PhD project: Bootstrap Methods for Standard Model Processes

Project description

Quantum field theory—the mathematical framework that allows physicists to probe the basic microscopic laws of the universe—has given rise to some of the most precise predictions in the history of science. Even so, methods for carrying out calculations in quantum field theory remain tragically underdeveloped, as the results of arduous multi-year calculations are regularly observed to collapse to unexpectedly-simple expressions only in the last step. This indicates that a dramatic change is required in how we go about carrying out these computations in order to properly account for this mathematical simplicity. 

Over the last few years, novel bootstrap methods have been developed in supersymmetric theories that leverage our increasingly-sophisticated understanding of the mathematical structure of scattering amplitudes to construct the functional form of amplitudes directly. These new methods have already given rise to some of the highest-order results in perturbative quantum field theory, extending in some cases up to eight loops. PhD students involved in this project will help deepen our understanding of the mathematical properties of non-supersymmetric amplitudes in order to begin applying bootstrap methods to Standard Model processes. This will involve projects related to one or more of the following topics: 

(i) Systematically understanding the types of special functions that scattering amplitudes evaluate to, which are now known to include integrals over Calabi-Yau manifolds of arbitrarily high dimension.

(ii) Exploring the implications of new number-theoretic symmetries amplitudes have been observed to exhibit under the action of the ‘Cosmic Galois group’.

(iii) Developing the computational tools needed to carry out the first bootstrap calculations of Standard Model amplitudes.

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