Search for direct $CP$ violation in singly Cabibbo-suppressed $D^{\mathbf{\pm }}\to K^{\mathbf{+}}{K}^{\mathbf{-}}{\pi }^{\mathbf{\pm }}$ decays

We report on a search for direct $CP$ violation in the singly Cabibbo-suppressed decay $D^{+}\to K^{+}{K}^{-}{\pi }^{+}$ using a data sample of $476{\mathrm{fb}}^{-1}$ of $e^{+}{e}^{-}$ annihilation data accumulated with the BABAR detector at the SLAC PEP-II electron-positron collider, running at and just below the energy of the ${\rm Y}(4S)$ resonance. The integrated $CP$-violating decay rate asymmetry $A_{CP}$ is determined to be $(0.37\pm 0.30\pm 0.15)\%$. Model-independent and model-dependent Dalitz plot analysis techniques are used to search for $CP$-violating asymmetries in the various intermediate states. We find no evidence for $CP$-violation asymmetry.

Figure 1

Charged pion tracking efficiency asymmetry [defined in Eq. (2)] as a function of the pion momentum in the laboratory frame determined from the decays of $\tau$ leptons. The horizontal error bars indicate the range of pion momentum [21].

Figure 2

$CP$ asymmetry as a function of $|\cos ({\theta }_{\mathrm{CM}})|$. The solid line represents the central value of $A_{CP}$ and the dashed lines the $\pm 1$ standard deviation statistical uncertainty, determined from a ${\chi }^2$ fit to a constant value.

Figure 3

Combined reconstructed invariant mass distribution $m(K^{+}{K}^{-}{\pi }^{\pm })$ and projection of the fit result. The points show the data, the solid curve the fit model, and the dashed curve shows the background PDF. The signal region is indicated by the dashed vertical lines, and the sideband regions by the solid vertical lines. The lower figure shows the fit on a logarithmic scale with the radiative component of the signal PDF shown separately as a smooth curve.

Figure 4

$D^{\pm }\to K^{+}{K}^{-}{\pi }^{\pm }$ Dalitz plot and fit projections assuming no $CPV$, with the regions used for model-independent comparisons indicated as boxes. The A/B boundary is at $m_{K\pi }=0.6{\mathrm{GeV}}^2/c^4$, the B/C boundary at $m_{K\pi }=1.0{\mathrm{GeV}}^2/c^4$, and the C/D boundary at $m_{KK}=1.3{\mathrm{GeV}}^2/c^4$. In the fit projections, the data are represented by points with error bars and the fit results by the histograms. The normalized residuals below each projection, defined as $(N_{\mathrm{Data}}-N_{\mathrm{MC}})/\sqrt{N_{\mathrm{MC}}}$, lie between $\pm 5\sigma$. The horizontal lines correspond to $\pm 3\sigma$.

Figure 5

Normalized residuals of the $D^{+}$ and $D^{-}$ Dalitz plots in equally populated intervals (top) and their distribution fitted with a Gaussian function (bottom).

Figure 6

The difference between the $D^{+}$ and $D^{-}$ Dalitz plot projections of data (points) and of the fit (cyan band). The width of the band represents the $\pm 1$ standard deviation statistical uncertainty expected for the size of our data sample.