Pursuit of new physics within the ${\Lambda }_c\to \Delta K$ decays

Abstract

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 ${\Lambda }_c^{+}\to {\Delta }^{++}{K}^{-}$, ${\Lambda }_c^{+}\to {\Delta }^{+}{K}_{S,L}^0$ 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.

Comments: 13 pages, 1 figure, published version