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CMS-PAS-BPH-23-005

Search for $CP$ violation in $\mathrm{D}^0\to\mathrm{K}^0_{\mathrm{S}}\mathrm{K}^0_{\mathrm{S}}$ decay from proton-proton collisions at 13 TeV

CMS Collaboration

26 March 2024

Abstract: A search is reported for $CP$ violation in the $\mathrm{D}^0\to\mathrm{K}^0_{\mathrm{S}}\mathrm{K}^0_{\mathrm{S}}$ decay, using data collected from proton-proton collisions at $\sqrt{s} =$ 13 TeV recorded by the CMS experiment in 2018. A dedicated data set of about 10 billion events containing a pair of b hadrons, nearly all of which decay to charm hadrons, is used. The flavor of the neutral D meson is determined by the pion charge in the reconstructed decays $\mathrm{D}^{*+}\to\mathrm{D}^0\pi^+$ and $\mathrm{D}^{*-}\to\overline{\mathrm{D}}^0\pi^-$. The $CP$ asymmetry in $\mathrm{D}^0\to\mathrm{K}^0_{\mathrm{S}}\mathrm{K}^0_{\mathrm{S}}$ is measured to be $A_{CP}(\mathrm{K}^0_{\mathrm{S}}\mathrm{K}^0_{\mathrm{S}}) =$ 6.2 $\pm$ 3.0 (stat) $\pm$ 0.2 (syst) $\pm$ 0.8 $(A_{CP}(\mathrm{K}^0_{\mathrm{S}}\pi^+\pi^-))$ %, where the last uncertainty is the $CP$ asymmetry in the $\mathrm{D}^0\to\mathrm{K}^0_{\mathrm{S}}\pi^+\pi^-$ decay. This result is consistent with no $CP$ violation within 2 standard deviations. This is the first measurement of $CP$ violation in the charm sector by the CMS experiment, and the first measurement of $CP$ asymmetry in the fully hadronic final state performed by CMS at the nominal LHC luminosity, using the new data parking technique.

Links: CDS record (PDF) ; CADI line (restricted) ; These preliminary results are superseded in this paper, Submitted to EPJC. The superseded preliminary plots can be found here.

Figures
png pdf	Figure 1: The decay of neutral charm meson $\mathrm{D^0}$ (top) or $\overline{\mathrm{D}}^{0}$ (bottom) to two neutral kaons: exchange diagram (left) and penguin annihilation diagram (right).
png pdf	Figure 1-a: The decay of neutral charm meson $\mathrm{D^0}$ (top) or $\overline{\mathrm{D}}^{0}$ (bottom) to two neutral kaons: exchange diagram (left) and penguin annihilation diagram (right).
png pdf	Figure 1-b: The decay of neutral charm meson $\mathrm{D^0}$ (top) or $\overline{\mathrm{D}}^{0}$ (bottom) to two neutral kaons: exchange diagram (left) and penguin annihilation diagram (right).
png pdf	Figure 1-c: The decay of neutral charm meson $\mathrm{D^0}$ (top) or $\overline{\mathrm{D}}^{0}$ (bottom) to two neutral kaons: exchange diagram (left) and penguin annihilation diagram (right).
png pdf	Figure 1-d: The decay of neutral charm meson $\mathrm{D^0}$ (top) or $\overline{\mathrm{D}}^{0}$ (bottom) to two neutral kaons: exchange diagram (left) and penguin annihilation diagram (right).
png pdf	Figure 2: Simultaneous fit of the $\mathrm{D}^{*+}$ (left) and $\mathrm{D}^{*-}$ (right) candidate invariant mass distributions in the $\mathrm{K^0_S}\pi^{+}\pi^{-}$ channel.
png pdf	Figure 2-a: Simultaneous fit of the $\mathrm{D}^{*+}$ (left) and $\mathrm{D}^{*-}$ (right) candidate invariant mass distributions in the $\mathrm{K^0_S}\pi^{+}\pi^{-}$ channel.
png pdf	Figure 2-b: Simultaneous fit of the $\mathrm{D}^{*+}$ (left) and $\mathrm{D}^{*-}$ (right) candidate invariant mass distributions in the $\mathrm{K^0_S}\pi^{+}\pi^{-}$ channel.
png pdf	Figure 3: Results of the 2D fit to $m(\mathrm{D}\pi^{\pm}) \times\ m(\mathrm{K^0_S}\mathrm{K^0_S})$ distribution for the signal channel, for $\mathrm{D}^{*+}$ (left) and $\mathrm{D}^{*-}$ (right) candidates: projections of the 2D fit on the $m(\mathrm{D}\pi^{\pm})$ (top) and $m(\mathrm{K^0_S}\mathrm{K^0_S})$ (bottom) axes.
png pdf	Figure 3-a: Results of the 2D fit to $m(\mathrm{D}\pi^{\pm}) \times\ m(\mathrm{K^0_S}\mathrm{K^0_S})$ distribution for the signal channel, for $\mathrm{D}^{*+}$ (left) and $\mathrm{D}^{*-}$ (right) candidates: projections of the 2D fit on the $m(\mathrm{D}\pi^{\pm})$ (top) and $m(\mathrm{K^0_S}\mathrm{K^0_S})$ (bottom) axes.
png pdf	Figure 3-b: Results of the 2D fit to $m(\mathrm{D}\pi^{\pm}) \times\ m(\mathrm{K^0_S}\mathrm{K^0_S})$ distribution for the signal channel, for $\mathrm{D}^{*+}$ (left) and $\mathrm{D}^{*-}$ (right) candidates: projections of the 2D fit on the $m(\mathrm{D}\pi^{\pm})$ (top) and $m(\mathrm{K^0_S}\mathrm{K^0_S})$ (bottom) axes.
png pdf	Figure 3-c: Results of the 2D fit to $m(\mathrm{D}\pi^{\pm}) \times\ m(\mathrm{K^0_S}\mathrm{K^0_S})$ distribution for the signal channel, for $\mathrm{D}^{*+}$ (left) and $\mathrm{D}^{*-}$ (right) candidates: projections of the 2D fit on the $m(\mathrm{D}\pi^{\pm})$ (top) and $m(\mathrm{K^0_S}\mathrm{K^0_S})$ (bottom) axes.
png pdf	Figure 3-d: Results of the 2D fit to $m(\mathrm{D}\pi^{\pm}) \times\ m(\mathrm{K^0_S}\mathrm{K^0_S})$ distribution for the signal channel, for $\mathrm{D}^{*+}$ (left) and $\mathrm{D}^{*-}$ (right) candidates: projections of the 2D fit on the $m(\mathrm{D}\pi^{\pm})$ (top) and $m(\mathrm{K^0_S}\mathrm{K^0_S})$ (bottom) axes.
png pdf	Figure 4: Results of the 2D fit to $m(\mathrm{D}\pi^{\pm}):m(\mathrm{K^0_S}\mathrm{K^0_S})$ for the signal channel in measured data, $\mathrm{D}^{*+}$ candidates. Top row: the projections of the 2D fit on $m(\mathrm{D}\pi^{\pm})$ in the ranges of $m(\mathrm{K^0_S}\mathrm{K^0_S})$: region of $\mathrm{D}_{s}^{\pm}\to\mathrm{K^0_S}\mathrm{K^0_S}\pi^{\pm}$ contamination (left) and signal region of $\mathrm{K^0_S}\mathrm{K^0_S}$ (right). Middle row: projections of the 2D fit on $m(\mathrm{D}\pi^{\pm})$ in the ranges of $m(\mathrm{K^0_S}\mathrm{K^0_S})$: left sideband (left) and right sideband (right). Bottom row: projections of the 2D fit on $m(\mathrm{K^0_S}\mathrm{K^0_S})$ in the ranges of $m(\mathrm{D}\pi^{\pm})$: left sideband (left), signal region of $\mathrm{D^0}\pi^{+}$ (center), and right sideband (right). The green line corresponds to the signal component, the blue short-dashed line shows the combinatorial background, the purple long-dashed line shows the combinations of $\mathrm{D^0}$ with background pions, and the magenta dash-dotted line illustrates the contamination of $\mathrm{D}_{s}^{\pm}\to\mathrm{K^0_S}\mathrm{K^0_S}\pi^{\pm}$ decay.
png pdf	Figure 4-a: Results of the 2D fit to $m(\mathrm{D}\pi^{\pm}):m(\mathrm{K^0_S}\mathrm{K^0_S})$ for the signal channel in measured data, $\mathrm{D}^{*+}$ candidates. Top row: the projections of the 2D fit on $m(\mathrm{D}\pi^{\pm})$ in the ranges of $m(\mathrm{K^0_S}\mathrm{K^0_S})$: region of $\mathrm{D}_{s}^{\pm}\to\mathrm{K^0_S}\mathrm{K^0_S}\pi^{\pm}$ contamination (left) and signal region of $\mathrm{K^0_S}\mathrm{K^0_S}$ (right). Middle row: projections of the 2D fit on $m(\mathrm{D}\pi^{\pm})$ in the ranges of $m(\mathrm{K^0_S}\mathrm{K^0_S})$: left sideband (left) and right sideband (right). Bottom row: projections of the 2D fit on $m(\mathrm{K^0_S}\mathrm{K^0_S})$ in the ranges of $m(\mathrm{D}\pi^{\pm})$: left sideband (left), signal region of $\mathrm{D^0}\pi^{+}$ (center), and right sideband (right). The green line corresponds to the signal component, the blue short-dashed line shows the combinatorial background, the purple long-dashed line shows the combinations of $\mathrm{D^0}$ with background pions, and the magenta dash-dotted line illustrates the contamination of $\mathrm{D}_{s}^{\pm}\to\mathrm{K^0_S}\mathrm{K^0_S}\pi^{\pm}$ decay.
png pdf	Figure 4-b: Results of the 2D fit to $m(\mathrm{D}\pi^{\pm}):m(\mathrm{K^0_S}\mathrm{K^0_S})$ for the signal channel in measured data, $\mathrm{D}^{*+}$ candidates. Top row: the projections of the 2D fit on $m(\mathrm{D}\pi^{\pm})$ in the ranges of $m(\mathrm{K^0_S}\mathrm{K^0_S})$: region of $\mathrm{D}_{s}^{\pm}\to\mathrm{K^0_S}\mathrm{K^0_S}\pi^{\pm}$ contamination (left) and signal region of $\mathrm{K^0_S}\mathrm{K^0_S}$ (right). Middle row: projections of the 2D fit on $m(\mathrm{D}\pi^{\pm})$ in the ranges of $m(\mathrm{K^0_S}\mathrm{K^0_S})$: left sideband (left) and right sideband (right). Bottom row: projections of the 2D fit on $m(\mathrm{K^0_S}\mathrm{K^0_S})$ in the ranges of $m(\mathrm{D}\pi^{\pm})$: left sideband (left), signal region of $\mathrm{D^0}\pi^{+}$ (center), and right sideband (right). The green line corresponds to the signal component, the blue short-dashed line shows the combinatorial background, the purple long-dashed line shows the combinations of $\mathrm{D^0}$ with background pions, and the magenta dash-dotted line illustrates the contamination of $\mathrm{D}_{s}^{\pm}\to\mathrm{K^0_S}\mathrm{K^0_S}\pi^{\pm}$ decay.
png pdf	Figure 4-c: Results of the 2D fit to $m(\mathrm{D}\pi^{\pm}):m(\mathrm{K^0_S}\mathrm{K^0_S})$ for the signal channel in measured data, $\mathrm{D}^{*+}$ candidates. Top row: the projections of the 2D fit on $m(\mathrm{D}\pi^{\pm})$ in the ranges of $m(\mathrm{K^0_S}\mathrm{K^0_S})$: region of $\mathrm{D}_{s}^{\pm}\to\mathrm{K^0_S}\mathrm{K^0_S}\pi^{\pm}$ contamination (left) and signal region of $\mathrm{K^0_S}\mathrm{K^0_S}$ (right). Middle row: projections of the 2D fit on $m(\mathrm{D}\pi^{\pm})$ in the ranges of $m(\mathrm{K^0_S}\mathrm{K^0_S})$: left sideband (left) and right sideband (right). Bottom row: projections of the 2D fit on $m(\mathrm{K^0_S}\mathrm{K^0_S})$ in the ranges of $m(\mathrm{D}\pi^{\pm})$: left sideband (left), signal region of $\mathrm{D^0}\pi^{+}$ (center), and right sideband (right). The green line corresponds to the signal component, the blue short-dashed line shows the combinatorial background, the purple long-dashed line shows the combinations of $\mathrm{D^0}$ with background pions, and the magenta dash-dotted line illustrates the contamination of $\mathrm{D}_{s}^{\pm}\to\mathrm{K^0_S}\mathrm{K^0_S}\pi^{\pm}$ decay.
png pdf	Figure 4-d: Results of the 2D fit to $m(\mathrm{D}\pi^{\pm}):m(\mathrm{K^0_S}\mathrm{K^0_S})$ for the signal channel in measured data, $\mathrm{D}^{*+}$ candidates. Top row: the projections of the 2D fit on $m(\mathrm{D}\pi^{\pm})$ in the ranges of $m(\mathrm{K^0_S}\mathrm{K^0_S})$: region of $\mathrm{D}_{s}^{\pm}\to\mathrm{K^0_S}\mathrm{K^0_S}\pi^{\pm}$ contamination (left) and signal region of $\mathrm{K^0_S}\mathrm{K^0_S}$ (right). Middle row: projections of the 2D fit on $m(\mathrm{D}\pi^{\pm})$ in the ranges of $m(\mathrm{K^0_S}\mathrm{K^0_S})$: left sideband (left) and right sideband (right). Bottom row: projections of the 2D fit on $m(\mathrm{K^0_S}\mathrm{K^0_S})$ in the ranges of $m(\mathrm{D}\pi^{\pm})$: left sideband (left), signal region of $\mathrm{D^0}\pi^{+}$ (center), and right sideband (right). The green line corresponds to the signal component, the blue short-dashed line shows the combinatorial background, the purple long-dashed line shows the combinations of $\mathrm{D^0}$ with background pions, and the magenta dash-dotted line illustrates the contamination of $\mathrm{D}_{s}^{\pm}\to\mathrm{K^0_S}\mathrm{K^0_S}\pi^{\pm}$ decay.
png pdf	Figure 4-e: Results of the 2D fit to $m(\mathrm{D}\pi^{\pm}):m(\mathrm{K^0_S}\mathrm{K^0_S})$ for the signal channel in measured data, $\mathrm{D}^{*+}$ candidates. Top row: the projections of the 2D fit on $m(\mathrm{D}\pi^{\pm})$ in the ranges of $m(\mathrm{K^0_S}\mathrm{K^0_S})$: region of $\mathrm{D}_{s}^{\pm}\to\mathrm{K^0_S}\mathrm{K^0_S}\pi^{\pm}$ contamination (left) and signal region of $\mathrm{K^0_S}\mathrm{K^0_S}$ (right). Middle row: projections of the 2D fit on $m(\mathrm{D}\pi^{\pm})$ in the ranges of $m(\mathrm{K^0_S}\mathrm{K^0_S})$: left sideband (left) and right sideband (right). Bottom row: projections of the 2D fit on $m(\mathrm{K^0_S}\mathrm{K^0_S})$ in the ranges of $m(\mathrm{D}\pi^{\pm})$: left sideband (left), signal region of $\mathrm{D^0}\pi^{+}$ (center), and right sideband (right). The green line corresponds to the signal component, the blue short-dashed line shows the combinatorial background, the purple long-dashed line shows the combinations of $\mathrm{D^0}$ with background pions, and the magenta dash-dotted line illustrates the contamination of $\mathrm{D}_{s}^{\pm}\to\mathrm{K^0_S}\mathrm{K^0_S}\pi^{\pm}$ decay.
png pdf	Figure 4-f: Results of the 2D fit to $m(\mathrm{D}\pi^{\pm}):m(\mathrm{K^0_S}\mathrm{K^0_S})$ for the signal channel in measured data, $\mathrm{D}^{*+}$ candidates. Top row: the projections of the 2D fit on $m(\mathrm{D}\pi^{\pm})$ in the ranges of $m(\mathrm{K^0_S}\mathrm{K^0_S})$: region of $\mathrm{D}_{s}^{\pm}\to\mathrm{K^0_S}\mathrm{K^0_S}\pi^{\pm}$ contamination (left) and signal region of $\mathrm{K^0_S}\mathrm{K^0_S}$ (right). Middle row: projections of the 2D fit on $m(\mathrm{D}\pi^{\pm})$ in the ranges of $m(\mathrm{K^0_S}\mathrm{K^0_S})$: left sideband (left) and right sideband (right). Bottom row: projections of the 2D fit on $m(\mathrm{K^0_S}\mathrm{K^0_S})$ in the ranges of $m(\mathrm{D}\pi^{\pm})$: left sideband (left), signal region of $\mathrm{D^0}\pi^{+}$ (center), and right sideband (right). The green line corresponds to the signal component, the blue short-dashed line shows the combinatorial background, the purple long-dashed line shows the combinations of $\mathrm{D^0}$ with background pions, and the magenta dash-dotted line illustrates the contamination of $\mathrm{D}_{s}^{\pm}\to\mathrm{K^0_S}\mathrm{K^0_S}\pi^{\pm}$ decay.
png pdf	Figure 4-g: Results of the 2D fit to $m(\mathrm{D}\pi^{\pm}):m(\mathrm{K^0_S}\mathrm{K^0_S})$ for the signal channel in measured data, $\mathrm{D}^{*+}$ candidates. Top row: the projections of the 2D fit on $m(\mathrm{D}\pi^{\pm})$ in the ranges of $m(\mathrm{K^0_S}\mathrm{K^0_S})$: region of $\mathrm{D}_{s}^{\pm}\to\mathrm{K^0_S}\mathrm{K^0_S}\pi^{\pm}$ contamination (left) and signal region of $\mathrm{K^0_S}\mathrm{K^0_S}$ (right). Middle row: projections of the 2D fit on $m(\mathrm{D}\pi^{\pm})$ in the ranges of $m(\mathrm{K^0_S}\mathrm{K^0_S})$: left sideband (left) and right sideband (right). Bottom row: projections of the 2D fit on $m(\mathrm{K^0_S}\mathrm{K^0_S})$ in the ranges of $m(\mathrm{D}\pi^{\pm})$: left sideband (left), signal region of $\mathrm{D^0}\pi^{+}$ (center), and right sideband (right). The green line corresponds to the signal component, the blue short-dashed line shows the combinatorial background, the purple long-dashed line shows the combinations of $\mathrm{D^0}$ with background pions, and the magenta dash-dotted line illustrates the contamination of $\mathrm{D}_{s}^{\pm}\to\mathrm{K^0_S}\mathrm{K^0_S}\pi^{\pm}$ decay.
png pdf	Figure 5: Results of the 2D fit to $m(\mathrm{D}\pi^{\pm}):m(\mathrm{K^0_S}\mathrm{K^0_S})$ for the signal channel in measured data, $\mathrm{D}^{*-}$ candidates. Top row: the projections of the 2D fit on $m(\mathrm{D}\pi^{\pm})$ in the ranges of $m(\mathrm{K^0_S}\mathrm{K^0_S})$: region of $\mathrm{D}_{s}^{\pm}\to\mathrm{K^0_S}\mathrm{K^0_S}\pi^{\pm}$ contamination (left) and signal region of $\mathrm{K^0_S}\mathrm{K^0_S}$ (right). Middle row: projections of the 2D fit on $m(\mathrm{D}\pi^{\pm})$ in the ranges of $m(\mathrm{K^0_S}\mathrm{K^0_S})$: left sideband (left) and right sideband (right). Bottom row: projections of the 2D fit on $m(\mathrm{K^0_S}\mathrm{K^0_S})$ in the ranges of $m(\mathrm{D}\pi^{\pm})$: left sideband (left), signal region of $\overline{\mathrm{D}}^{0}\pi^{-}$ (center), and right sideband (right). The green line corresponds to the signal component, the blue short-dashed line shows the combinatorial background, the purple long-dashed line shows the combinations of $\overline{\mathrm{D}}^{0}$ with background pions, and the magenta dash-dotted line illustrates the contamination of $\mathrm{D}_{s}^{\pm}\to\mathrm{K^0_S}\mathrm{K^0_S}\pi^{\pm}$ decay.
png pdf	Figure 5-a: Results of the 2D fit to $m(\mathrm{D}\pi^{\pm}):m(\mathrm{K^0_S}\mathrm{K^0_S})$ for the signal channel in measured data, $\mathrm{D}^{*-}$ candidates. Top row: the projections of the 2D fit on $m(\mathrm{D}\pi^{\pm})$ in the ranges of $m(\mathrm{K^0_S}\mathrm{K^0_S})$: region of $\mathrm{D}_{s}^{\pm}\to\mathrm{K^0_S}\mathrm{K^0_S}\pi^{\pm}$ contamination (left) and signal region of $\mathrm{K^0_S}\mathrm{K^0_S}$ (right). Middle row: projections of the 2D fit on $m(\mathrm{D}\pi^{\pm})$ in the ranges of $m(\mathrm{K^0_S}\mathrm{K^0_S})$: left sideband (left) and right sideband (right). Bottom row: projections of the 2D fit on $m(\mathrm{K^0_S}\mathrm{K^0_S})$ in the ranges of $m(\mathrm{D}\pi^{\pm})$: left sideband (left), signal region of $\overline{\mathrm{D}}^{0}\pi^{-}$ (center), and right sideband (right). The green line corresponds to the signal component, the blue short-dashed line shows the combinatorial background, the purple long-dashed line shows the combinations of $\overline{\mathrm{D}}^{0}$ with background pions, and the magenta dash-dotted line illustrates the contamination of $\mathrm{D}_{s}^{\pm}\to\mathrm{K^0_S}\mathrm{K^0_S}\pi^{\pm}$ decay.
png pdf	Figure 5-b: Results of the 2D fit to $m(\mathrm{D}\pi^{\pm}):m(\mathrm{K^0_S}\mathrm{K^0_S})$ for the signal channel in measured data, $\mathrm{D}^{*-}$ candidates. Top row: the projections of the 2D fit on $m(\mathrm{D}\pi^{\pm})$ in the ranges of $m(\mathrm{K^0_S}\mathrm{K^0_S})$: region of $\mathrm{D}_{s}^{\pm}\to\mathrm{K^0_S}\mathrm{K^0_S}\pi^{\pm}$ contamination (left) and signal region of $\mathrm{K^0_S}\mathrm{K^0_S}$ (right). Middle row: projections of the 2D fit on $m(\mathrm{D}\pi^{\pm})$ in the ranges of $m(\mathrm{K^0_S}\mathrm{K^0_S})$: left sideband (left) and right sideband (right). Bottom row: projections of the 2D fit on $m(\mathrm{K^0_S}\mathrm{K^0_S})$ in the ranges of $m(\mathrm{D}\pi^{\pm})$: left sideband (left), signal region of $\overline{\mathrm{D}}^{0}\pi^{-}$ (center), and right sideband (right). The green line corresponds to the signal component, the blue short-dashed line shows the combinatorial background, the purple long-dashed line shows the combinations of $\overline{\mathrm{D}}^{0}$ with background pions, and the magenta dash-dotted line illustrates the contamination of $\mathrm{D}_{s}^{\pm}\to\mathrm{K^0_S}\mathrm{K^0_S}\pi^{\pm}$ decay.
png pdf	Figure 5-c: Results of the 2D fit to $m(\mathrm{D}\pi^{\pm}):m(\mathrm{K^0_S}\mathrm{K^0_S})$ for the signal channel in measured data, $\mathrm{D}^{*-}$ candidates. Top row: the projections of the 2D fit on $m(\mathrm{D}\pi^{\pm})$ in the ranges of $m(\mathrm{K^0_S}\mathrm{K^0_S})$: region of $\mathrm{D}_{s}^{\pm}\to\mathrm{K^0_S}\mathrm{K^0_S}\pi^{\pm}$ contamination (left) and signal region of $\mathrm{K^0_S}\mathrm{K^0_S}$ (right). Middle row: projections of the 2D fit on $m(\mathrm{D}\pi^{\pm})$ in the ranges of $m(\mathrm{K^0_S}\mathrm{K^0_S})$: left sideband (left) and right sideband (right). Bottom row: projections of the 2D fit on $m(\mathrm{K^0_S}\mathrm{K^0_S})$ in the ranges of $m(\mathrm{D}\pi^{\pm})$: left sideband (left), signal region of $\overline{\mathrm{D}}^{0}\pi^{-}$ (center), and right sideband (right). The green line corresponds to the signal component, the blue short-dashed line shows the combinatorial background, the purple long-dashed line shows the combinations of $\overline{\mathrm{D}}^{0}$ with background pions, and the magenta dash-dotted line illustrates the contamination of $\mathrm{D}_{s}^{\pm}\to\mathrm{K^0_S}\mathrm{K^0_S}\pi^{\pm}$ decay.
png pdf	Figure 5-d: Results of the 2D fit to $m(\mathrm{D}\pi^{\pm}):m(\mathrm{K^0_S}\mathrm{K^0_S})$ for the signal channel in measured data, $\mathrm{D}^{*-}$ candidates. Top row: the projections of the 2D fit on $m(\mathrm{D}\pi^{\pm})$ in the ranges of $m(\mathrm{K^0_S}\mathrm{K^0_S})$: region of $\mathrm{D}_{s}^{\pm}\to\mathrm{K^0_S}\mathrm{K^0_S}\pi^{\pm}$ contamination (left) and signal region of $\mathrm{K^0_S}\mathrm{K^0_S}$ (right). Middle row: projections of the 2D fit on $m(\mathrm{D}\pi^{\pm})$ in the ranges of $m(\mathrm{K^0_S}\mathrm{K^0_S})$: left sideband (left) and right sideband (right). Bottom row: projections of the 2D fit on $m(\mathrm{K^0_S}\mathrm{K^0_S})$ in the ranges of $m(\mathrm{D}\pi^{\pm})$: left sideband (left), signal region of $\overline{\mathrm{D}}^{0}\pi^{-}$ (center), and right sideband (right). The green line corresponds to the signal component, the blue short-dashed line shows the combinatorial background, the purple long-dashed line shows the combinations of $\overline{\mathrm{D}}^{0}$ with background pions, and the magenta dash-dotted line illustrates the contamination of $\mathrm{D}_{s}^{\pm}\to\mathrm{K^0_S}\mathrm{K^0_S}\pi^{\pm}$ decay.
png pdf	Figure 5-e: Results of the 2D fit to $m(\mathrm{D}\pi^{\pm}):m(\mathrm{K^0_S}\mathrm{K^0_S})$ for the signal channel in measured data, $\mathrm{D}^{*-}$ candidates. Top row: the projections of the 2D fit on $m(\mathrm{D}\pi^{\pm})$ in the ranges of $m(\mathrm{K^0_S}\mathrm{K^0_S})$: region of $\mathrm{D}_{s}^{\pm}\to\mathrm{K^0_S}\mathrm{K^0_S}\pi^{\pm}$ contamination (left) and signal region of $\mathrm{K^0_S}\mathrm{K^0_S}$ (right). Middle row: projections of the 2D fit on $m(\mathrm{D}\pi^{\pm})$ in the ranges of $m(\mathrm{K^0_S}\mathrm{K^0_S})$: left sideband (left) and right sideband (right). Bottom row: projections of the 2D fit on $m(\mathrm{K^0_S}\mathrm{K^0_S})$ in the ranges of $m(\mathrm{D}\pi^{\pm})$: left sideband (left), signal region of $\overline{\mathrm{D}}^{0}\pi^{-}$ (center), and right sideband (right). The green line corresponds to the signal component, the blue short-dashed line shows the combinatorial background, the purple long-dashed line shows the combinations of $\overline{\mathrm{D}}^{0}$ with background pions, and the magenta dash-dotted line illustrates the contamination of $\mathrm{D}_{s}^{\pm}\to\mathrm{K^0_S}\mathrm{K^0_S}\pi^{\pm}$ decay.
png pdf	Figure 5-f: Results of the 2D fit to $m(\mathrm{D}\pi^{\pm}):m(\mathrm{K^0_S}\mathrm{K^0_S})$ for the signal channel in measured data, $\mathrm{D}^{*-}$ candidates. Top row: the projections of the 2D fit on $m(\mathrm{D}\pi^{\pm})$ in the ranges of $m(\mathrm{K^0_S}\mathrm{K^0_S})$: region of $\mathrm{D}_{s}^{\pm}\to\mathrm{K^0_S}\mathrm{K^0_S}\pi^{\pm}$ contamination (left) and signal region of $\mathrm{K^0_S}\mathrm{K^0_S}$ (right). Middle row: projections of the 2D fit on $m(\mathrm{D}\pi^{\pm})$ in the ranges of $m(\mathrm{K^0_S}\mathrm{K^0_S})$: left sideband (left) and right sideband (right). Bottom row: projections of the 2D fit on $m(\mathrm{K^0_S}\mathrm{K^0_S})$ in the ranges of $m(\mathrm{D}\pi^{\pm})$: left sideband (left), signal region of $\overline{\mathrm{D}}^{0}\pi^{-}$ (center), and right sideband (right). The green line corresponds to the signal component, the blue short-dashed line shows the combinatorial background, the purple long-dashed line shows the combinations of $\overline{\mathrm{D}}^{0}$ with background pions, and the magenta dash-dotted line illustrates the contamination of $\mathrm{D}_{s}^{\pm}\to\mathrm{K^0_S}\mathrm{K^0_S}\pi^{\pm}$ decay.
png pdf	Figure 5-g: Results of the 2D fit to $m(\mathrm{D}\pi^{\pm}):m(\mathrm{K^0_S}\mathrm{K^0_S})$ for the signal channel in measured data, $\mathrm{D}^{*-}$ candidates. Top row: the projections of the 2D fit on $m(\mathrm{D}\pi^{\pm})$ in the ranges of $m(\mathrm{K^0_S}\mathrm{K^0_S})$: region of $\mathrm{D}_{s}^{\pm}\to\mathrm{K^0_S}\mathrm{K^0_S}\pi^{\pm}$ contamination (left) and signal region of $\mathrm{K^0_S}\mathrm{K^0_S}$ (right). Middle row: projections of the 2D fit on $m(\mathrm{D}\pi^{\pm})$ in the ranges of $m(\mathrm{K^0_S}\mathrm{K^0_S})$: left sideband (left) and right sideband (right). Bottom row: projections of the 2D fit on $m(\mathrm{K^0_S}\mathrm{K^0_S})$ in the ranges of $m(\mathrm{D}\pi^{\pm})$: left sideband (left), signal region of $\overline{\mathrm{D}}^{0}\pi^{-}$ (center), and right sideband (right). The green line corresponds to the signal component, the blue short-dashed line shows the combinatorial background, the purple long-dashed line shows the combinations of $\overline{\mathrm{D}}^{0}$ with background pions, and the magenta dash-dotted line illustrates the contamination of $\mathrm{D}_{s}^{\pm}\to\mathrm{K^0_S}\mathrm{K^0_S}\pi^{\pm}$ decay.

Tables
png pdf	Table 1: Optimized selection criteria in the signal channel $\mathrm{D^0}\to\mathrm{K^0_S}\mathrm{K^0_S}$.
png pdf	Table 2: Results of the simultaneous fit to the selected $\mathrm{D}^{*+}\to\mathrm{D^0}\pi^{+}$ and $\mathrm{D}^{*-}\to\overline{\mathrm{D}}^{0}\pi^{-}$ candidates, where $\mathrm{D^0}\,(\overline{\mathrm{D}}^{0}) \to\mathrm{K^0_S}\pi^{+}\pi^{-}$. The ${\mathrm{D}^{\ast}(2010)^{\pm}}$ signal yields $N$ given in the second column are used in the evaluation of $A_{CP}^{\text{raw}}$. The uncertainties are statistical only.
png pdf	Table 3: Results of the simultaneous 2D fit to the selected $\mathrm{D}^{*+}\to\mathrm{D^0}\pi^{+}$ and $\mathrm{D}^{*-}\to\overline{\mathrm{D}}^{0}\pi^{-}$ candidates, where $\mathrm{D^0}\,(\overline{\mathrm{D}}^{0}) \to\mathrm{K^0_S}\mathrm{K^0_S}$. The yields $N$ given in the second column correspond to the $\mathrm{D^0} \,\times\,{\mathrm{D}^{\ast}(2010)^{\pm}}$ component in the 2D fit and are used in the evaluation of $A_{CP}^{\text{raw}}$. The $\chi^2$ corresponds to the fit projection with 100 bins in the $x=m(\mathrm{D}\pi^{\pm})$ axis and 90 bins in the $y=m(\mathrm{K^0_S}\mathrm{K^0_S})$ axis, as shown in Fig 3. The uncertainties are statistical only.
png pdf	Table 4: Absolute systematic uncertainties in the measurement of $\Delta A_{CP}$.

Summary

This is the first CMS measurement of $CP$ violation in the charm sector, paving the way for future measurements with more data, using refined techniques, and in different channels.

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