Time reversal symmetry violation in entangled pseudoscalar neutral charmed mesons

The direct observation of time reversal symmetry violation (TV) is important for the test of $CPT$ conservation and the Standard Model. In this paper, we study both time-dependent and time-independent genuine TV signals in entangled $D^0-\bar{D}^0$ pairs. A possible $CPT$-violation effect called the $\omega$ effect is also investigated. In the $C=-1$ entangled state, the asymmetries due to TV are calculated to be of the order of $10^{-5}$ to $10^{-4}$ within the Standard Model, but the modification due to the $\omega$ effect in the $C=-1$ states is found to be about $10\%-30\%$ when $|\omega|\sim 10^{-4}$. This result is consistent with our Monte Carlo simulation, which implies that with $10^9$ to $10^{10}$ events, TV signals can be observed in the entangled $D^0-\bar{D}^0$ pairs, and the bound of $\omega \sim 10^{-3}$ can be reached. The time-dependent and the time-independent asymmetries in the $C=-1$ $D^0-\bar{D}^0$ system provides a window to detect new physics such as the $\omega$ effect, although they are not easily observable.