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

An amplitude analysis of ${\mathrm{\Lambda }}_c^{+}\to p{K}^{-}{\pi }^{+}$ decays together with a measurement of the ${\mathrm{\Lambda }}_c^{+}$ polarization vector in semileptonic beauty hadron decays is presented. A sample of $400000$ candidates is selected from proton-proton collisions recorded by the LHCb detector at a center-of-mass energy of 13 TeV. An amplitude model is developed and the resonance fractions as well as two- and three-body decay parameters are reported. The mass and width of the $\mathrm{\Lambda }(2000)$ state are also determined. A significant ${\mathrm{\Lambda }}_c^{+}$ polarization is found. A large sensitivity of the ${\mathrm{\Lambda }}_c^{+}\to p{K}^{-}{\pi }^{+}$ decay to the polarization is seen, making the amplitude model suitable for ${\mathrm{\Lambda }}_c^{+}$ polarization measurements in other systems.