Time-integrated and time-dependent angular analyses of B -> J/psi K pi: A measurement of cos2 beta with no sign ambiguity from strong phases

We present results on B-->J/psiKpi decays using e(+)e(-)annihilation data collected with the BABAR detector at the Y(4S) resonance. The detector is located at the PEP-II asymmetric-energy storage ring facility at the Stanford Linear Accelerator Center. Using approximately 88x10(6) B (B) over bar pairs, we measure the decay amplitudes for the flavor eigenmodes and observe strong-phase differences indicative of final-state interactions with a significance of 7.6 standard deviations. We use the interference between the Kpi S-wave and P-wave amplitudes in the region of the K-*(892) to resolve the ambiguity in the determination of these strong phases. We then perform an ambiguity-free measurement of cos2beta using the angular and time-dependent asymmetry in B-->J/psiK(*0)(K(S)(0)pi(0)) decays. With sin2beta fixed at its measured value and cos2beta treated as an independent parameter, we find cos2beta=2.72(-0.79)(+0.50)(stat)+/-0.27(syst), determining the sign of cos2beta to be positive at 86% C.L.