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: A measurement is presented of decay-time-dependent CP violation in the decays B-0 -> J/psi K-S(0) and B-0 -> psi(2S) K-S(0), where the J/psi is reconstructed from two electrons and the psi(2S) from two muons. The analysis uses a sample of pp collision data recorded with the LHCb experiment at centre-of-mass energies of 7 and 8 TeV, corresponding to an integrated luminosity of 3 fb(-1). The CP-violation observables are measured to be C(B-0 -> J/psi K-S(0)) = 0.12 +/- 0.07 +/- 0.02, S(B-0 -> J/psi K-S(0)) = 0.83 +/- 0.08 +/- 0.01, C(B-0 -> psi(2S) K-S(0)) = -0.05 +/- 0.10 +/- 0.01, S(B-0 -> psi(2S) K-S(0)) = 0.84 +/- 0.10 +/- 0.01, where C describes CP violation in the direct decay, and S describes CP violation in the interference between the amplitudes for the direct decay and for the decay after B-0-(B) over bar (0) oscillation. The first uncertainties are statistical and the second are systematic. The two sets of results are compatible with the previous LHCb measurement using B-0 -> J/psi K-S(0) decays, where the J/psi meson was reconstructed from two muons. The averages of all three sets of LHCb results are C(B-0 -> [c (c) over bar] K-S(0)) = -0.017 +/- 0.029, S(B-0 -> [c (c) over bar] K-S(0)) = 0.760 +/- 0.034, under the assumption that higher-order contributions to the decay amplitudes are negligible. The uncertainties include statistical and systematic contributions.

Abstract: A model-dependent amplitude analysis of the decay B (0) -> D(K (S) (0) pi (+) pi (-))K (au 0) is performed using proton-proton collision data corresponding to an integrated luminosity of 3.0 fb(-1), recorded at and 8 TeV by the LHCb experiment. The CP violation observables x (+/-) and y (+/-), sensitive to the CKM angle gamma, are measured to be x- = 0.15 +/- 0.14 +/- 0.03 +/- 0.01; y- = 0.25 +/- 0.15 +/- 0.06 +/- 0.01; x+ = 0.05 +/- 0.24 +/- 0.04 +/- 0.01; y+ = 0.65(-0.23)(+0.24) +/- 0.08 +/- 0.01; where the first uncertainties are statistical, the second systematic and the third arise from the uncertainty on the D -> K (S) (0) pi (+) pi (-) amplitude model. These are the most precise measurements of these observables. They correspond to gamma = (80 (- 22) (+ 21) )A degrees and , where is the magnitude of the ratio of the suppressed and favoured B (0) -> DK (+) pi (-) decay amplitudes, in a K pi mass region of +/- 50 MeV around the K (*)(892)(0) mass and for an absolute value of the cosine of the K (*0) decay angle larger than 0.4.

Abstract: A binned Dalitz plot analysis of B-+/- -> DK +/- decays, with D -> K-S(0)pi(+)pi(-) and D -> (KSK+K-)-K-0, is used to perform a measurement of the CP-violating observables x(+/-) and y(+/-), which are sensitive to the Cabibbo-Kobayashi-Maskawa angle gamma. The analysis is performed without assuming any D decay model, through the use of information on the strong-phase variation over the Dalitz plot from the CLEO collaboration. Using a sample of proton-proton collision data collected with the LHCb experiment in 2015 and 2016, and corresponding to an integrated luminosity of 2.0 fb(-1), the values of the CP violation parameters are found to be x = (9.0 +/- 1.7 +/- 0.7 +/- 0.4) x 10(-2), y = (2.1 +/- 2.2 +/- 0.5 +/- 1.1) x 10(-2), x(+) = (-7.7 +/- 1.9 +/- 0.7 +/- 0.4) x 10(-2), and y(+) = (-1.0 +/- 1.9 +/- 0.4 +/- 0.9) x10(-2). The first uncertainty is statistical, the second is systematic, and the third is due to the uncertainty on the strong-phase measurements. These values are used to obtain gamma = (87(+)(12)(+11))degrees, r(B) = 0.086(-)(0.1)(43)(+0.013), and delta(B) = (101 +/- 11), where r(B) is the ratio between the suppressed and favoured B-decay amplitudes and delta(B) is the corresponding strong-interaction phase difference. This measurement is combined with the result obtained using 2011 and 2012 data collected with the LHCb experiment, to give gamma = (80(-9)(+10))degrees, r(B) = 0.080 +/- 0.011, and delta(B) = (110 +/- 10)degrees.

Abstract: A measurement of CP-violating observables is performed using the decays B-+/- -> DK +/- and B-+/- -> D pi(+/-), where the D meson is reconstructed in one of the self-conjugate three-body final states K-S(0)pi(+)pi(-) and (KSK+K-)-K-0 (commonly denoted K(S)(0)h(+)h(-)). The decays are analysed in bins of the D-decay phase space, leading to a measurement that is independent of the modelling of the D-decay amplitude. The observables are inter- preted in terms of the CKM angle gamma. Using a data sample corresponding to an integrated luminosity of 9 fb(-1) collected in proton-proton collisions at centre-of mass energies of 7, 8, and 13 TeV with the LHCb experiment, gamma is measured to be (68.7(-5.1)(+5.2))degrees. The hadronic parameters r(B)(DK), r(B)(D pi), delta(DK)(B), and delta(D pi)(B), which are the ratios and strong-phase differences of the suppressed and favoured B-+/- decays, are also reported.