Measurement of the $CP$ Violation Parameter $A_{\mathrm{\Gamma }}$ in $D^0\to K^{+}{K}^{-}$ and $D^0\to {\pi }^{+}{\pi }^{-}$ Decays

Asymmetries in the time-dependent rates of $D^0\to K^{+}{K}^{-}$ and $D^0\to {\pi }^{+}{\pi }^{-}$ decays are measured in a $pp$ collision data sample collected with the LHCb detector during LHC Run 1, corresponding to an integrated luminosity of $3{\mathrm{fb}}^{-1}$. The asymmetries in effective decay widths between $D^0$ and ${\overline{D}}^0$ decays, sensitive to indirect $CP$ violation, are measured to be $A_{\mathrm{\Gamma }}(K^{+}{K}^{-})=(-0.30\pm 0.32\pm 0.10)\times {10}^{-3}$ and $A_{\mathrm{\Gamma }}({\pi }^{+}{\pi }^{-})=(0.46\pm 0.58\pm 0.12)\times {10}^{-3}$, where the first uncertainty is statistical and the second systematic. These measurements show no evidence for $CP$ violation and improve on the precision of the previous best measurements by nearly a factor of two.

Figure 1

Results from $A_{\mathrm{\Gamma }}$ fits in each subsample before (solid red squares) and after (empty black dots) the asymmetry correction. Fit qualities (${\chi }^2/\mathrm{number}$ of degrees of freedom) are also reported to the right of each graph. The weighted average of the four $A_{\mathrm{\Gamma }}$ values is indicated before (red hatched band) and after (black hatched band) the correction. The numerical values for the averages are $A_{\mathrm{\Gamma }}(K^{-}{\pi }^{+})=(0.41\pm 0.10)\times {10}^{-3}$, $A_{\mathrm{\Gamma }}(K^{+}{K}^{-})=(0.93\pm 0.31)\times {10}^{-3}$, and $A_{\mathrm{\Gamma }}({\pi }^{+}{\pi }^{-})=(1.77\pm 0.57)\times {10}^{-3}$ before the correction and $A_{\mathrm{\Gamma }}(K^{-}{\pi }^{+})=(0.16\pm 0.10)\times {10}^{-3}$, $A_{\mathrm{\Gamma }}(K^{+}{K}^{-})=(-0.30\pm 0.32)\times {10}^{-3}$, and $A_{\mathrm{\Gamma }}({\pi }^{+}{\pi }^{-})=(0.46\pm 0.58)\times {10}^{-3}$ after the correction. The label 2011 (2012) is abbreviated 11 (12) and MagUp (MagDown) is abbreviated $\mathit{U}(\mathit{D})$.

Figure 2

(Left) Sum and (right) asymmetry of distributions of positive and negative soft pions in the $(k,q_s{\theta }_x)$ plane for the 2011 MagUp $D^0\to K^{-}{\pi }^{+}$ subsample after integration over ${\theta }_y$.

Figure 3

Measured asymmetry $A(t)$ in bins of $t/{\tau }_D$, where ${\tau }_D=0.410\mathrm{ps}$ [16] for (top) $D^0\to K^{+}{K}^{-}$ and (bottom) $D^0\to {\pi }^{+}{\pi }^{-}$, averaged over the full Run 1 data sample. Solid lines show the time dependence with a slope equal to the best estimates of $-A_{\mathrm{\Gamma }}$.

Figure 4

Distribution of $\ln \mathbf{(}{\chi }_{\mathrm{IP}}^2(D^0)\mathbf{)}$ for the $D^0\to K^{+}{K}^{-}$ candidates selected in the second of the three 2012 data-taking periods with magnetic field pointing downwards. The unbinned maximum likelihood fit results are overlaid. Gaussian kernels are used to smooth the combinatorial and partially reconstructed backgrounds.