Scalar mesons in $\eta'\to3\pi^{0},\pi^{0}\pi^{+}\pi^{-}$ decays

TL;DR

This paper analyzes the decays of eta-prime into three pions using an isobar model, explaining the decay rates and Dalitz-plot distributions through meson contributions, and providing predictions sensitive to model parameters.

Contribution

The study applies an isobar model to describe eta-prime decays into three pions, highlighting the roles of $a_0$ and $\sigma$ mesons and predicting Dalitz-plot distributions.

Findings

Branching ratio and Dalitz-plot shape of $ o3 ext{pi}^0$ decay explained by meson contributions.

The $ o ext{pi}^0 ext{pi}^+ ext{pi}^-$ decay branching ratio calculated within the model.

Dalitz-plot predictions for $ o ext{pi}^0 ext{pi}^+ ext{pi}^-$ are highly model-dependent.

Abstract

The decays $\eta'\to3\pi^{0}$ and $\pi^{0}\pi^{+}\pi^{-}$ were consider in isobar model approach. Branching ratio and Dalitz-plot shape of the decay $\eta'\to3\pi^{0}$ can be explain by $a0$- and $\sigma$-meson contributions. The $\sigma$ meson term is needed for the Dalitz-plot distribution reconstruction. The branching ratio of the decay $\eta'\to \pi^{0}\pi^{+}\pi^{-}$ can be calculated in the same isobar framework. The prediction for the Dalitz-plot of this decay is shown which strongly dependents from model parameters.