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

We present results on $B\to J/\psi\xspace K\pi$ decays using $e^+e^-$ annihilation data collected with the BABAR detector at the $\Upsilon(4S)$ 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 $K\pi$ $S$-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 $\cos2\beta$ using the angular and time-dependent asymmetry in $B\to J/\psi\xspace K^{*0}(K_S^0\pi^0$) dec With $\sin 2 \beta$ fixed at its measured value and $\cos 2 \beta$ treated as an in we find $\cos 2\beta=2.72_{-0.79}^{+0.50}\mathrm{(stat)} \pm 0.27\mathrm{(syst)}$, de sign of $\cos 2\beta$ to be positive at 86% CL.