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

TL;DR

This paper develops a dispersive analysis framework for $D^+ o ar{K} \pi \pi^+$ decays that respects fundamental symmetries and describes final-state interactions, successfully fitting experimental Dalitz plot data.

Contribution

It introduces a novel dispersive formalism for three-body charm decays that incorporates unitarity, analyticity, and crossing symmetry, and applies it to experimental data for the first time.

Findings

Consistent description of BESIII, CLEO, and FOCUS Dalitz plots.

Improved constraints on subtraction constants via isospin relations.

Demonstration of the formalism's effectiveness in modeling strong final-state interactions.

Abstract

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.