High-Energy Physics

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Particle physics provides an extraordinarily precise description of matter at the shortest of distances: the Standard Model, a particular quantum field theory. As experiments actively search for hints of physics beyond the Standard Model, notably at the Large Hadron Collider, detailed comparison with theory becomes increasingly crucial. Quantum fields can interact weakly or strongly, and this proposal will develop new analytic techniques to calculate in these two regimes, and to constrain gravitational interactions.This proposal builds on a powerful realization: there is often a unique quantum field theory compatible with given symmetries and universal principles. Quantum field theory was born of the union of relativity and quantum mechanics, and developments from recent years have shown that, thanks to this uniqueness, starting from the most basic principles is a very effective strategy for calculations.Precision calculations of scattering amplitudes are fundamental to particle physics: they describe the relative probabilities of all the possible outcomes of a collision. So-called on-shell approaches have dramatically improved precision in recent years, in a weak coupling approximation, by exploiting basic principles to break complicated processes into simpler ones. This proposal will address outstanding challenges for the next generation of amplitude calculations, notably how to glue back subprocesses, by bringing new mathematical tools from algebraic geometry.Beyond weak coupling, bootstrap methods have been successfully applied to conformal (scale-less) theories. This proposal will extend their use to scattering amplitudes in more general models, including the theory of the strong force. The applicant's group will develop exact sum rules to bound errors in the weak coupling approximation at intermediate energies. The same techniques will be applied to scattering of gravitons. In the current absence of a unique predictive theory of quantum gravity, it is important to limit the possibilities: How different from Einstein's general relativity could a causal theory be?This research will have a direct impact on the field of precision calculations of Standard Model processes. The notion that quantitative predictions can be extracted directly from general principles is far-reaching. It will have a profound and long-lasting influence on the way microscopic interactions are understood, used, and taught by practitioners in many subfields.