Hadronic contributions to the muon g-2 at higher precision

The study of how elementary particles respond to external electromagnetic fields has been pivotal in shaping our current understanding of fundamental interactions. The electron and its heavier siblings like the muon behave like spinning magnets. Currently a primary goal of the particle physics community is to further enhance the comparison between increasingly precise experimental measurements and the most advanced theoretical predictions of the muons anomalous magnetic moment. Any confirmed discrepancy between theory and experiment would strongly indicate the existence of previously unknown subatomic particles in nature. However, the precision of upcoming measurements at the Fermi National Accelerator Laboratory (USA), is not yet fully matched by current theoretical calculations. The main challenge lies in accurately accounting for strong-interaction effects, particularly those involving virtual exchanges of hadrons, like pions and heavier mesons. The proposed research aims to improve the situation by making use of sophisticated field theoretic techniques, based on general principles like causality and analyticity, to compute the relevant quantum transition amplitudes to the required precision. The project specifically aims to improve the determination of the hadronic light-by-light contribution to the muon`s anomalous magnetic moment, which is governed by hadronic correlation functions involving four external photons. Utilizing a newly developed theoretical framework, the project will address effects previously inaccessible to other methodscritical for achieving the necessary precision. This will be accomplished through a novel evaluation of the relevant hadronic quantum transition amplitudes, enabling us to express key contributions in terms of experimentally accessible quantities. The planned research project will yield analytic results and numerical evaluations that, when combined with previously known contributions and experimental input, will lead to the first complete and most precise data-driven determination of the hadronic light-by-light. This evaluation, characterized by controlled uncertainties, will provide a critical tool to enhance our search for new physics in the muons anomalous magnetic moment.