Amplitude analysis of the ${\mathrm{\Xi }}_c^{+}\to p{K}^{-}{\pi }^{+}$ decay and ${\mathrm{\Xi }}_c^{+}$ baryon polarization measurement in semileptonic beauty-hadron decays

An amplitude analysis of the ${\mathrm{\Xi }}_c^{+}\to p{K}^{-}{\pi }^{+}$ decay together with a measurement of the ${\mathrm{\Xi }}_c^{+}$ polarization vector in semileptonic beauty-hadron decays is presented. The analysis is performed using proton-proton collision data collected by the LHCb experiment, corresponding to an integrated luminosity of 9 ${\mathrm{f}\mathrm{b}}^{-1}$. An amplitude model is developed and the resonance fractions as well as two- and three-body decay parameters are reported. A sizeable ${\mathrm{\Xi }}_c^{+}$ polarization is found. A large sensitivity of the ${\mathrm{\Xi }}_c^{+}\to p{K}^{-}{\pi }^{+}$ decay to the polarization is seen, making the amplitude model suitable for ${\mathrm{\Xi }}_c^{+}$ polarization measurements in other systems.