Measurement of Branching Fraction and Longitudinal Polarization in $B^0\to {\rho }^{+}{\rho }^{-}$ Decays at Belle II

We present a measurement of the branching fraction and longitudinal polarization of $B^0\to {\rho }^{+}{\rho }^{-}$ decays. SuperKEKB electron-positron collision data corresponding to 189~fb${}^{-1}$ of integrated luminosity and containing $198\times {10}^{6}B\bar{B}$ pairs collected with the Belle II detector are used. We obtain \begin{eqnarray*} $\mathcal{B}$(B^0\toρ^+ρ^-) &=& [2.67\pm0.28,($\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}$),\pm0.28,($\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}$)] \times 10^{-5}, \end{eqnarray*} \begin{eqnarray*} f_L &=& 0.956\pm0.035,($\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}$),\pm 0.033,($\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}$), \end{eqnarray*} These results are consistent with previous measurements and can be used to constrain penguin pollution and to extract the quark-mixing angle ${\phi }_2$.