Evidence forB0→ρ0ρ0Decays and Implications for the Cabibbo-Kobayashi-Maskawa Angleα

We search for the decays $B^0\to {\rho }^0{\rho }^0$, $B^0\to {\rho }^0{f}_0(980)$, and $B^0\to f_0(980)f_0(980)$ in a sample of about $384\times {10}^6$ ${\rm Y}(4S)\to B\overline{B}$ decays collected with the BABAR detector at the PEP-II asymmetric-energy $e^{+}{e}^{-}$ collider at Stanford Linear Accelerator Center. We find evidence for $B^0\to {\rho }^0{\rho }^0$ with $3.5\sigma$ significance and measure the branching fraction $\mathcal{B}=(1.07\pm 0.33\pm 0.19)\times {10}^{-6}$ and longitudinal polarization fraction $f_L=0.87\pm 0.13\pm 0.04$, where the first uncertainty is statistical, and the second is systematic. The uncertainty on the Cabibbo-Kobayashi-Maskawa quark-mixing matrix unitarity angle $\alpha$ due to penguin contributions in $B\to \rho \rho$ decays is 18° at the $1\sigma$ level. We also set upper limits on the $B^0\to {\rho }^0{f}_0(980)$ and $B^0\to f_0(980)f_0(980)$ decay rates.