Measurement of branching fractions and search for CP violation in D 0 → π + π − η, D 0 → K + K − η, and D 0 → ϕη at Belle

We measure the branching fractions and CP asymmetries for the singly Cabibbo-suppressed decays D$^{0}$ → π$^{+}$ π$^{-}$ η, D$^{0}$ → K$^{+}$ K$^{-}$ η, and D$^{0}$ → ϕη, using 980 fb$^{-1}$ of data from the Belle experiment at the KEKB e$^{+}$e$^{-}$ collider. We obtain B(D$^{0}$ → π$^{+}$ π$^{-}$ η) = [1.22 ± 0.02 (stat) ± 0.02 (syst) ± 0.03(B$_{ref}$)] x 10$^{-3}$ B(D$^{0}$ → K$^{+}$ K$^{-}$ η) = [1.22$_{-0.06}$$^{+0.07}$(stat) ± 0.04 (syst) ± 0.05(B$_{ref}$)] x 10$^{-4}$ B(D$^{0}$ → ϕη) = [1.84 ± 0.09 (stat) ± 0.06 (syst) ± 0.05(B$_{ref}$)] x 10$^{-4}$ where the third uncertainty (B$_{ref}$) is from the uncertainty in the branching fraction of the reference mode D$^{0}$ → K$^{-}$π$^{+}$η . The color-suppressed decay D$^{0}$ → ϕη is observed for the first time, with very high significance. The results for the CP asymmetries are A$_{CP}$(D$^{0}$ → π$^{+}$ π$^{-}$ η) = [0.9 ± 1.2 (stat) ± 0.5 (syst)]%, A$_{CP}$(D$^{0}$ → K$^{+}$ K$^{-}$ η) = [-1.4 ± 3.3 (stat) ± 0.6 (syst)]%, A$_{CP}$(D$^{0}$ → ϕη) = [-1.9 ± 4.4 (stat) ± 0.6 (syst)]%, The results for D$^{0}$ → π$^{+}$ π$^{-}$ η are a significant improvement over previous results. The branching fraction and A$_{CP}$ results for D$^{0}$ → K$^{+}$ K$^{-}$ η, and the ACP result for D$^{0}$ → ϕη, are the first such measurements. No evidence for CP violation is found in any of these decays.