Measurements of Branching Fraction, Polarization, and Charge Asymmetry ofB±→ρ±ρ0and a Search forB±→ρ±f0(980)

We measure the branching fraction ($\mathcal{B}$), polarization ($f_L$), and $CP$ asymmetry ($A_{CP}$) of $B^{\pm }\to {\rho }^{\pm }{\rho }^0$ decays and search for the decay $B^{\pm }\to {\rho }^{\pm }{f}_0(980)$ based on a data sample of $231.8\times {10}^6$ ${\rm Y}(4S)\to B\overline{B}$ decays collected with the BABAR detector at the SLAC PEP-II asymmetric-energy $B$ factory. In $B^{\pm }\to {\rho }^{\pm }{\rho }^0$ decays we measure $\mathcal{B}=(16.8\pm 2.2\pm 2.3)\times {10}^{-6}$, $f_L=0.905\pm {0.042}_{-0.027}^{+0.023}$, and $A_{CP}=-0.12\pm 0.13\pm 0.10$, and find an upper limit on the branching fraction of $B^{\pm }\to {\rho }^{\pm }{f}_0(980)(\to {\pi }^{+}{\pi }^{-})$ decays of $1.9\times {10}^{-6}$ at 90% confidence level.