Scalar mesons in ${\eta }^{\prime }\to 3{\pi }^0,{\pi }^0{\pi }^{+}{\pi }^{-}$ decays

Abstract

The decays ${\eta }^{\prime }\to 3{\pi }^0$ and ${\pi }^0{\pi }^{+}{\pi }^{-}$ were consider in isobar model approach. Branching ratio and Dalitz-plot shape of the decay ${\eta }^{\prime }\to 3{\pi }^0$ 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 ${\eta }^{\prime }\to {\pi }^0{\pi }^{+}{\pi }^{-}$ 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.

Comments: 10 pages, 6 figures