Invariant mass distributions of $ K ^0_{\mathrm{ \scriptscriptstyle S}} \pi ^+ \pi ^- $ candidates, summing the two years of data taking and the two $ K ^0_{\mathrm{ \scriptscriptstyle S}}$ reconstruction categories. The sum of the partially reconstructed contributions from $ B $ to open charm decays, charmless hadronic decays, $\overline{ B }{} {}^0 \rightarrow \eta ^{\prime} K ^0_{\mathrm{ \scriptscriptstyle S}} $ and charmless radiative decays are denoted $\overline{ B }{} ^0_{(s)} \rightarrow K ^0_{\mathrm{ \scriptscriptstyle S}} \pi ^+ \pi ^- (X)$.

Projections of the sum of all data categories (black points) and the nominal fit function onto the DP variables (left) $m_{K_{\rm S}^0\pi^+}^2$, (right) $m_{K_{\rm S}^0\pi^-}^2$ and (bottom) $m_{\pi^+\pi^-}^2$, restricted to the two-body low invariant-mass regions. The full fit is shown by the solid blue line and the signal model by the dashed red line. The observed difference is due to the (green) combinatorial and (light red) cross-feed background contributions, barely visible in these projections.

Animated gif made out of all figures.

Components of the DP model used in the fit. The individual amplitudes are referred to by the resonance they contain. The parameter values are given in $ {\mathrm{ Me V /}c^2}$ for the masses and $\mathrm{ Me V}$ for the widths, except for $f_0(980)$ resonance. The parameter $m_0$ is the pole mass of the resonance and $\Gamma_0$ its natural width. The mass-dependent lineshapes employed to model the resonances are indicated in the third column. Relativistic Breit-Wigner and Gounaris-Sakurai lineshapes are denoted RBW and GS, respectively. EFKLLM is a parameterisation of the $ K ^0_{\mathrm{ \scriptscriptstyle S}} \pi^{-}$ S-wave lineshape, $(K\pi)^{-}_0$.