The scattering matrix (S-matrix) is the fundamental mathematical tool used to describe particle interactions in collider experiments. The bootstrap research program was originally proposed in the 1960s to understand the scattering dynamics of strong nuclear forces. It aimed to construct S-matrix elements by imposing consistency with fundamental principles such as causality and unitarity, but it fell out of favor with the development of Quantum Chromodynamics.
In this talk, we review the modern revival of the bootstrap program enabled by numerical tools such as semidefinite optimization. We then explore the space of interacting theories of massive real scalar particles in 3+1 dimensions, focusing on regions where a perturbative effective field theory (EFT) expansion is valid. This framework provides guidance in the search for Beyond the Standard Model physics, particularly in the Higgs sector, by placing theoretical bounds on dimension-six Wilson coefficients in the Standard Model EFT. Finally, we discuss the use of neural networks as a novel tool for solving nonlinear bootstrap equations.
