Physicists are chasing a ghost in the Standard Model—a gap in our best theory of the universe that leaves it unable to explain why matter exists at all. This project tackles that gap by testing the Standard Model’s limits through three precise calculations involving hadrons: pion scattering, the muon’s magnetic moment, and kaon decays. The core problem is that the strong nuclear force, which binds quarks inside hadrons, is notoriously difficult to compute. The researcher will use a combination of effective field theory and lattice QCD—a method that simulates particle interactions on a discrete grid—to include electromagnetic and sub-leading strong-force effects that are currently missing or approximated. Without these corrections, future experiments cannot reach the sub-percent precision needed to spot signs of new particles or forces. This is fundamental science with no immediate practical application. But similar work on the muon’s magnetic moment has already hinted at a tension with theory that could point to unknown physics. If successful, these calculations will sharpen the search for new forces and particles, potentially rewriting our understanding of the universe’s fundamental laws.
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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 fundamental constraints from QCD derived by myself and collaborators in recent years, needed to reach the 10 percent precision goal on the light-by-light. In (C) I will use the quantisation condition from pion scattering in (A) to lay out a lattice QCD strategy for decay of kaons into two pions including electromagnetism. This decay is particularly interesting as it is related to the matter asymmetry observed in the Universe, and it is special since the sizeable electromagnetic effects are expected to be at the 20 percent level. The work will entail finding a relation between what can be obtained in lattice QCD and the physical decay, known as a Lellouch-Lüscher factor. This kind of factor is typically needed for hadronic decays, and the one obtained here will be the first to include also electromagnetic effects. The results will therefore open for a wide variety of future lattice simulations. This heavily impactful project exploits the complementarity between effective field theory and lattice QCD. The host organisation is The University of Edinburgh, which has a long tradition of numerical expertise and thus nicely complements my own background. The work will be successful as I have extensive background with the needed ingredients, thus making the novel results highly feasible. Without the expected results in (A) and (C) it will not be possible to do Standard Model precision tests including scattering effects in lattice QCD at (sub-)percent precision.
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