Extracting maximum information from polarised baryon decays via amplitude analysis: the $\Lambda^+_c \to pK^-\pi^+$ case

We consider which is the maximum information measurable from the decay distributions of polarised baryon decays via amplitude analysis in the helicity formalism. We focus in particular on the analytical study of the $\Lambda^+_c \to pK^-\pi^+$ decay distributions, demonstrating that the full information on its decay amplitudes can be extracted from its distributions, allowing a simultaneous measurement of both helicity amplitudes and the polarisation vector. This opens the possibility to use the $\Lambda^+_c \to pK^-\pi^+$ decay for applications ranging from New Physics searches to low-energy QCD studies, in particular its use as absolute polarimeter for the $\Lambda^+_c$ baryon. This result is valid as well for baryon decays having the same spin structure and it is cross-checked numerically by means of a toy amplitude fit with Monte Carlo pseudo-data.