Deriving Scattering Amplitudes from Hadron Spectra: Novel Quantization Conditions in Lattice QCD and Their Applications

Abstract

The Standard Model of particle physics, the most precise scientific description of nature yet devised, is a comprehensive framework that encapsulates our understanding of the fundamental particles and their interactions. A keystone of this model is quantum chromodynamics (QCD), a quantum field theory describing the strong nuclear force, which binds together fundamental particles known as quarks to form composite particles such as protons and neutrons, and which binds these protons and neutrons together to form atomic nuclei. Together with electrons, which orbit these nuclei, quarks constitute the basic building blocks of all matter, forming the atoms that compose us and making up everything we have ever seen and ever touched. One of the most powerful computational tools for understanding the dynamics of quarks is lattice QCD. By discretizing a finite volume of space and time onto a four-dimensional grid, lattice QCD enables the calculation of correlation functions that capture the behavior of quarks and the gluons that bind them together. This framework provides a bridge between the mathematical formulation of QCD and experimental results, allowing for tests of the Standard Model and offering insights into the behavior of particles and their interactions under extreme conditions that may be inaccessible to direct observation. To connect lattice calculations with experimental results and the real, infinite-volume world, one must account for the effects of finite volume and boundary conditions through the use of quantization conditions. It is these quantization conditions, their derivation, and implementation, that form the heart of this body of work.