Measurements of the $CP$-even fractions of $D^0\to\pi^{+}\pi^{-}\pi^{0}$ and $D^0\to K^{+}K^{-}\pi^{0}$ at BESIII

TL;DR

This paper measures the $CP$-even fractions of specific $D^0$ decays using quantum-correlated data from BESIII, significantly improving the precision of these measurements, which are crucial for understanding $CP$ violation and the CKM angle $oldsymbol{ extgamma}$.

Contribution

It provides the most precise measurements to date of the $CP$-even fractions for $D^0 o extpi^{+} extpi^{-} extpi^{0}$ and $D^0 o K^{+}K^{-} extpi^{0}$ decays, aiding $CP$ violation studies.

Findings

$F_{+}^{ extpi^{+} extpi^{-} extpi^{0}}=0.9406\

$F_{+}^{K^{+}K^{-} extpi^{0}}=0.631$

Uncertainties reduced by factors of 3.9 and 2.6 respectively.

Abstract

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.