Measurement of the Decay Amplitudes and Branching Fractions of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="italic">B</mml:mi><mml:mspace/><mml:mo>→</mml:mo><mml:mspace/><mml:mi mathvariant="italic">J</mml:mi><mml:mi mathvariant="italic">/</mml:mi><mml:mi>ψ</mml:mi><mml:mi/><mml:mrow><mml:msup><mml:mrow><mml:mi>K</mml:mi></mml:mrow><mml:mrow><mml:mi>*</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:math>and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="italic">B</mml:mi><mml:mspace/><mml:mo>→</mml:mo><mml:mspace/><mml:mi mathvariant="italic">J</mml:mi><mml:mi mathvariant="italic">/</mml:mi><mml:mi>ψ</mml:mi><mml:mi/><mml:mi mathvariant="italic">K</mml:mi></mml:math>Decays

Using data taken with the CLEO II detector at the Cornell Electron Storage Ring, we present the first full angular analysis in the color-suppressed modes ${B}^{0}\ensuremath{\rightarrow}J/\ensuremath{\psi}{K}^{*0}$ and ${B}^{+}\ensuremath{\rightarrow}J/\ensuremath{\psi}{K}^{*+}$. This leads to a complete determination of the decay amplitudes of these modes including the longitudinal polarization ${\ensuremath{\gamma}}_{L}/\ensuremath{\gamma}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.52\ifmmode\pm\else\textpm\fi{}0.07\ifmmode\pm\else\textpm\fi{}0.04$ and the $P$ wave component $|P{|}^{2}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.16\ifmmode\pm\else\textpm\fi{}0.08\ifmmode\pm\else\textpm\fi{}0.04$. In addition, we update the branching fractions for $B\ensuremath{\rightarrow}J/\ensuremath{\psi}K$ and $B\ensuremath{\rightarrow}J/\ensuremath{\psi}{K}^{*}$.