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 D0 → π+π−η, D0 → K+K−η, and D0 → ϕη, using 980 fb−1 of data from the Belle experiment at the KEKB e+e− collider. We obtain$$ {\displaystyle \begin{array}{c}\mathcal{B}\left({D}^0\to {\pi}^{+}{\pi}^{-}\eta \right)=\left[1.22\pm 0.02\left(\mathrm{stat}\right)\pm 0.02\left(\mathrm{syst}\right)\pm 0.03\left({\mathcal{B}}_{\mathrm{ref}}\right)\right]\times {10}^{-3},\\ {}\mathcal{B}\left({D}^0\to {K}^{+}{K}^{-}\eta \right)=\left[{1.80}_{-0.06}^{+0.07}\left(\mathrm{stat}\right)\pm 0.04\left(\mathrm{syst}\right)\pm 0.05\left({\mathcal{B}}_{\mathrm{ref}}\right)\right]\times {10}^{-4},\\ {}\mathcal{B}\left({D}^0\to \phi \eta \right)=\left[1.84\pm 0.09\left(\mathrm{stat}\right)\pm 0.06\left(\mathrm{syst}\right)\pm 0.05\left({\mathcal{B}}_{\mathrm{ref}}\right)\right]\times {10}^{-4},\end{array}} $$ B D 0 → π + π − η = 1.22 ± 0.02 stat ± 0.02 syst ± 0.03 B ref × 10 − 3 , B D 0 → K + K − η = 1.80 − 0.06 + 0.07 stat ± 0.04 syst ± 0.05 B ref × 10 − 4 , B D 0 → ϕη = 1.84 ± 0.09 stat ± 0.06 syst ± 0.05 B ref × 10 − 4 , where the third uncertainty ($$ \mathcal{B} $$ B ref) is from the uncertainty in the branching fraction of the reference mode D0 → K−π+η. The color-suppressed decay D0 → ϕη is observed for the first time, with very high significance. The results for the CP asymmetries are$$ {\displaystyle \begin{array}{c}{A}_{CP}\left({D}^0\ {\pi}^{+}{\pi}^{-}\eta \right)=\left[0.9\pm 1.2\left(\mathrm{stat}\right)\pm 0.5\left(\mathrm{syst}\right)\right]\%,\\ {}{A}_{CP}\left({D}^0\to {K}^{+}{K}^{-}\eta \right)=\left[-1.4\pm 3.3\left(\mathrm{stat}\right)\pm 1.1\left(\mathrm{syst}\right)\right]\%,\\ {} ACP\ \left({D}^0\to \phi \eta \right)=\left[-1.9\pm 4.4\left(\mathrm{stat}\right)\pm 0.6\left(\mathrm{syst}\right)\right]\%.\end{array}} $$ 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 ± 1.1 syst % , ACP D 0 → ϕη = − 1.9 ± 4.4 stat ± 0.6 syst % . The results for D0 → π+π−η are a significant improvement over previous results. The branching fraction and ACP results for D0 → K+K−η, and the ACP result for D0 → ϕη, are the first such measurements. No evidence for CP violation is found in any of these decays.