Study of $mathbf{B^{0}rightarrowrho^{+}rho^{-}}$ decays and implications for the CKM angle $mathbf{phi_2}$

We present a measurement of the branching fraction and the longitudinal polarization fraction of $B^{0}rightarrowrho^+rho^-$ decays, as well as the time-dependent $CP$ violating parameters in decays into longitudinally polarized $rho^{+}rho^{-}$ pairs with Belles final data set of $772times 10^6$ $Bbar{B}$ pairs, at the $Upsilon(4S)$ resonance, collected at the asymmetric-energy $e^+ e^-$ collider KEKB. We obtain ${cal B}(B^0 rightarrow rho^+ rho^-)=(28.3pm 1.5;(rm stat) pm 1.5;(rm syst))times 10^{-6}$, $f_L = 0.988pm 0.012;(rm stat ) pm0.023;(rm syst)$, ${cal A}_{CP} = 0.00pm0.10;(rm stat ) pm0.06;(rm syst)$, ${cal S}_{CP} = -0.13pm0.15;(rm stat ) pm0.05;(rm syst).$ We perform an isospin analysis to constrain the CKM angle $phi_2$ and obtain two solutions with begin{eqnarray} phi_{2} = (93.7pm10.6)^{circ}, onumber end{eqnarray} being most compatible with other Standard-Model based fits to the data.