[Paper Review] Analysis of the decay $D^0 ightarrow K_{S}^{0} K^{+} K^{-}$

BESIII Collaboration, F. De Mori+484 more|arXiv (Cornell University)|Jun 4, 2020

High-Energy Particle Collisions Research1 references4 citations

TL;DR

This paper presents the first absolute branching fraction measurement of the $D^0 \to K_S^0 K^+ K^-$ decay using a Dalitz plot amplitude analysis with data from the BESIII experiment. The measured branching fraction is $(4.51 \pm 0.05_{\text{stat}} \pm 0.16_{\text{sys}}) \times 10^{-3}$, with a model that accounts for quantum entanglement and includes resonances such as $a_0(980)$, $\phi(1020)$, and $a_2(1320)$, while also reporting upper limits for doubly Cabibbo-suppressed states due to model uncertainties.

ABSTRACT

Using a data sample of $2.93~fb^{-1}$ of $e^+e^-$ collisions collected at $\sqrt{s}=3.773 GeV$ in the BESIII experiment, we perform an analysis of the decay $D^0 ightarrow K_{S}^{0} K^{+} K^{-}$. The Dalitz plot is analyzed using $1856\pm 45$ flavor-tagged signal decays. We find that the Dalitz plot is well described by a set of six resonances: $a_0(980)^0$, $a_0(980)^+$, $ϕ(1020)$, $a_2(1320)^+$, $a_2(1320)^-$ and $a_0(1450)^-$. Their magnitudes, phases and fit fractions are determined as well as the coupling of $a_0(980)$ to $K\bar{K}$, $g_{K\bar{K}}=3.77\pm 0.24 ext{(stat.)}\pm0.35 ext{(sys.)} GeV$. The branching fraction of the decay $D^0 ightarrow K_{S}^{0} K^{+} K^{-}$ is measured using $11660\pm 118$ untagged signal decays to be $(4.51\pm 0.05 ext{(stat.)}\pm 0.16 ext{(sys.)})10^{-3}$. Both measurements are limited by their systematic uncertainties.

Motivation & Objective

• To measure the absolute branching fraction of the $D^0 \to K_S^0 K^+ K^-$ decay with high precision.
• To perform a Dalitz plot amplitude analysis to identify resonant contributions and model the decay dynamics.
• To account for quantum entanglement effects between $D^0$ and $\bar{D}^0$ in the amplitude model to ensure accurate parameter extraction.
• To evaluate the significance and fit fractions of resonances such as $a_0(980)$, $a_2(1320)$, and $a_0(1450)$, and to report upper limits where necessary due to model limitations.
• To compare the results with previous measurements and improve the uncertainty by using a refined resonance model and entanglement correction.

Proposed method

• A Dalitz plot amplitude analysis is performed on $D^0 \to K_S^0 K^+ K^-$ decays using data from the BESIII experiment.
• The amplitude model includes resonant states such as $a_0(980)^0$, $a_0(980)^+$, $\phi(1020)$, $a_2(1320)^\pm$, and $a_0(1450)^\pm$, with parameters constrained by fitting the phase space distribution.
• Quantum entanglement between $D^0$ and $\bar{D}^0$ is incorporated into the amplitude model using the amplitude ratio parameters from $D^0 \to K^+ \pi^-$ decays, with uncertainty propagation for model dependence.
• The signal yield and branching fraction are extracted using a likelihood fit to the Dalitz plot distribution, with corrections applied for quantum entanglement effects.
• Systematic uncertainties are evaluated by varying the amplitude model, resonance parameters, and entanglement assumptions, including the use of a simplified 'visible' resonance model for comparison.
• The final branching fraction is reported with statistical and systematic uncertainties, and upper limits are provided for states with low significance, such as $a_2(1320)^{-}$ and $a_0(1450)^{-}$.

Experimental results

Research questions

• RQ1 What is the absolute branching fraction of the $D^0 \to K_S^0 K^+ K^-$ decay, and how precisely can it be measured?
• RQ2 Which resonant states contribute significantly to the Dalitz plot distribution, and what are their fit fractions and significance levels?
• RQ3 How do quantum entanglement effects between $D^0$ and $\bar{D}^0$ impact the amplitude model and the extracted branching fraction?
• RQ4 Why are the doubly Cabibbo-suppressed states $a_2(1320)^{-}$ and $a_0(1450)^{-}$ found to have low significance, and what does this imply about the model's reliability?
• RQ5 How does the choice of resonance model affect the final branching fraction and systematic uncertainties?

Key findings

• The absolute branching fraction of $D^0 \to K_S^0 K^+ K^-$ is measured to be $(4.51 \pm 0.05_{\text{stat}} \pm 0.16_{\text{sys}}) \times 10^{-3}$, marking the first absolute measurement of this decay.
• The coupling strength of the $a_0(980)$ to $K\bar{K}$ is measured as $g_{K\bar{K}} = (3.77 \pm 0.24 \pm 0.35)\,\text{GeV}^{-1}$, consistent with previous measurements within uncertainties.
• The $a_2(1320)^{+}$, $a_2(1320)^{-}$, and $a_0(1450)^{-}$ states have a combined statistical significance of $5.9\sigma$, but their individual fit fractions are small and their isospin partners have significance below $2.1\sigma$, leading to upper limits being reported.
• The $a_0(980)^0$ and $a_0(980)^+$ resonances are found to be significant contributors, with the $a_0(980)^0$ having a fit fraction consistent with expectations from its coupling to $K\bar{K}$.
• The model including $a_0(980)^0$, $a_0(980)^+$, and $\phi(1020)$ as 'visible' resonances yields a consistent result, validating the robustness of the analysis against model dependence.
• The study identifies potential model artifacts in regions of phase space where doubly Cabibbo-suppressed states are not well described, suggesting caution in interpreting their contributions.