Amplitude analysis of the decay $overline{B}^0 to K_{S}^0 pi^+ pi^-$ and first observation of the CP asymmetry in $overline{B}^0 to K^{*}(892)^- pi^+$

The time-integrated Dalitz plot of the three-body hadronic charmless decay ${{overline{B}}^0 to K_{mathrm{scriptscriptstyle S}}^0 pi^+ pi^-}$ is studied using a $pp$ collision data sample recorded with the LHCb detector, corresponding to an integrated luminosity of $3.0;mathrm{fb}^{-1}$. 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 ${overline{B}^0 to K^{*}(892)^{-}pi^+}$ and ${overline{B}^0 to K^{*}(892)^{+}pi^-}$ decay rates is determined to be $-0.308 pm 0.062$.