Improved Measurement of the Cabibbo-Kobayashi-Maskawa Angle<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>α</mml:mi></mml:math>Using<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mi>B</mml:mi><mml:mn>0</mml:mn></mml:msup><mml:mo stretchy="false">(</mml:mo><mml:mover accent="true"><mml:mi>B</mml:mi><mml:mo>¯</mml:mo></mml:mover><mml:mo stretchy="false">)</mml:mo><mml:mo>→</mml:mo><mml:msup><mml:mi>ρ</mml:mi><mml:mo>+</mml:mo></mml:msup><mml:msup><mml:mi>ρ</mml:mi><mml:mo>−</mml:mo></mml:msup></mml:math>Decays

We present results from an analysis of ${B}^{0}({\overline{B}}^{0})\ensuremath{\rightarrow}{\ensuremath{\rho}}^{+}{\ensuremath{\rho}}^{\ensuremath{-}}$ using $232\ifmmode\times\else\texttimes\fi{}{10}^{6}$ $\ensuremath{\Upsilon}(4S)\ensuremath{\rightarrow}B\overline{B}$ decays collected with the BABAR detector at the PEP-II asymmetric-energy $B$ factory at SLAC. We measure the longitudinal polarization fraction ${f}_{L}=0.978\ifmmode\pm\else\textpm\fi{}0.014(\mathrm{stat})\genfrac{}{}{0}{}{+0.021}{\ensuremath{-}0.029}(\mathrm{syst})$ and the $CP$-violating parameters ${S}_{L}=\ensuremath{-}0.33\ifmmode\pm\else\textpm\fi{}0.24(\mathrm{stat})\genfrac{}{}{0}{}{+0.08}{\ensuremath{-}0.14}(\mathrm{syst})$ and ${C}_{L}=\ensuremath{-}0.03\ifmmode\pm\else\textpm\fi{}0.18(\mathrm{stat})\ifmmode\pm\else\textpm\fi{}0.09(\mathrm{syst})$. Using an isospin analysis of $B\ensuremath{\rightarrow}\ensuremath{\rho}\ensuremath{\rho}$ decays, we determine the unitarity triangle parameter $\ensuremath{\alpha}$. The solution compatible with the standard model is $\ensuremath{\alpha}=(100\ifmmode\pm\else\textpm\fi{}13)\ifmmode^\circ\else\textdegree\fi{}$.

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