The Perturbative Scattering Amplitude Bootstrap

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The Standard Model of particle physics represents one of the major achievements of modern science, and with the discovery of the Higgs boson at the Large Hadron Collider its predictions have been tested to unprecedented levels of precision. These measurements will continue to improve as more data is collected in the coming years, allowing us to probe the fundamental laws of physics to an unparalleled degree. However, to benefit from these measurements, the precision with which we can make theoretical predictions in quantum field theory must also be drastically improved. This in particular requires improving our understanding of scattering amplitudes, which provide essential input for these calculations. While scattering amplitudes are notoriously difficult to compute, they have been found to exhibit an immensely rich mathematical structure, with deep ties to number theory, algebraic geometry, and string theory. These connections have recently fueled a revolution in our ability to compute highly nontrivial amplitudes in supersymmetric theories to unprecedented levels of precision. Building on this progress, I propose three lines of investigation for developing the same level of insight into the mathematical structure of Standard Model amplitudes, and for bypassing the difficult integration problems that have traditionally been required for their evaluation: 1) the derivation of new constraints on the analytic structure of amplitudes from basic physical requirements such as causality and locality 2) an in-depth study of the types of special functions that appear in amplitudes and the development of new tools for working with them 3) the development of perturbative bootstrap methods for Standard Model amplitudes These lines of research will give rise to deep new insights into the universal properties of perturbative quantum field theory, and facilitate the development of groundbreaking new methods for making precision predictions for collider experiments.