Abstract: The first untagged decay-time-integrated amplitude analysis of B 0 s ! K 0 S K decays is performed using a sample corresponding to 3: 0 fb of pp collision data recorded with the LHCb detector during 2011 and 2012. The data are described with an amplitude model that contains contributions from the intermediate resonances K 9892) 0;+, K 2 91430) 0;+ and K 0 91430) 0;+, and their charge conjugates. Measurements of the branching fractions of the decay modes B 0 s ! K 9892) K and B 0 s ! K 9892) 0 K 0 are in agreement with, and more precise than, previous results. The decays B 0 s ! K 0 91430) K and B 0 s ! K 0 91430) 0 K 0 are observed for the fi rst time, each with signi fi cance over 10 standard deviations.

Abstract: We analyze the decay B-0 -> K+ pi(-) pi(0) with a sample of 4.54 x 10(8) B (B) over bar events collected by the BABAR detector at the PEP-II asymmetric-energy B factory at SLAC, and extract the complex amplitudes of seven interfering resonances over the Dalitz plot. These results are combined with amplitudes measured in B-0 -> K-S(0)pi(+)pi(-) decays to construct isospin amplitudes from B-0 -> K* pi and B-0 -> rho K decays. We measure the phase of the isospin amplitude Phi(3/2), useful in constraining the Cabibbo-Kobayashi-Maskawa unitarity triangle angle gamma and evaluate a CP rate asymmetry sum rule sensitive to the presence of new physics operators. We measure direct CP violation in B-0 -> K*(+) pi(-) decays at the level of 3 sigma when measurements from both B-0 -> K+ pi(-) pi(0) and B-0 -> K-S(0) pi(+) pi(-) decays are combined.

Abstract: The results of an amplitude analysis of the charmless three-body decay B+ -> pi(+)pi(+)pi(-) , in which CP-violation effects are taken into account, are reported. The analysis is based on a data sample corresponding to an integrated luminosity of 3 fb(-1) of pp collisions recorded with the LHCb detector. The most challenging aspect of the analysis is the description of the behavior of the pi(+)pi(-) S-wave contribution, which is achieved by using three complementary approaches based on the isobar model, the K-matrix formalism, and a quasi-model-independent procedure. Additional resonant contributions for all three methods are described using a common isobar model, and include the rho(770)(0), omega(782)(0) and rho(1450)(0) resonances in the pi(+)pi(-) P-wave, the f(2) (1270) resonance in the pi(+)pi D- -wave, and the rho(3) (1690)(0) resonance in the pi(+)pi(-) F-wave. Significant CP-violation effects are observed in both S- and D-waves, as well as in the interference between the S- and P-waves. The results from all three approaches agree and provide new insight into the dynamics and the origin of CP-violation effects in B+ -> pi(+)pi(+)pi(-) decays.