We point out the $CP$ asymmetry in the chain decay of $\Lambda_c^+\to \Delta^+K(t)(\to \pi^+\pi^-)$ is determined by the branching fractions of $\Lambda^+_c\to \Delta^{ ++} K^-$, $\Lambda^+_c\to \Delta^{ +} K^0_{ S,L}$ and $\Lambda^+_c\to \Delta^{ 0} K^+$ modes under the isospin symmetry. The ambiguities from loop-induced quantities and $SU(3)_F$ breaking hadronic effects are avoided. Once the $CP$ asymmetry in the $\Lambda_c^+$ decays into $\Delta^+$ and neutral kaons is confirmed by experiments, we can check if it is beyond the Standard Model, or verify the $CP$-violating effect resulted from the interference between the Cabibbo-favored and the doubly Cabibbo-suppressed amplitudes with the neutral kaon mixing. Future measurements of branching fractions play a critical role in reducing the uncertainties.
Categories: hep-ph hep-ex