Measurement of the branching fraction, polarization, and time-dependent $CP$ asymmetry in $B^0\to {\rho }^{+}{\rho }^{-}$ decays and constraint on the CKM angle ${\varphi }_2$

Abstract

We present a measurement of the branching fraction and fraction of longitudinal polarization of $B^0\to {\rho }^{+}{\rho }^{-}$ decays, which have two ${\pi }^0$'s in the final state. We also measure time-dependent {\it CP} violation parameters for decays into longitudinally polarized ${\rho }^{+}{\rho }^{-}$ pairs. This analysis is based on a data sample containing $(387\pm 6)\times 10^6$ ${\rm Y}(4S)$ mesons collected with the Belle~II detector at the SuperKEKB asymmetric-energy $e^{+}{e}^{-}$ collider in 2019-2022. We obtain $\mathcal{B}(B^0\to {\rho }^{+}{\rho }^{-})=(2.89_{-0.22}^{+0.23}{}_{-0.27}^{+0.29})\times 10^{-5},f_L=0.921_{-0.025}^{+0.024}{}_{-0.015}^{+0.017}$, \mbox{$S=-0.26\pm 0.19\pm 0.08$}, and $C=-0.02\pm 0.12_{-0.05}^{+0.06}$, 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 ${\varphi }_2$ and obtain two solutions; the result consistent with other Standard Model constraints is ${\varphi }_2=(92.6_{-4.7}^{+4.5}{)}^{\circ }$.

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