Measurement of branching fractions and search for CP violation in D⁰ → π⁺π⁻η, D⁰ → K⁺K⁻η, and D⁰ → ϕη at Belle

Abstract

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

$$ {\displaystyle \begin{array}{c}\mathcal{B}\left({D}^0\to {\pi}^{+}{\pi}^{-}\eta \right)=\left[1.22\pm 0.02\left(\mathrm{stat}\right)\pm 0.02\left(\mathrm{syst}\right)\pm 0.03\left({\mathcal{B}}_{\mathrm{ref}}\right)\right]\times {10}^{-3},\\ {}\mathcal{B}\left({D}^0\to {K}^{+}{K}^{-}\eta \right)=\left[{1.80}_{-0.06}^{+0.07}\left(\mathrm{stat}\right)\pm 0.04\left(\mathrm{syst}\right)\pm 0.05\left({\mathcal{B}}_{\mathrm{ref}}\right)\right]\times {10}^{-4},\\ {}\mathcal{B}\left({D}^0\to \phi \eta \right)=\left[1.84\pm 0.09\left(\mathrm{stat}\right)\pm 0.06\left(\mathrm{syst}\right)\pm 0.05\left({\mathcal{B}}_{\mathrm{ref}}\right)\right]\times {10}^{-4},\end{array}} $$

where the third uncertainty ($\mathcal{B}$_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

$$ {\displaystyle \begin{array}{c}{A}_{CP}\left({D}^0\ {\pi}^{+}{\pi}^{-}\eta \right)=\left[0.9\pm 1.2\left(\mathrm{stat}\right)\pm 0.5\left(\mathrm{syst}\right)\right]\%,\\ {}{A}_{CP}\left({D}^0\to {K}^{+}{K}^{-}\eta \right)=\left[-1.4\pm 3.3\left(\mathrm{stat}\right)\pm 1.1\left(\mathrm{syst}\right)\right]\%,\\ {} ACP\ \left({D}^0\to \phi \eta \right)=\left[-1.9\pm 4.4\left(\mathrm{stat}\right)\pm 0.6\left(\mathrm{syst}\right)\right]\%.\end{array}} $$

The results for D⁰ → π⁺π⁻η are a significant improvement over previous results. The branching fraction and A_CP 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.