Modern field and scattering theory for fundamental physics

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"In the coming decades in high energy physics, we will see many big experiments generate big datasets, such as the revamped HL-LHC proton-proton collider, and the LIGO-Virgo-KAGRA collective of gravitational wave detectors. Our predictions for many of these experiments come from an underlying field theory, and its corresponding amplitudes that describe scattering processes.Common to these big experiments are two bottlenecks. One, there is a large number of possibilities for what we might see. Two, our analytical and numerical field theoretic predictions for each of these possibilities can take a long time to produce.This proposal aims to improve our search for new fundamental physics discoveries on both counts, including by:1. narrowing down the possibilities for what we might see in colliders, such as Belle II, the LHC and future colliders. This will involve a comprehensive survey of simplified models of new physics in the electroweak sector, calculating their current and projected constraints from Higgs, electroweak precision, and flavour data.2. extending functional and on-shell methods, such as constructability algorithms, to work with the numerous local interactions produced by heavy new particles in high energy experiments, as encoded by SMEFT or HEFT.3. applying the same to effective field theories relevant for numerical relativity calculations of gravitational waveforms to generate faster, more precise calculational techniques."