Amplitude Analysis of the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mi>B</mml:mi><mml:mo>±</mml:mo></mml:msup><mml:mo>→</mml:mo><mml:mi>φ</mml:mi><mml:msup><mml:mi>K</mml:mi><mml:mo>*</mml:mo></mml:msup><mml:mo stretchy="false">(</mml:mo><mml:mn>892</mml:mn><mml:msup><mml:mo stretchy="false">)</mml:mo><mml:mo>±</mml:mo></mml:msup></mml:math>Decay

We perform an amplitude analysis of ${B}^{\ifmmode\pm\else\textpm\fi{}}\ensuremath{\rightarrow}\ensuremath{\varphi}(1020){K}^{*}(892{)}^{\ifmmode\pm\else\textpm\fi{}}$ decay with a sample of about $384\ifmmode\times\else\texttimes\fi{}{10}^{6}$ $B\overline{B}$ pairs recorded with the BABAR detector. Overall, twelve parameters are measured, including the fractions of longitudinal ${f}_{L}$ and parity-odd transverse ${f}_{\ensuremath{\perp}}$ amplitudes, branching fraction, strong phases, and six parameters sensitive to $CP$ violation. We use the dependence on the $K\ensuremath{\pi}$ invariant mass of the interference between the ${J}^{P}={1}^{\ensuremath{-}}$ and ${0}^{+}$ $K\ensuremath{\pi}$ components to resolve the discrete ambiguity in the determination of the strong and weak phases. Our measurements of ${f}_{L}=0.49\ifmmode\pm\else\textpm\fi{}0.05\ifmmode\pm\else\textpm\fi{}0.03$, ${f}_{\ensuremath{\perp}}=0.21\ifmmode\pm\else\textpm\fi{}0.05\ifmmode\pm\else\textpm\fi{}0.02$, and the strong phases point to the presence of a substantial helicity-plus amplitude from a presently unknown source.

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