[Paper Review] Three-body final state interaction in $\eta o 3 \pi$ revisited

Peng Guo, V. Mathieu+3 more|arXiv (Cornell University)|Aug 4, 2016

Quantum Chromodynamics and Particle Interactions3 citations

TL;DR

This paper revisits the three-body final state interaction in the $ar{K}^0 \to \eta \pi^+ \pi^- \pi^0$ decay using a unitary dispersive model that incorporates rescattering effects among the three pions. By fitting KLOE-2 and WASA-at-COSY data simultaneously with just two real parameters, it determines the quark mass double ratio $Q = 21.6 \pm 0.4$ and predicts a slope parameter $\alpha = -0.025 \pm 0.004$ for the neutral channel, consistent with PDG values.

ABSTRACT

In view of the recent high-statistic KLOE-2 data for the $\eta o \pi^+ \pi^- \pi^0$ decay, a new determination of the quark mass double ratio has been done. Our approach relies on a unitary dispersive model that takes into account rescattering effects between three pions. The latter is essential to reproduce the Dalitz plot distribution. A simultaneous description of the KLOE-2 and WASA-at-COSY data is achieved in terms of just two real parameters. From a global fit, we determine $Q=21.6 \pm 0.4$. The predicted slope parameter for the neutral channel $\alpha=-0.025\pm 0.004$ is in a reasonable agreement with the PDG average value.

Motivation & Objective

• To improve the determination of the quark mass double ratio $Q$ using high-statistics KLOE-2 data for the $\eta \pi^+ \pi^- \pi^0$ decay.
• To address the challenge of accurately modeling the Dalitz plot distribution, which is strongly influenced by three-pion final state interactions.
• To achieve a simultaneous description of KLOE-2 and WASA-at-COSY data using a minimal set of parameters.
• To test the consistency of the predicted slope parameter $\alpha$ for the neutral channel with the PDG average value.

Proposed method

• A unitary dispersive model is employed to describe the $\eta \pi^+ \pi^- \pi^0$ decay amplitude, incorporating dynamic rescattering effects among the three pions.
• The model ensures unitarity and analyticity, essential for describing the non-trivial Dalitz plot distribution observed in the data.
• Rescattering effects between the three pions are explicitly included via a dispersive representation of the amplitude.
• The fit is performed on both KLOE-2 and WASA-at-COSY data sets simultaneously, using only two real parameters to describe the dynamics.
• The quark mass double ratio $Q$ is extracted as a key physical output of the global fit.
• The slope parameter $\alpha$ for the neutral channel is predicted from the model and compared with experimental averages.

Experimental results

Research questions

• RQ1 What is the precise value of the quark mass double ratio $Q$ when including three-body final state interactions in the $\eta \pi^+ \pi^- \pi^0$ decay?
• RQ2 How well can a unitary dispersive model with minimal parameters describe both KLOE-2 and WASA-at-COSY data simultaneously?
• RQ3 To what extent do three-pion rescattering effects shape the Dalitz plot distribution in this decay?
• RQ4 Is the predicted slope parameter $\alpha$ for the neutral channel consistent with the PDG average value?
• RQ5 Can a single set of two real parameters describe the dynamics of the $\eta \pi^+ \pi^- \pi^0$ decay across different experimental data sets?

Key findings

• The quark mass double ratio is determined as $Q = 21.6 \pm 0.4$ from a global fit to KLOE-2 and WASA-at-COSY data.
• The model successfully describes the Dalitz plot distribution by including three-pion final state interactions through a unitary dispersive framework.
• The predicted slope parameter for the neutral channel is $\alpha = -0.025 \pm 0.004$, which is in reasonable agreement with the PDG average.
• The simultaneous description of both data sets is achieved with only two real parameters, indicating a high degree of model consistency and predictive power.
• The results support the validity of the unitary dispersive approach in capturing essential dynamics of three-body hadronic decays.