Measurement of the branching fraction, polarization, and time-dependent $CP$ asymmetry in $B^0 \to ρ^+ρ^-$ decays and constraint on the CKM angle $φ_2$

Abstract: We present a measurement of the branching fraction and fraction of longitudinal polarization of $B⁰ \to \rho⁺ \rho<sup>-$ decays, which have two $\pi<sup>0$'s in the final state. We also measure time-dependent {\it CP} violation parameters for decays into longitudinally polarized $\rho⁺ \rho<sup>-$ pairs. This analysis is based on a data sample containing $(387\pm6) \times 10<sup>6$ $\Upsilon(4S)$ mesons collected with the Belle~II detector at the SuperKEKB asymmetric-energy $e<sup>+e<sup>-$ collider in 2019-2022. We obtain $$\mathcal{B}(B^{0\to\rho^{+\rho^-)}} = (2.89 ^{{+0.23}_{-0.22}} {}^{{+0.29}_{-0.27})} \times 10^{-5}, f_{L} = 0.921 ^{{+0.024}_{-0.025}} {}<sup>{+0.017}_{-0.015}$$, \mbox{$S = -0.26\pm0.19\pm0.08$}, and $C = -0.02\pm0.12<sup>{+0.06}_{-0.05}$, where the first uncertainties are statistical and the second are systematic. We use these results to perform an isospin analysis to constrain the CKM angle $\phi_2$ and obtain two solutions; the result consistent with other Standard Model constraints is $\phi_2 = (92.6<sup>{+4.5}_{-4.7})<sup>\circ$.