Determination of U-spin breaking parameters with an amplitude analysis of the decay $D^0 \to K_{\rm L}^0\pi^+\pi^-$

TL;DR

This paper performs the first amplitude analysis of the decay $D^0 o K_L^0\pi^+\pi^-$, measuring U-spin breaking parameters and exploring CP violation effects, revealing significant symmetry breaking in the process.

Contribution

It introduces the first amplitude analysis involving a $K_L^0$, providing the first measurement of complex U-spin breaking parameters in this decay mode.

Findings

U-spin breaking parameters have moduli from 0.4 to 12.1, indicating substantial symmetry breaking.

Fractional resonant contributions and strong-phase parameters are measured for both $K_S^0\pi^+\pi^-$ and $K_L^0\pi^+\pi^-$ modes.

The ratio of branching fractions and CP-even fraction of the $K_L^0\pi^+\pi^-$ state are reported.

Abstract

We present a study of the resonant structure of the decay $D^0 \to K_{\rm L}^0\pi^+\pi^-$, using quantum-correlated $D^0\bar{D}^0$ data produced at $\sqrt{s}=3.773$ GeV. The data sample was collected by the BESIII experiment and corresponds to an integrated luminosity of $2.93$ fb$^{-1}$. This study is the first amplitude analysis of a decay mode involving a $K_{\rm L}^0$, which also results in the first measurement of the complex $\textit{U-spin breaking parameters}$ ($\hat{\rho}$) related to various $\mathit{CP}$-eigenstate resonant modes through which the three-body decay proceeds. The moduli of the $\hat{\rho}$ parameters have central values in a wide range from $0.4$ to $12.1$, which indicates substantial U-spin symmetry breaking. We present the fractional resonant contributions and average strong-phase parameters over regions of phase space for both $K_{\rm S}^0\pi^+\pi^-$ and $K_{\rm L}^0\pi^+\pi^-$ modes. We also report the ratio of the branching fractions between $K_{\rm L}^0\pi^+\pi^-$ and $K_{\rm S}^0\pi^+\pi^-$ decay modes and the $\mathit{CP}$-even fraction of the $K_{\rm L}^0\pi^+\pi^-$ state calculated using the U-spin breaking parameters.