Revisiting the $B^{0} \to \pi^{0}\pi^{0} $ decays in the perturbative QCD approach

We recalculate the branching ratio and CP asymmetry for $\bar{B}^{0} (B^{0})\to \pi^{0}\pi^{0}$ decays in the Perturbative QCD approach. In this approach, we consider all the possible diagrams including non-factorizable contributions and annihilation contributions. We obtain $Br(\bar{B}^{0} (B^{0})\to \pi^{0}\pi^{0})=(1.17_{-0.12}^{+0.11})\times 10^{-6}$. Our result is in agreement with the latest measured branching ratio of $B^{0}\to\pi^{0}\pi^{0}$ by the Belle and HFAG Collaborations. We also predict large direct CP asymmetry and mixing CP asymmetry in $B^{0}\to\pi^{0}\pi^{0}$ decays, which can be tested by the coming Belle-II experiments.