Isospin symmetry breaking in double-pion production in the region of ${d^*(2380)}$ and the scalar ${\sigma}$ meson

The first attempt is made to provide a quantitative theoretical interpretation of the WASA-at-COSY experimental data on the basic double-pion production reactions $pn\ensuremath{\rightarrow}d{\ensuremath{\pi}}^{0}{\ensuremath{\pi}}^{0}$ and $pn\ensuremath{\rightarrow}d{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ in the energy region ${T}_{p}=1--1.3\text{ }\text{ }\mathrm{GeV}$ [Adlarson et al., Phys. Lett. B 721, 229 (2013)]. The data are analyzed within a model based on the production and decay of an intermediate $I({J}^{P})=0({3}^{+})$ dibaryon resonance ${\mathcal{D}}_{03}$ [also denoted as ${d}^{*}(2380)$]. The observed decrease of the near-threshold enhancement (the so-called ABC effect) in the reaction $pn\ensuremath{\rightarrow}d{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ in comparison to that in the reaction $pn\ensuremath{\rightarrow}d{\ensuremath{\pi}}^{0}{\ensuremath{\pi}}^{0}$ is explained (at least partially) to be due to isospin symmetry violation in the two-pion decay of an intermediate near-threshold scalar $\ensuremath{\sigma}$ meson emitted from the ${\mathcal{D}}_{03}$ dibaryon resonance under conditions of partial chiral symmetry restoration.