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CP violation is an excellent tool for probing flavor dynamics as we learntfirst with $K_L \to 2 \pi$ and later also with the weak decays of beautymesons. LHCb 2019 data have shown CP violation for the first time in $D^0\toK^-K^+$ vs. $D^0\to\pi^-\pi^+$. Searching for CP asymmetries is of greatinterest in charm quark sector in the Standard Model (SM) or even more beyondit. 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 arerare. 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 CPasymmetries in the decays $\Lambda^+_c \to p K^-\pi^+\pi^0$/$\Lambda\pi^+\pi^+\pi^-$/$pK_S\pi^+\pi^-$, where the SM gives zero values for the firsttwo channels, while $3.3 \times 10^{-3}$ for the last one due to $K^0 - \barK^0$ oscillation. We performed a fast Monte Carlo simulation study by usingelectron-positron annihilation data of 1~$\textrm{ab}^{-1}$ at center-of-massenergy $\sqrt{s}\, =\, 4.64$ GeV. The data is expected to be available by thenext generation Super Tau Charm Facility proposed by China and Russia with oneyear (or even less) data taking operation. The results indicate that asensitivity 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 as1%.

Prospects for CP & P violation in $\Lambda_{c}^+$ decay at STCF