Measurement of $CP$-violating asymmetries in $D^0\to {\pi }^{+}{\pi }^{-}$ and $D^0\to K^{+}{K}^{-}$ decays at CDF

We report on a measurement of $CP$-violating asymmetries ($A_{CP}$) in the Cabibbo-suppressed $D^0\to {\pi }^{+}{\pi }^{-}$ and $D^0\to K^{+}{K}^{-}$ decays reconstructed in a data sample corresponding to $5.9{\mathrm{fb}}^{-1}$ of integrated luminosity collected by the upgraded Collider Detector at Fermilab. We use the strong decay $D^{*+}\to D^0{\pi }^{+}$ to identify the flavor of the charmed meson at production and exploit $CP$-conserving strong $c\overline{c}$ pair production in $p\overline{p}$ collisions. High-statistics samples of Cabibbo-favored $D^0\to K^{-}{\pi }^{+}$ decays with and without a $D^{*\pm }$ tag are used to correct for instrumental effects and significantly reduce systematic uncertainties. We measure $A_{CP}(D^0\to {\pi }^{+}{\pi }^{-})=(+0.22\pm 0.24(\mathrm{stat})\pm 0.11(\mathrm{syst}))\%$ and $A_{CP}(D^0\to K^{+}{K}^{-})=(-0.24\pm 0.22(\mathrm{stat})\pm 0.09(\mathrm{syst}))\%$, in agreement with $CP$ conservation. These are the most precise determinations from a single experiment to date. Under the assumption of negligible direct $CP$ violation in $D^0\to {\pi }^{+}{\pi }^{-}$ and $D^0\to K^{+}{K}^{-}$ decays, the results provide an upper limit to the $CP$-violating asymmetry in $D^0$ mixing, $|A_{CP}^{\mathrm{ind}}(D^0)|<0.13\%$ at the 90% confidence level.

Figure 1

Observed asymmetry between the number of reconstructed $D^{*+}$ and $D^{*-}$ mesons as a function of the soft pion’s transverse momentum for pure samples of $D^{*+}\to D^0(\to {\pi }^{+}{\pi }^{-}){\pi }_s^{+}$ and $D^{*-}\to {\overline{D}}^0(\to {\pi }^{+}{\pi }^{-}){\pi }_s^{-}$ decays. The soft pion transverse momentum spectrum is also shown.

Figure 2

Comparison between the $K^{-}{\pi }^{+}$-mass distributions of (a) the untagged sample and of (b) a simulated sample of inclusive charm decays. See text for explanation of contributions.

Figure 3

Distributions of (a) ${\pi }^{+}{\pi }^{-}$, (b) $K^{+}{K}^{-}$, and (c) $K\pi$ mass. Regions used to define the tagged samples are shaded. Distribution of $D^0{\pi }_s$ mass for tagged (d) $D^0\to {\pi }^{+}{\pi }^{-}$, (e) $D^0\to K^{+}{K}^{-}$, and (f) $D^0\to K^{-}{\pi }^{+}$ samples selected in the shaded regions.

Figure 4

Comparison between normalized kinematic distributions of the various tagged and untagged samples used in the analysis: (a), (c) soft pion transverse momentum, and (b), (d) pseudorapidity of $h{h}^{*}$ and $K{\pi }^{*}$ events; (e) $D^0$ transverse momentum and (f) pseudorapidity of $K\pi$ and $K{\pi }^{*}$ events. Tagged distributions are background-subtracted.

Figure 5

Distribution of $K^{-}{\pi }^{+}$ mass as a function of $K^{+}{\pi }^{-}$ mass for the untagged sample. Note the logarithmic scale on the $z$ axis.

Figure 6

Distribution of $D^0{\pi }_s$ mass of tagged $D^0\to K^{-}{\pi }^{+}$ decays with fit results overlaid. The total fit projection (solid line) is shown along with the double Gaussian bulk (dotted line), the Johnson tail (dashed line), and the background (full hatching).

Figure 7

Results of the combined fit of the tagged $D^0\to K^{-}{\pi }^{+}$ samples. Distribution of $D^0{\pi }_s$ mass for (a) charm and (b) anticharm decays, and (c) asymmetry as a function of the mass. Fit results are overlaid.

Figure 8

Results of the combined fit of the tagged $D^0\to {\pi }^{+}{\pi }^{-}$ and $D^0\to K^{+}{K}^{-}$ samples. Distribution of $D^0{\pi }_s$ mass for (a), (d) charm and (b), (e) anticharm decays, and (c), (f) asymmetry as a function of the mass (c, f). Fit results are overlaid.

Figure 9

Average ($m$) of the distribution of $K^{+}{\pi }^{-}$ mass in the even sample and $K^{-}{\pi }^{+}$ mass in the odd sample with fit projections overlaid.

Figure 10

Results of the combined fit of the untagged $D^0\to K^{-}{\pi }^{+}$ sample. Distribution of $D^0{\pi }_s$ mass for (a) charm and (b) anticharm decays, and (c) asymmetry as a function of the mass. Fit results are overlaid.

Figure 11

Impact parameter distribution of $D^0$ candidates in the $D^0\to K^{-}{\pi }^{+}$ signal region. The top plot with data and fit projections overlaid uses a logarithmic scale vertically. The bottom plot shows fractional difference between data and the fit on a linear scale.

Figure 12

Shape of $D^0{\pi }_s$ mass as extracted from simulation without tuning, with data tuning and with anti–data tuning.

Figure 13

Shapes of $K^{\pm }{\pi }^{\mp }$ mass from simulation without tuning, with data tuning, and with anti–data tuning for (a) right-sign and (b) wrong-sign $K^{\pm }{\pi }^{\mp }$ decays, and for (c) ${\pi }^{+}{\pi }^{-}$ decays.

Figure 14

Distribution of proper decay time (in units of $D^0$ lifetime) for sideband-subtracted tagged (a) $D^0\to {\pi }^{+}{\pi }^{-}$ and (b) $D^0\to K^{+}{K}^{-}$ data. Fit results are overlaid including the component from secondary charmed mesons (full hatching).

Figure 15

Comparison of the present results with Belle and BABAR measurements of time-integrated $CP$-violating asymmetry in (a) $D^0\to {\pi }^{+}{\pi }^{-}$ and (b) $D^0\to K^{+}{K}^{-}$ decays displayed in the $(A_{CP}^{\mathrm{ind}},A_{CP}^{\mathrm{dir}})$ plane. The point with error bars denotes the central value of the combination of the three measurements with one-dimensional 68% confidence level uncertainties.

Figure 16

Comparison of the present results with results from Belle and BABAR assuming (a), (c) no direct, or (b), (d) no indirect $CP$ violation. In each plot the $1\sigma$ band of the $B$ factories’ average is bounded by the dashed lines, while the new average that includes the CDF result is shown in full hatching.

Figure 17

Difference between direct $CP$-violating asymmetries in the $K^{+}{K}^{-}$ and ${\pi }^{+}{\pi }^{-}$ final states as a function of the indirect asymmetry. Belle and BABAR measurements are also reported for comparison. The point with error bars denotes the central value of the combination of the three measurements with one-dimensional 68% confidence level uncertainties.

Figure 18

Curves corresponding to simulated ratios of efficiencies for reconstructing positive versus negative pions as a function of transverse momentum.

Figure 19

Asymmetry residual as a function of the input quantity varied. Other effects are assumed zero (empty dots) or different from zero (filled dots).

Figure 20

Asymmetry residual as a function of the physical $CP$-violating asymmetry in $D^0\to {\pi }^{+}{\pi }^{-}$ decays. Realistic effects other than shown in the scan are also simulated. The line represents the value averaged over the $-5\%<A_{CP}(\pi \pi )<5\%$ range.