Study of B → Kππγ decays with the BABAR Experiment: the photon helicity and the resonant structure of the Kππ system

We present a measurement of the time-dependent CP asymmetry in the radiative-penguin decay B⁰ → K⁰_Sπ⁺π^-γ, using a sample of 470.9 million Υ(4S) → BB-bar events recorded with the BABAR detector at the PEP-II e⁺e^- storage ring at SLAC. Using events with m_Kππ < 1.8 GeV/c², 0.6 < m_ππ < 0.9 GeV/c² and with m_Kπ < 0.845 GeV/c² and m_Kπ > 0.945 GeV/c², we obtain the CP-violating parameters S(K⁰_Sπ⁺π^-γ) = 0.137±0.249^+0.042_-0.033 and C(K⁰_Sπ⁺π^-γ) = -0.390±0.204^+0.045_-0.050, where the first quoted errors are statistical and the second are systematic. We extract from this measurement the time-dependent CP asymmetry related to the hadronic CP eigenstate ρ⁰K⁰_S and obtain S(K⁰_Sργ) = 0.249±0.455^+0.076_-0.060. This observable provides information on the photon polarization in the underlying b → sγ transition. To extract S(K⁰_S ργ) from S(K⁰_S π⁺π^γ), assuming isospin symmetry, we study B⁺ → K⁺π⁺π^-γ decays and measure intermediate resonant amplitudes of different resonances decaying to Kππ through the intermediate states ρ⁰K⁺, K*⁰π⁺ and (Kπ)_S-waveπ⁺. In addition to the need of this information for the extraction of S(K⁰_S ργ), it provides input on the B → Kππ system, which is useful for other studies of the photon polarization. The fractions of the different K_res → Kππ states as well as the overall fractions of the ρ⁰K⁺, K*⁰π⁺ and (Kπ)_S-waveπ⁺ components are also measured. (author)