Ambiguity-Free Measurement of cos2beta: Time-Integrated and Time-Dependent Angular Analyses of B to J/psi K pi

We present results on B → J/ψ Kπ decays using e+e- annihilation data collected with the BABAR detector at the Υ(4S) resonance. The detector is located at the PEP-II asymmetric-energy storage ring facility at the Stanford Linear Accelerator Center. Using approximately 88 million B(bar B) 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 Kπ 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 cos 2β using the angular and time-dependent asymmetry in B → J/ψ K*0 (KS0π0) decays. With sin2β fixed at its measured value and cos2β treated as an independent parameter, we find cos 2β = 2.72-0.79+0.50(stat) ± 0.27(syst), determining the sign of cos 2β to be positive at 86% CL