CP asymmetries in $D\to K_{S,L}^{0}P$ and $D\to K_{S,L}^{0}V$ decays

Abstract

$D$ meson decays into neutral kaons involve both Cabibbo-favored and doubly Cabibbo-suppressed amplitudes as well as final-state kaon mixing, providing abundant sources of CP violation. In this work, we analyze CP asymmetries in the $D\to K_{S,L}^{0}P$ and $D\to K_{S,L}^{0}V$ decays, where $P$ and $V$ denote pseudoscalar and vector mesons respectively. The formulas of the time-dependent and time-integrated CP asymmetries in these modes are derived, in which the $D^0-{\overline{D}}^0$ mixing effects and the $K_L^0$ modes are considered for the first time. The hadronic parameters that determine CP asymmetries are extracted by the global fit of branching fractions within the topological diagram approach. A significant result is that the tension between theoretical predictions and experimental data for the $K_S^0-K_L^0$ asymmetries in $D^0\to K_{S,L}^0\omega$ and $D^0\to K_{S,L}^0\varphi$ modes is mitigated. The CP-violating effects arising from the interference between Cabibbo-favored and doubly Cabibbo-suppressed amplitudes with neutral kaon mixing could reach to $\mathcal{O}(10^{-3})$ order in the $D^{+}\to K_S^0{\pi }^{+}$, $D_s^{+}\to K_S^0{K}^{+}$, $D^0\to K_S^0{\rho }^0$, and $D^0\to K_S^0\varphi$ modes. The difference between the CP asymmetries in the $D^{+}\to K_S^0{\pi }^{+}$ and $D_s^{+}\to K_S^0{K}^{+}$ modes will be available on LHCb and Belle II in the near future.

Comments: 19 pages, 5 figures