Time Dependent Analysis of Decays $\Lambda_b\to \Lambda +D^0$ and $\Lambda_b\to \Lambda +\bar{D}^0$

The time-dependent analysis of the decays $\Lambda_b\to \Lambda +D^0(t)$ and $\Lambda_b\to \Lambda +\bar{D}^0(t)$ is discussed. The effect of particle mixing due to time evolution of $D^0$ and $\bar{D}^0$ on the observables for these decays viz the branching ratio of decay widths and the asymmetry parameters $\alpha ,\beta$ and $\gamma$ are analysed. It is shown that it is possible to extract information about $(\Delta m/\Gamma)\sin \hat{\gamma}$ from the experimental data for these observables. Here $\Delta m=m_{D_1^0}-m_{D_2^0},\Gamma$ is the decay widths for $D^{\prime}s$ and $\hat{\gamma}$ is the weak phase.