Measurement of the $CP$ asymmetry in $D^0\toπ^+π^-π^0$ decays at Belle II

TL;DR

This work measures the time- and phase-space-integrated CP asymmetry $A_{CP}$ in the decay $D^0 \to \pi^+\pi^-\pi^0$ using 428 fb$^{-1}$ of Belle II data. A flavor tag from $D^{*+} \to D^0\pi^+$ and control samples $D^0 \to K^-\pi^+$ are employed to correct reconstruction-induced asymmetries, with production asymmetries canceled by dividing data into eight bins of $\cos\theta_{\rm CM}^{D^0}$ and averaging symmetric bins. An unbinned extended maximum-likelihood fit to $M$ and $\Delta M$ in each bin yields the raw asymmetries, which are corrected for tag-pion effects and production asymmetries to obtain $A_{CP}$. The result, $A_{CP}(D^0 \to \pi^+\pi^-\pi^0) = (0.29 \pm 0.27 \text{(stat)} \pm 0.13 \text{(syst)})\%$, is the most precise to date and consistent with CP conservation, representing a ~34% improvement in precision over the previous best measurement for similar luminosity. This demonstrates the efficacy of the kinematic weighting and per-bin approach in controlling systematic biases in CP-violation studies in charm.

Abstract

We measure the time- and phase-space-integrated $CP$ asymmetry $A_{CP}$ in $D^0\toπ^+π^-π^0$ decays reconstructed in $e^+e^-\to c\bar c$ events collected by the Belle II experiment from 2019 to 2022. This sample corresponds to an integrated luminosity of 428 fb$^{-1}$. We require $D^0$ mesons to be produced in $D^{*+}\to D^0π^+$ decays to determine their flavor at production. Control samples of $D^0\to K^-π^+$ decays are used to correct for reconstruction-induced asymmetries. The result, $A_{CP}(D^0\toπ^+π^-π^0)=(0.29\pm0.27\pm0.13)\%$, where the first uncertainty is statistical and the second systematic, is the most precise result to date and is consistent with $CP$ conservation.

Figures (7)

• Figure 1: Background-subtracted distributions of the variables used for the kinematic weighting for $\cos{\theta_{\rm CM}\xspace^{D\xspace\xspace^0\xspace}}\xspace\in[-0.208,0)$. Top row: $p_{\rm T}$ and $\cos\theta$ of the tag pion in the signal and tagged samples. Middle row: $p_{\rm T}$ and $\cos\theta$ of the kaon in the untagged and tagged samples. Bottom row: $p_{\rm T}$ and $\cos\theta$ of the pion, and $\cos{\theta_{\rm CM}\xspace^{D\xspace\xspace^0\xspace}}$ of the $D\xspace\xspace^0$ meson, in the untagged and tagged samples. The black lines show the distribution for the sample that we aim to match, i.e., the signal sample in the top row and the tagged sample in the middle and bottom rows. The circles show the distribution for the other sample before (red empty circles) and after (blue filled circles) applying the weights. The bottom plots of each panel show the ratios between circles and black line.
• Figure 2: D0 -> pi+ pi- pi0 sample: distributions of the $D\xspace\xspace^0$ candidate invariant mass (left) and ${\Delta M}$ (right) for $\cos{\theta_{\rm CM}\xspace^{D\xspace\xspace^0\xspace}}\xspace\in[-0.208,0)$, with fit functions overlaid. The middle plots of each panel show the pull (difference between data and fit result divided by the data uncertainty). The bottom plots show the $D\xspace\xspace^0$--$\overline{ D\xspace}{}\xspace^0$ asymmetry of the data (black points) and of the total *PDF (blue line).
• Figure 3: D0 -> pi+ pi- pi0 raw asymmetries from the fit in the eight $\cos{\theta_{\rm CM}\xspace^{D\xspace\xspace^0\xspace}}$ bins. The error bars show statistical uncertainties.
• Figure 4: D0 -> K- pi+ tagged sample: ${\Delta M}$ distribution with fit functions overlaid, for $\cos{\theta_{\rm CM}\xspace^{D\xspace\xspace^0\xspace}}\xspace\in[-0.208,0)$. The middle plot shows the pull, while the bottom plot shows the $D\xspace\xspace^0$--$\overline{ D\xspace}{}\xspace^0$ asymmetry of the data (black points) and the total *PDF (blue line).
• Figure 5: D0 -> K- pi+ untagged sample: $M$ distribution with fit functions overlaid, for $\cos{\theta_{\rm CM}\xspace^{D\xspace\xspace^0\xspace}}\xspace\in[-0.208,0)$. The middle plot shows the pull, while the bottom plot shows the $D\xspace\xspace^0$--$\overline{ D\xspace}{}\xspace^0$ asymmetry of the data (black points) and the total *PDF (blue line).