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

We present results on B {yields} J/{psi} K{pi} decays using e{sup +}e{sup -} 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 cos 2{beta} using the angular and time-dependent asymmetry in B {yields} J/{psi} K*{sup 0} (K{sub S}{sup 0}{pi}{sup 0}) decays. With sin2{beta} fixed at its measured value and cos2{beta} treated as an independent parameter, we find cos 2{beta} = 2.72{sub -0.79}{sup +0.50}(stat) {+-} 0.27(syst), determining the sign of cos 2{beta} to be positive at 86% CL.