Consistent Dalitz plot analysis of Cabibbo-favored [formula omitted] decays

Franz Niecknig,Bastian Kubis

doi:10.1016/j.physletb.2018.03.048

Abstract

We resume the study of the Cabibbo-favored charmed-meson decays D+→K¯ππ+ 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+→KSπ0π+ Dalitz plot obtained by the BESIII collaboration as well as the D+→K−π+π+ 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.

Highlights

Three-body decays of heavy mesons provide a powerful mean for Standard Model tests and beyond
We begin with the comparison to the Dalitz plot data of the D+ → KS0 π0π+ decay measured by the BESIII collaboration [39]
In this letter we have resumed the study of strong finalstate interactions in the D+ → K−π+π+/K 0π0π+ decays utilizing dispersion relations in the form of Khuri–Treiman-type equations

Summary

Introduction

Three-body decays of heavy mesons provide a powerful mean for Standard Model tests and beyond. The strong final-state interactions of both decay channels are isospin-related and can be described by the same single-variable amplitudes FLI of isospin I and angular momentum L. The constants aiI,jLk denote the Clebsch–Gordan coefficients corresponding to the single-variable amplitudes for the final states i jk ∈ {0 ̄0+, − + +}. The solutions to these unitarity relations, Eq (6), are given in the form of inhomogeneous Omnes solutions: F02(u). We will focus on the D+ → KS0 π0π+ data from the BESIII collaboration and subsequently perform combined fits to the D+ → KS0 π0π+/K−π+π+ data sets to use the isospin relation between these channels to full capacity, as well as to check the extracted subtraction constants for consistency. The explicit numerical solution strategy to determine the basis functions via matrix inversion is discussed in detail in Ref. [26]

Comparison to the BESIII data

Alternative D-wave model

Conclusion