We present a measurement of the decay amplitudes in $B\to J/\psi K^{*}\left(892\right)$ channels using $20.7\mathrm{fb}{}^{-1\mathrm{}}$ of data collected at the $\Upsilon \left(4S\right)$ resonance with the BABAR detector at PEP-II. We measure a $P$-wave fraction $R_{\perp }=(16.0\pm 3.2\pm 1.4)\%$ and a longitudinal polarization fraction $(59.7\pm 2.8\pm 2.4)\%$. The measurement of a relative phase that is neither 0 nor $\pi$, ${\phi }_{\parallel }=2.50\mathrm{}\pm 0.20\pm 0.08$ radians, favors a departure from the factorization hypothesis. Although the decay $B\to J/\psi K\pi$ proceeds mainly via $K^{*}\left(892\right)$, there is also evidence for $K_2^{*}\left(1430\right)$ and $K\pi$ $S$-wave contributions.

• Received 20 July 2001

DOI:https://doi.org/10.1103/PhysRevLett.87.241801