Measurements of Indirect $CP$ Asymmetries in $D^0\to K^{-}{K}^{+}$ and $D^0\to {\pi }^{-}{\pi }^{+}$ Decays

A study of indirect $CP$ violation in $D^0$ mesons through the determination of the parameter $A_{\mathrm{\Gamma }}$ is presented using a data sample of $pp$ collisions, corresponding to an integrated luminosity of $1.0{\mathrm{fb}}^{-1}$, collected with the LHCb detector and recorded at the center-of-mass energy of 7 TeV at the LHC. The parameter $A_{\mathrm{\Gamma }}$ is the asymmetry of the effective lifetimes measured in decays of $D^0$ and $\overline{D}{}^0$ mesons to the $CP$ eigenstates $K^{-}{K}^{+}$ and ${\pi }^{-}{\pi }^{+}$. Fits to the data sample yield $A_{\mathrm{\Gamma }}(KK)=(-0.35\pm 0.62\pm 0.12)\times {10}^{-3}$ and $A_{\mathrm{\Gamma }}(\pi \pi )=(0.33\pm 1.06\pm 0.14)\times {10}^{-3}$, where the first uncertainties are statistical and the second systematic. The results represent the world’s best measurements of these quantities. They show no difference in $A_{\mathrm{\Gamma }}$ between the two final states and no indication of $CP$ violation.

Figure 1

Fit of $\mathrm{\Delta }m$ for one of the eight subsets, containing the $\overline{D}{}^0\to K^{-}{K}^{+}$ candidates with magnet polarity down for the earlier run period.

Figure 2

Top: fit of decay time to $\overline{D}{}^0\to K^{-}{K}^{+}$ and corresponding pull plot for candidates with magnet polarity down for the earlier run period, where pull is defined as $(\text{data}-\text{model})/\text{uncertainty}$. Middle and bottom: the ratio of $\overline{D}{}^0$ to $D^0$ data and fit model for decays to $K^{-}{K}^{+}$ and ${\pi }^{-}{\pi }^{+}$ for all data, respectively.

Figure 3

Fits of $\ln ({\chi }_{\text{IP}}^2)$ for $\overline{D}{}^0\to K^{-}{K}^{+}$ candidates for decay-time bins (left to right) 0.25–0.37 ps, 0.74–0.78 ps, and 1.55–1.80 ps.