Requirement of the single-track selection of the first-stage software trigger in the $\chi^2_{\text{IP}}$ vs. $ p_{\mathrm{T}}$ plane, for the three configurations employed during data taking. The dashed region is excluded by the loosest configuration.

Distribution of $ m( D ^0 \pi ^{+}_{\mathrm{ \scriptscriptstyle tag}} )$ for (top) $ D ^0 \rightarrow K ^- \pi ^+ $ , (left) $ D ^0 \rightarrow K ^+ K ^- $ and (right) $ D ^0 \rightarrow \pi ^+ \pi ^- $ candidates. The signal window and the lateral window employed to remove the combinatorial background (grey filled area) are delimited by the vertical dashed lines. Fit projections are overlaid.

Distribution of $ m( h ^+ h ^- )$ for (top) $ D ^0 \rightarrow K ^- \pi ^+ $ , (left) $ D ^0 \rightarrow K ^+ K ^- $ and (right) $ D ^0 \rightarrow \pi ^+ \pi ^- $ background-subtracted candidates. The signal window is delimited by the vertical dashed lines.

(Left) sum and (right) asymmetry of the distributions of the momentum of $\pi ^{+}_{\mathrm{ \scriptscriptstyle tag}}$ and $\pi ^{-}_{\mathrm{ \scriptscriptstyle tag}}$ candidates, projected on the (top) $k$ vs. $\theta_x$ and (bottom) $\theta_y$ vs. $\theta_x$ planes, for the $ D ^0 \rightarrow K ^- \pi ^+ $ candidates collected in 2017 with the Mag Up polarity. The angles $\theta_{x(y)}$ and the curvature $k$ are defined in the text. The asymmetries during the other data-taking years are similar, and opposite in sign for the data collected with the MagDown polarity. The regions of the distributions with asymmetries whose magnitude is larger than 20% are plotted with the same colour as $\pm 20\%$. These regions are discarded from the data sample after the kinematic weighting.

(Top) Normalised distributions of the $ D ^0$ transverse momentum, in different colours for each decay-time interval. Decay time increases from blue to yellow colour. (Centre) Asymmetry between the normalised $ p_{\mathrm{T}} $ distributions of $ D ^0$ and $\overline{ D } {}^0$ mesons. (Bottom) Linear fit to the time-dependent asymmetry (red) before and (black) after the kinematic weighting. All plots correspond to $ D ^0 \rightarrow K ^- \pi ^+ $ candidates recorded with the Mag Up polarity in (left) 2016 and (right) 2017.

Results of the fits to the time-dependent asymmetry for each subsample, for (top) $ K ^- \pi ^+ $ , (bottom left) $ K ^+ K ^- $ and (bottom right) $\pi ^+ \pi ^- $ final states. In the $y$-axis labels, the data-taking year is abbreviated with the last two digits only and the magnet polarity Mag Up ( MagDown ) is abbreviated as "Up" ("Dw"), while "Avg." denotes the weighted average. The fit $\chi^2/\mathrm{ndf}$ are reported on the right of each plot. Empty red squares and solid black dots correspond to data before and after the equalisation of the $\pi ^{+}_{\mathrm{ \scriptscriptstyle tag}}$ and $ D ^0$ kinematics, respectively, and prior to subtracting the contribution of secondary decays described in Sect. 6.

Impact parameter distribution of the $ D ^0 \rightarrow K ^- \pi ^+ $ candidates for the (top) first, (left) middle and (right) last decay-time interval. The projections of the two-dimensional template fit are superimposed.

(Left) Fraction of secondary decays from $ B $ mesons measured in the template fit. Only statistical uncertainties are displayed. (Right) Measured asymmetry, after the kinematic weighting, of data with $\mathrm{IP}( D ^0 ) > 100 \upmu\text{m} $ in the enlarged $ m( D ^0 \pi ^{+}_{\mathrm{ \scriptscriptstyle tag}} )$ signal window. The fit of a constant function is shown in red, while the $1\sigma$ band corresponding to the possible impact of $ B ^0$ mixing is plotted in cyan.

Asymmetry, $A_\mathrm{sig}(t)$, of $ D ^0 \rightarrow K ^- \pi ^+ $ candidates as a function of decay time. A linear fit is superimposed. The $\chi^2/\mathrm{ndf}$ of the fit is $17/19$.

Relative shift of the $ D ^{*+}$ and $ D ^{*-}$ mass peaks as a function of decay time for the $ K ^- \pi ^+ $ decay channel.

Distributions of $ m( h ^+ h ^- )$ of (top) $ K ^- \pi ^+ $ , (left) $ K ^+ K ^- $ and (right) $\pi ^+ \pi ^- $ final states, with the results superimposed. The background components are stacked; the $ m( h ^+ h ^- )$ template PDF of the $ D ^+_ s \rightarrow K ^+ K ^- \pi ^+ $ decay has a negative contribution to the left of the known $ D ^0$ mass due to the subtraction of the $ m( D ^0 \pi ^{+}_{\mathrm{ \scriptscriptstyle tag}} )$ background. The vertical dashed lines delimit the signal region.

Asymmetry, $A_\mathrm{sig}(t)$, as a function of decay time for (top) $ D ^0 \rightarrow K ^+ K ^- $ and (bottom) $ D ^0 \rightarrow \pi ^+ \pi ^- $ candidates. A linear fit is superimposed. The $\chi^2/\mathrm{ndf}$ of the fits are $15/19$ and $21/19$, respectively.

Animated gif made out of all figures.

Summary of the systematic uncertainties, in units of $10^{-4}$. The statistical uncertainties are reported for comparison.

Supplementary material full pdf