Measurement of the direct $CP$-violating parameter $A_{CP}$ in the decay $D^{+}\to K^{-}{\pi }^{+}{\pi }^{+}$

We measure the direct $CP$-violating parameter $A_{CP}$ for the decay of the charged charm meson, $D^{+}\to K^{-}{\pi }^{+}{\pi }^{+}$ (and charge conjugate), using the full $10.4{\mathrm{fb}}^{-1}$ sample of $p\overline{p}$ collisions at $\sqrt{s}=1.96\mathrm{TeV}$ collected by the D0 detector at the Fermilab Tevatron collider. We extract the raw reconstructed charge asymmetry by fitting the invariant mass distributions for the sum and difference of charge-specific samples. This quantity is then corrected for detector-related asymmetries using data-driven methods and for possible physics asymmetries (from $B\to D$ processes) using input from Monte Carlo simulation. We measure $A_{CP}=[-0.16\pm 0.15(\text{stat})\pm 0.09(\text{syst})]\%$, which is consistent with zero, as expected from the standard model prediction of $CP$ conservation, and is the most precise measurement of this quantity to date.

Figure 1

(a) Invariant mass distribution $M(K\pi \pi )$ after all selections have been applied (data markers). Also shown is the result of the fit to the data, as described in the text (solid line). To illustrate the contributions of the three separate components, the total background (dashed line) and polynomial function (dot-dashed line) are shown separately. (b) Fit residuals $[N_{\text{data}}-N_{\mathrm{fit}}]/\sqrt{N_{\text{data}}}$, demonstrating the agreement between the data and the fit model.

Figure 2

Invariant mass distribution $M(K\pi \pi )$ for the difference $N(D^{+})-N(D^{-})$ (data markers). Also shown are the result of the fit to the data (solid line) and the overall background contribution (dashed line).