Search for $CP$ violation in $D^{+}\to K^{-}{K}^{+}{\pi }^{+}$ decays

A model-independent search for direct $CP$ violation in the Cabibbo-suppressed decay $D^{+}\to K^{-}{K}^{+}{\pi }^{+}$ in a sample of approximately 370 000 decays is carried out. The data were collected by the LHCb experiment in 2010 and correspond to an integrated luminosity of $35{\mathrm{pb}}^{-1}$. The normalized Dalitz plot distributions for $D^{+}$ and $D^{-}$ are compared using four different binning schemes that are sensitive to different manifestations of $CP$ violation. No evidence for $CP$ asymmetry is found.

Figure 1

Fitted mass spectra of (a) $K^{-}{\pi }^{+}{\pi }^{+}$ and (b) $K^{-}{K}^{+}{\pi }^{+}$ candidates from samples 1 and 3, $D^{+}$ and $D^{-}$ combined. The signal mass windows and sidebands defined in the text are labeled.

Figure 2

Dalitz plot of the $D^{+}\to K^{-}{K}^{+}{\pi }^{+}$ decay for selected candidates in the signal window. The vertical ${\overline{K}}^{*}(892{)}^0$ and horizontal $\varphi (1020)$ contributions are clearly visible in the data.

Figure 3

${\mathcal{S}}_{CP}$ across the Dalitz plot in a Monte Carlo pseudo-experiment with a large number of events with (a) no CPV and (b) a 4° CPV in the $\varphi \pi$ phase. Note the difference in color scale between (a) and (b).

Figure 4

Layout of the (a) “Adaptive I” and (b) “Adaptive II” binnings on the Dalitz plot of data.

Figure 5

(a) Distribution of ${\mathcal{S}}_{CP}$ values from $D^{+}\to K^{-}{\pi }^{+}{\pi }^{+}$ from a test with 900 uniform bins. The mean of the fitted Gaussian distribution is $0.015\pm 0.034$ and the width is $0.996\pm 0.023$. (b) Distribution of ${\mathcal{S}}_{CP}$ values from $D_s^{+}\to K^{-}{K}^{+}{\pi }^{+}$ with 129 bins. The fitted mean is $-0.011\pm 0.084$ and the width is $0.958\pm 0.060$.

Figure 6

Dalitz plots of (a) $D^{+}\to K^{-}{\pi }^{+}{\pi }^{+}$, showing the 25-bin adaptive scheme with the ${\mathcal{S}}_{CP}$ values, and (b) $D_s^{+}\to K^{-}{K}^{+}{\pi }^{+}$, showing the three regions referred to in the text. The higher and lower $K^{-}{\pi }^{+}$ invariant mass combinations are plotted in (a) as there are identical pions in the final state.

Figure 7

Distribution of ${\mathcal{S}}_{CP}^i$ in the Dalitz plot for (a) “Adaptive I,” (b) “Adaptive II,” (c) “Uniform I” and (d) “Uniform II.” In (c) and (d) bins at the edges are not shown if the number of entries is not above a threshold of 50 (see Sec. 3).

Figure 8

Distribution of ${\mathcal{S}}_{CP}^i$ fitted to Gaussian functions, for (a) “Adaptive I,” (b) “Adaptive II,” (c) “Uniform I” and (d) “Uniform II.” The fit results are given in Table 9.