The LHCb collaboration has presented first experimental evidence that spin-carrying matter and antimatter differ. The study looked at four-body decays of the [Formula: see text] baryon. Differences in the behaviour of matter and antimatter are associated with the non-invariance of fundamental interactions under the combined charge-conjugation and parity transformations, known as CP violation. We discuss purely baryonic decay processes, i.e. decay processes involving only spin-carrying particles. They are yet unexplored elementary processes. Their study opens a new chapter of flavour physics in the route towards a better understanding of CP violation. It may help us understand the observed matter and antimatter asymmetry of the Universe.