Study of the B 0 → ρ(770)°K * (892) 0 decay with an amplitude analysis of B 0 → (π + π − )(K + π − ) decays

An amplitude analysis of B-0 ((+-))(K+-) decays is performed in the two-body invariant mass regions 300 < m((+-)) < 1100 MeV/c(2), accounting for the (0), , f(0)(500), f(0)(980) and f(0)(1370) resonances, and 750 < m(K+-) < 1200 MeV/c(2), which is dominated by the K-*(892)(0) meson. The analysis uses 3 fb(-1) of proton-proton collision data collected by the LHCb experiment at centre-of-mass energies of 7 and 8 TeV. The CP averages and asymmetries are measured for the magnitudes and phase differences of the con- tributing amplitudes. The CP-averaged longitudinal polarisation fractions of the vector-vector modes are found to be fK*0 = 0.164 +/- 0.015 +/- 0.022 and fK*0 = 0.68 +/- 0.17 +/- 0.16, and their CP asymmetries, AK*0 = -0.62 +/- 0.09 +/- 0.09 and AK*0 = -0.13 +/- 0.27 +/- 0.13, where the first uncertainty is statistical and the second systematic.