Prospects for ${B}_{(s)}^0 $ → π$^0$π$^0$ and ${B}_{(s)}^0 $ → ηη modes and corresponding CP asymmetries at Tera-Z
The physics potential of measuring $B^0_{(s)}$ → $π^0π^0$ and $B^0_{(s)}$ → $ηη$ decays via four-photon final states at Tera-Z phase of CEPC or FCC-ee is investigated in this paper. We propose an electromagnetic calorimeter (ECAL) with both high energy resolution and excellent separation power to efficiently reconstruct $π^0$ and $η$ from hadronic final states with high photon multiplicity. The resulting B-meson mass resolution is approximately 30 MeV, allowing 3 $σ$ separation between B 0 and $B^0_{(s)}$. With the assistance of the b-jet tagging, the relative sensitivities to B 0 → $π^0π^0$, $B^0_{(s)}$ → $π^0π^0$, B 0 → $ηη$, and $B^0_{(s)}$ → $ηη$ signal strengths at Tera-Z are projected as 0.45%, 4.5%, 18%, and 0.95%, respectively. Their dependence on various detector performances is also discussed. In addition, B 0 → $π^0π^0$ and its two isospin-related modes are paid special attention due to their roles in the determination of the CKM angle α (Φ 2 ). The anticipated precisions of their branching-ratio and CP-asymmetry measurements at Tera-Z are evaluated. We show that the measurement of the time-integrated B 0 → $π^0π^0$ CP asymmetry at Tera-Z is complementary to B-factory ones. The precision on α combining Z- and B-factory results reaches 0.4°, lower than the systematic uncertainties attached to isospin breaking.