$CP$ violation is an excellent tool for probing flavor dynamics as we learned first with $K_L\to 2\pi$ and later also with the weak decays of beauty mesons. LHCb 2019 data have shown $CP$ violation for the first time in $D^0\to K^{-}{K}^{+}$ vs $D^0\to {\pi }^{-}{\pi }^{+}$. Searching for $CP$ asymmetries is of great interest in the charm quark sector in the Standard Model (SM) or even more beyond it. In charm hadron decays, lots of work had focused on two-body final states, and the measurements of $CP$ asymmetries in three- or four-body final states are rare. Dalitz plots have shown an excellent record for three-body final states, and more results are desired for four-body ones. In this work we study $CP$ asymmetries in the decays ${\mathrm{\Lambda }}_c^{+}\to p{K}^{-}{\pi }^{+}{\pi }^0/\mathrm{\Lambda }{\pi }^{+}{\pi }^{+}{\pi }^{-}/p{K}_S{\pi }^{+}{\pi }^{-}$, where the SM gives zero values for the first two channels, while $3.3\times {10}^{-3}$ is given for the last one due to $K^0-{\overline{K}}^0$ oscillation. We performed a fast Monte Carlo simulation study by using electron-positron annihilation data of $1{\mathrm{ab}}^{-1}$ at center-of-mass energy $\sqrt{s}=4.64\mathrm{GeV}$. The data is expected to be available by the next generation Super Tau Charm Facility proposed by China and Russia with one year (or even less) of the data taking operation. The results indicate that a sensitivity at the level of $0.2\sim 0.5\%$ is accessible for these processes, which would be enough to measure nonzero $CP$-violating asymmetries as large as 1%. Furthermore $A_{T\text{-odd}}\ne 0$ can establish parity violation by themselves and likewise for ${\overline{A}}_{T\text{-odd}}\ne 0$. The SM is based on $W^{+/-}$ being 100% left handed. One can compare decay asymmetry parameters $a_{\text{P}}$ from ${\mathrm{\Lambda }}_c^{+}\to \mathrm{\Lambda }{e}^{+}\nu$ vs ${\overline{a}}_{\text{P}}$ from ${\overline{\mathrm{\Lambda }}}_c^{-}\to \overline{\mathrm{\Lambda }}{e}^{-}\overline{\nu }$. In the SM one gets $a_{\text{P}}=1$ and ${\overline{a}}_{\text{P}}=-1$ in the SM, while present data give the following: $(a_{\mathrm{P}}+{\overline{a}}_{\mathrm{P}})/2=0.00\pm 0.04$. Probing these nonleptonic decays of ${\mathrm{\Lambda }}_c^{+}$ would give new lessons about nonperturbative QCD or even indirect impact of new dynamics on parity violation.

• Received 31 July 2019

DOI:https://doi.org/10.1103/PhysRevD.100.113002

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Published by the American Physical Society