can naturally be utilized to explore gravity amplitudes by the BCJ double copy mechanism. This mechanism is used to study relations between QCD amplitudes and gravity. One of the main results of this thesis is the proof of the CHY representation of QCD, towards finding a closed integrand of the CHY representation. The second result is the proposal of a new gravitational theory built from QCD amplitudes, which may be relevant for discussions about dark matter. Finally, with the aid of the techniques introduced in this thesis, relations among Einstein-Yang-Mills and Yang-Mills amplitudes are explored.

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