Study ofB0→ρ+ρ−decays and constraints on the CKM angleα

We present results from an analysis of $B^0\to {\rho }^{+}{\rho }^{-}$ decays using $(383.6\pm 4.2)\times {10}^6$ $B\overline{B}$ pairs collected by the BABAR detector at the PEP-II asymmetric-energy $B$ factory at SLAC. The measurements of the $B^0\to {\rho }^{+}{\rho }^{-}$ branching fraction, longitudinal polarization fraction $f_L$, and the $CP$-violating parameters $S_{\mathrm{long}}$ and $C_{\mathrm{long}}$ are as follows: $\mathcal{B}(B^0\to {\rho }^{+}{\rho }^{-})=(25.5\pm 2.1(\mathrm{stat}{)}_{-3.9}^{+3.6}(\mathrm{syst}))\times {10}^{-6}$, $f_L=0.992\pm 0.024(\mathrm{stat}{)}_{-0.013}^{+0.026}(\mathrm{syst})$, $S_{\mathrm{long}}=-0.17\pm 0.20(\mathrm{stat}{)}_{-0.06}^{+0.05}(\mathrm{syst})$, $C_{\mathrm{long}}=0.01\pm 0.15(\mathrm{stat})\pm 0.06(\mathrm{syst})$. We determine the unitarity triangle angle $\alpha$, using an isospin analysis of $B\to \rho \rho$ decays. One of the two solutions, $\alpha =[73.1,117.0]°$ at 68% confidence level, is compatible with standard model-based fits of existing data. Constraints on the unitarity triangle are also evaluated using an $SU(3)$ symmetry-based approach.