The $CP$-even fractions ($F_{ +}$) of the decays $D^0\to\pi^{ +}\pi^{ -}\pi^{ 0}$ and $D^0\to K^{ +}K^{ -}\pi^{ 0}$ are measured with a quantum-correlated $\psi(3770)\to D\bar{ D}$ data sample collected by the BESIII experiment corresponding to an integrated luminosity of 7.93 $\mathrm{ fb}^{ -1}$. The results are $F_{ +}^{ \pi^{ +}\pi^{ -}\pi^{ 0}}=0.9406\pm0.0036\pm0.0021$ and $F_{ +}^{ K^{ +}K^{ -}\pi^{ 0}}=0.631\pm0.014\pm0.011$, where the first uncertainties are statistical and the second systematic. These measurements are consistent with the previous determinations, and the uncertainties for $F_{ +}^{ \pi^{ +}\pi^{ -}\pi^{ 0}}$ and $F_{ +}^{ K^{ +}K^{ -}\pi^{ 0}}$ are reduced by factors of 3.9 and 2.6, respectively. The reported results provide important inputs for the precise measurement of the angle $\gamma$ of the Cabibbo-Kobayashi-Maskawa matrix and indirect $CP$ violation in charm mixing.
Categories: hep-ex