The indirect search for fundamental interactions, governing matter at the smallest scales, complements the direct search of new particles. Historically, direct discoveries have often been anticipated by “indirect” evidence, namely predicted effects in precision measurements. Many rare meson and baryon decays fall in this category and probe scales far beyond those accessible at the energy frontier. The thesis focuses on devising measurable decays that probe interactions with light spinless particles known as axions. Axions, while hypothetical, are highly plausible particles that address several conceptual and observational problems, such as the absence of CP violation in strong interactions and the nature of Dark Matter. Axions may be produced in decays of beauty mesons or hyperons. We plan to devise new search channels using decays with well-controlled backgrounds or reliably reconstructed decay products. These decays will be calculated within QCD at low energies (the “theory of pions”), augmented with an axion via the Noether procedure. This research will be a collaboration between LAPTh Annecy (FR) on theory, and the University of Cagliari (UniCa, IT) on experiment. The Annecy-UniCa collaboration is a long-standing one, with former students who are now CNRS staff or accomplished postdoctoral researchers. The thesis involves both theoretical and experimental work to train an all-round phenomenologist, and is funded by the IT/FR “Vinci” program.