Prospects for $P$ and $C\!P$ violation in $\Lambda_{c}^{+}$ decays with polarized beam at Super Tau-Charm Facility

Weak decays of the charmed baryons offer an ideal platform to study parity ($P$) and charge conjugation-parity ($C\!P$) violation in quark sector, to stringently test the Standard Model and search for new physics. It is a key goal in the next-generation positron-electron collider, such as the Super Tau-Charm Facility (STCF). Thanks to the quantum-entangled pair production with super high luminosity and the possibility of beam polarization, STCF provides a unique environment to probe such symmetry violations with unprecedented sensitivity. In this paper, we evaluate the precisions of the $P$-violating parameters and subsequently obtain the expected sensitivity of the $C\!P$-violating parameters in charmed baryon decays of $\Lambda_{c}^{+}\to p\pi^0$, $p\eta$, $\Lambda K^+$, $\Sigma^0 K^+$, and $\Sigma^+ K^0_S$, regarding to different polarization setups in STCF. The study suggests that the implementation of longitudinal beam polarization in STCF would greatly enhance the experimental capability in studying $P$ and $C\!P$ violation.