Searches for $CP$ violation in the two-body decays $D_{(s)}^{+}\rightarrow h^{+}\pi^{0}$ and $D_{(s)}^{+} \rightarrow h^{+}\eta$ (where $h^{+}$ denotes a $\pi^{+}$ or $K^{+}$ meson) are performed using $pp$ collision data collected by the LHCb experiment corresponding to either 9 fb$^{-1}$ or 6 fb$^{-1}$ of integrated luminosity. The $\pi^{0}$ and $\eta$ mesons are reconstructed using the $e^{+}e^{-}\gamma$ final state, which can proceed as three-body decays $\pi^{0}\rightarrow e^{+}e^{-}\gamma$ and $\eta \rightarrow e^{+}e^{-}\gamma$, or via the two-body decays $\pi^{0}\rightarrow \gamma\gamma$ and $\eta\rightarrow\gamma\gamma$ followed by a photon conversion. The measurements are made relative to the control modes $D_{(s)}^{+}\rightarrow K_{S}^{0} h^{+}$ to cancel the production and detection asymmetries. The $CP$ asymmetries are measured to be \begin{align} \mathcal{A}_{CP}(D^{+}\rightarrow \pi^{+}\pi^{0}) &= (-1.3 \pm 0.9 \pm 0.6 )\%, \end{align} \begin{align} \mathcal{A}_{CP}(D^{+}\rightarrow K^{+}\pi^{0}) &= (-3.2 \pm 4.7 \pm 2.1 )\%, \end{align} \begin{align} \mathcal{A}_{CP}(D^{+}\rightarrow \pi^{+}\eta) &= (-0.2 \pm 0.8 \pm 0.4 )\%, \end{align} \begin{align} \mathcal{A}_{CP}(D^{+}\rightarrow K^{+}\eta) &= (-6 \pm 10 \pm 4 )\%, \end{align} \begin{align} \mathcal{A}_{CP}(D_{s}^{+}\rightarrow K^{+}\pi^{0}) &= (-0.8 \pm 3.9 \pm 1.2 )\%, \end{align} \begin{align} \mathcal{A}_{CP}(D_{s}^{+}\rightarrow \pi^{+}\eta) &= (0.8 \pm 0.7 \pm 0.5 )\%, \end{align} \begin{align} \mathcal{A}_{CP}(D_{s}^{+}\rightarrow K^{+}\eta) &= (0.9 \pm 3.7 \pm 1.1 )\%, \end{align} where the first uncertainties are statistical and the second systematic. These results are consistent with no $CP$ violation and mostly constitute the most precise measurements of $\mathcal{A}_{CP}$ in these decay modes to date.
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Processes that contribute to the studied decays at tree-level include (top left) colour-favoured, (top right) colour-suppressed and (bottom left) annihilation topology decays. Contributions can also be received at loop-level from processes such as (bottom right) penguin topology decays. |
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Distribution of the (left) $m(h^{+}\pi ^0 )$ and (right) $m( e ^+ e ^- \gamma)$ mass for (top) $ D_{(s)}^{+} \rightarrow \pi ^+ \pi ^0 $ and (bottom) $ D_{(s)}^{+} \rightarrow K ^+ \pi ^0 $ candidates, summed over all categories of the simultaneous fit. Projections of the total fit result and individual fit components are overlaid. This includes $ D ^+ \rightarrow h^{+}\pi ^0 $ decays in dashed red, $ D ^+_ s \rightarrow h^{+}\pi ^0 $ decays in solid grey, pure combinatorial decays in dashed black and real- $\pi ^0$ combinatorial background in dotted green. The misidentification background is too small to be seen in these distributions. |
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Distribution of the (left) $m(h^{+}\eta )$ and (right) $m( e ^+ e ^- \gamma)$ mass for (top) $ D_{(s)}^{+} \rightarrow \pi ^+ \eta $ and (bottom) $ D_{(s)}^{+} \rightarrow K ^+ \eta $ candidates, summed over all categories of the simultaneous fit. Projections of the total fit result and individual fit components are overlaid. This includes $ D ^+ \rightarrow h^{+}\eta $ decays in dashed red, $ D ^+_ s \rightarrow h^{+}\eta $ decays in solid grey, pure combinatorial decays in dashed black and partially reconstructed background in dotted magenta. The misidentification background is too small to be seen in these distributions. |
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Distributions of the (left) $m( K ^0_{\mathrm{S}} \pi ^+ )$ and (right) $m( K ^0_{\mathrm{S}} K ^+ )$ mass of control mode candidates in (top) Run 1 and (bottom) Run 2. The total PDF and individual fit components are overlaid, including $ D ^+ \rightarrow K ^0_{\mathrm{S}} h^{+} $ decays in dashed red, $ D ^+_ s \rightarrow K ^0_{\mathrm{S}} h^{+} $ decays in solid grey and background decays in dashed black. |
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Animated gif made out of all figures. |
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Signal yields in each running period and corresponding raw asymmetries for $ D_{(s)}^{+} \rightarrow h^{+}\pi ^0 $ and $ D_{(s)}^{+} \rightarrow h^{+}\eta $ candidates. The uncertainties are statistical. |
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Correlation coefficients between the raw asymmetries determined for $ D_{(s)}^{+} \rightarrow h^{+}\pi ^0 $ and $ D_{(s)}^{+} \rightarrow h^{+}\eta $ decays. |
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Absolute systematic uncertainties (%) on the $ C P$ asymmetries for $ D ^{+}_{(s)} \rightarrow h^+\pi ^0 $ decays. |
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Absolute systematic uncertainties (%) on the $ C P$ asymmetries for $ D ^{+}_{(s)} \rightarrow h^+\eta $ decays. |
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Final $\mathcal{A}_ C P $ (%) results for the $ D_{(s)}^{+} \rightarrow h^{+}\pi ^0 $ modes. The uncertainties of $\mathcal{A}_{ C P }( D_{(s)}^{+} \rightarrow h^{+}\pi ^0 )$ are statistical and systematic respectively. The uncertainties of $A_{\text{Raw}}( D_{(s)}^{+} \rightarrow h^{+}\pi ^0 )$ are purely statistical. The uncertainties of $A_{\text{Mix}}(K^0)$ are systematic. Externally measured values of $\mathcal{A}_{ C P }( D_{(s)}^{+} \rightarrow K ^0_{\mathrm{S}} h^{+} )$ are taken from Refs. [18,37,38,39,40,41]. For comparison the unweighted control asymmetries are $\mathcal{A}_{\text{Raw}}( D ^+ \rightarrow K ^0_{\mathrm{S}} \pi ^+ ) = -0.45 \pm 0.02$, $\mathcal{A}_{\text{Raw}}( D ^+ \rightarrow K ^0_{\mathrm{S}} K ^+ ) = 0.47 \pm 0.05$ and $\mathcal{A}_{\text{Raw}}( D ^+_ s \rightarrow K ^0_{\mathrm{S}} K ^+ ) = 0.51 \pm 0.04$. |
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Final $\mathcal{A}_ C P $ (%) results for the $ D_{(s)}^{+} \rightarrow h^{+}\eta $ modes. The uncertainties of $\mathcal{A}_{ C P }( D_{(s)}^{+} \rightarrow h^{+}\eta )$ are statistical and systematic respectively. The uncertainties of $A_{\text{Raw}}( D_{(s)}^{+} \rightarrow h^{+}\eta )$ are purely statistical. The uncertainties of $A_{\text{Mix}}(K^0)$ are systematic. Externally measured values of $\mathcal{A}_{ C P }( D_{(s)}^{+} \rightarrow K ^0_{\mathrm{S}} h^{+} )$ are taken from Refs. [18,37,38,39,40,41]. For comparison the unweighted control asymmetries are $\mathcal{A}_{\text{Raw}}( D ^+ \rightarrow K ^0_{\mathrm{S}} \pi ^+ ) = -0.45 \pm 0.02$, $\mathcal{A}_{\text{Raw}}( D ^+_ s \rightarrow K ^0_{\mathrm{S}} \pi ^+ ) = -0.13 \pm 0.17$, $\mathcal{A}_{\text{Raw}}( D ^+ \rightarrow K ^0_{\mathrm{S}} K ^+ ) = 0.47 \pm 0.05$ and $\mathcal{A}_{\text{Raw}}( D ^+_ s \rightarrow K ^0_{\mathrm{S}} K ^+ ) = 0.51 \pm 0.04$. |
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| Supplementary material full pdf |
supple[..].pdf [461 KiB] |
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Created on 10 August 2024.