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Abstract The LHCb collaboration has presented first experimental evidence that spin-carrying matter and antimatter differ. The study looked at four-body decays of the $${{\boldsymbol{\Lambda }}}_{{\boldsymbol{b}}}^{{\bf{0}}}$$ Λb0 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.