Hadrons as a Portal to New Physics

The Standard Model of particle physics is our best theoretical knowledge of the Universe at the shortest length scales ever probed in experimental measurements. However, there is a number of things it does not seem to explain, such as the puzzle why there is observable matter in the Universe. Such shortcomings of the model can indicate the existence of new, hitherto unknown particles and forces that would have to be searched for in future measurements. In this project, I will test the limits of the Standard Model by performing timely and ambitious calculations, which when combined with high-precision experiments allow to indirectly search for new physics. I will focus on composite particles known as hadrons as a potential portal to the unknown, through (A) scattering of pions, (B) the muon magnetic moment and (C) decays of kaons. To handle effects from the strong nuclear force (QCD) in the hadrons, the work will rely on the complementary tools effective field theory and lattice QCD.

In (A) I will develop a framework to include electromagnetism and sub-leading QCD corrections in lattice QCD simulations of pion scattering. These effects are typically expected to be of the percent level size, and therefore must be taken into account for any precision goal at (sub-)percent level. The main goal here is to obtain a relation between the pion energy levels in the lattice simulation and physical scattering parameters, known as a quantisation condition. The developed formalism will solve a fundamental problem for lattice simulations, and set the stage for a wide range of future calculations. 

In (B) I will scrutinise a questioned tension between theory and experiment for the muon anomalous magnetic moment. I will consider one of the two most important hadronic contributions, the so-called light-by-light currently known at 20 percent relative precision. In dispersion theory evaluations of the light-by-light, parts of the calculations rely on models. Here I will use...