$CP$ asymmetries in the ${\Lambda }_c^{+}\to p{K}_S^0$ and ${\Xi }_c^{+}\to {\Sigma }^{+}{K}_S^0$ decays

Abstract

$CP$ asymmetry is a crucial element in interpreting the matter-antimatter asymmetry in the universe and searching for new physics beyond the Standard Model. In this work, we study the $CP$ asymmetries in the ${\Lambda }_c^{+}\to p{K}_S^0$ and ${\Xi }_c^{+}\to {\Sigma }^{+}{K}_S^0$ decays. The time-independent and time-integrated $\Gamma$-, $\alpha$-, $\beta$-, and $\gamma$-defined $CP$ asymmetries in the chain decay ${\mathcal{B}}_{c\overline{3}}\to \mathcal{B}K(t)(\to {\pi }^{+}{\pi }^{-})$ are derived. It is found that the $CP$ asymmetry in $K^0-{\overline{K}}^0$ mixing cancels out in the $\alpha$-, $\beta$-, and $\gamma$-defined $CP$ asymmetries. The $U$-spin analysis shows that the amplitudes of the ${\Lambda }_c^{+}\to p{K}^0$, ${\Lambda }_c^{+}\to p{\overline{K}}^0$, ${\Xi }_c^{+}\to {\Sigma }^{+}{K}^0$, and ${\Xi }_c^{+}\to {\Sigma }^{+}{\overline{K}}^0$ modes are not independent. The hadronic parameters determining $CP$ asymmetries in the ${\Lambda }_c^{+}\to p{K}_S^0$ and ${\Xi }_c^{+}\to {\Sigma }^{+}{K}_S^0$ decays could be extracted from the $K_S^0-K_L^0$ asymmetry and decay parameters $\alpha$, $\beta$, and $\gamma$ in these two decay modes. We find the $CP$-violating effect induced by the interference between charmed hadron decay and neutral kaon mixing in the ${\Xi }_c^{+}\to {\Sigma }^{+}{K}_S^0$ decay could reach to be $\mathcal{O}(10^{-3})$, which is several times larger than those in $D$ meson decays and at the same order as the $CP$ asymmetry in $K^0-{\overline{K}}^0$ mixing. In contrast, the same term in the ${\Lambda }_c^{+}\to p{K}_S^0$ mode are one order of magnitude smaller. Thus, the ${\Xi }_c^{+}\to {\Sigma }^{+}{K}_S^0$ decay is a promising mode for observing $CP$ asymmetry in the charmed hadron sector and verifying the $CP$-violating effect induced by the interference between charm decay and neutral kaon mixing.

Comments: 14 pages, 4 figures