Amplitude Analysis of the Decay ¯ B 0 → K 0 S π + π − and First Observation of the C P Asymmetry in ¯ B 0 → K ∗ ( 892 ) − π +

The time-integrated untagged Dalitz plot of the three-body hadronic charmless decay ¯B0→K0Sπ+π− is studied using a pp collision data sample recorded with the LHCb detector, corresponding to an integrated luminosity of 3.0  fb−1. The decay amplitude is described with an isobar model. Relative contributions of the isobar amplitudes to the ¯B0→K0Sπ+π− decay branching fraction and CPasymmetries of the flavor-specific amplitudes are measured. The CP asymmetry between the conjugate ¯B0→K∗(892)−π+ and B0→K∗(892)+π− decay rates is determined to be −0.308±0.062