Measurement of Time-Integrated Raw Asymmetry in  \(D^{0}\rightarrow K^{+}K^{-}\!\) Decay

The decay \(D^{0}\rightarrow K^{0}_{s}K^{0}_{s}\) is a singly Cabibbo-suppressed transition that involves the interference between \(c\overline{u}\rightarrow s\overline{s}\) and \(c\overline{u}\rightarrow d\overline{d}\) amplitudes, mediated by the exchange of a W boson at the tree level, that can generate CP asymmetries at the 1% level, even if the Cabibbo-Kobayashi-Maskawa phase is the only source of CP. Current experimental measurements of the CP asymmetry in \(D^{0}\rightarrow K^{0}_{s}K^{0}_{s}\) decays are still limited by the statistical precision, with the best measurement performed by Belle experiment using data at an integrated luminosity of 921 \(\text {fb}^{-1}\) : \(\mathcal {A}_{CP}({D^{0}\rightarrow K^{0}_{S}K^{0}_{S}}) = (-0.02 \pm 1.53 \pm 0.02 \pm 0.17) \%\) , where the first uncertainty is statistical, the second systematic and the third due to the CP asymmetry of the reference \(D^{0}\rightarrow K^{0}_{s}\pi ^{0}\) mode. \(\mathcal {A}_{CP}\) in \(D^{0}\rightarrow K^{+}K^{-}\) is measured with 0.11% precision and therefore, using \(D^{0}\rightarrow K^{+}K^{-}\) as the control mode reduces the uncertainty due to the control mode in addition to making the analysis simpler [1]. In this work, we report the preliminary measurement of the raw asymmetry of the \(D^{0}\rightarrow K^{+}K^{-}\) decay using the Belle II Simulation. The final goal of this analysis is to measure the CP asymmetry in \(D^{0}\rightarrow K^{0}_{s}K^{0}_{s}\) , \(D^{0}\rightarrow K^{+}K^{-}\) using as the reference mode.