Consistent Dalitz plot analysis of Cabibbo-favored $D^{+}\to \bar{K}\pi {\pi }^{+}$ decays

We resume the study of the Cabibbo-favored charmed-meson decays $D^+ \to \bar{K} \pi \pi^+$ in a dispersive framework that satisfies unitarity, analyticity, and crossing symmetry by construction. The formalism explicitly describes the strong final-state interactions between all three decay products and relies on pion-pion and pion-kaon phase shift input. For the first time, we show that the $D^{+}\to K_S{\pi }^0{\pi }^{+}$ Dalitz plot obtained by the BESIII collaboration as well as the $D^{+}\to K^{-}{\pi }^{+}{\pi }^{+}$ Dalitz plot data by CLEO and FOCUS can be described consistently, exploiting the isospin relation between the two coupled decay channels that provides better constraints on the subtraction constants.