Study of the DecayB0(B¯0)→ρ+ρ−, and Constraints on the Cabibbo-Kobayashi-Maskawa Angleα

Using a data sample of $89\times {10}^6$ ${\rm Y}(4S)\to B\overline{B}$ decays collected with the BABAR detector at the PEP-II asymmetric $B$ Factory at SLAC, we measure the $B^0({\overline{B}}^0)\to {\rho }^{+}{\rho }^{-}$ branching fraction as $[30\pm 4(\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t})\pm 5(\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t})]\times {10}^{-6}$ and a longitudinal polarization fraction of $f_L=0.99\pm 0.03(\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}{)}_{-0.03}^{+0.04}(\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t})$. We measure the time-dependent-asymmetry parameters of the longitudinally polarized component of this decay as $C_L=-0.17\pm 0.27(\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t})\pm 0.14(\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t})$ and $S_L=-0.42\pm 0.42(\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t})\pm 0.14(\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t})$. We exclude values of $\alpha$ between 19° and 71° (90% C.L.).