Amplitude analysis of the decay ${\bar{B}}^0\to K_S^0{\pi }^{+}{\pi }^{-}$ and first observation of the CP asymmetry in ${\bar{B}}^0\to K^{\ast }(892{)}^{-}{\pi }^{+}$

The time-integrated Dalitz plot of the three-body hadronic charmless decay ${\bar{B}}^0\to K_{\mathrm{S}}^0{\pi }^{+}{\pi }^{-}$ is studied using a $pp$ collision data sample recorded with the LHCb detector, corresponding to an integrated luminosity of $3.0{\mathrm{f}\mathrm{b}}^{-1}$. The decay amplitude is described with an isobar model. Relative contributions of the isobar amplitudes to the ${\overline{B}^0 \to K_{\mathrm{\scriptscriptstyle S}}^0 \pi^+ \pi^-}$ decay branching fraction and CP asymmetries of the flavour-specific amplitudes are measured. The CP asymmetry between the conjugate ${\bar{B}}^0\to K^{\ast }(892{)}^{-}{\pi }^{+}$ and ${\overline{B}^0 \to K^{*}(892)^{+}\pi^-}$decayratesisdeterminedtobe$-0.308 \pm 0.062$.