Prospects for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>P</mml:mi> </mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>C</mml:mi> <mml:mi>P</mml:mi> </mml:math> v

Weak decays of the charmed baryons offer an ideal platform to study parity ( <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>P</a:mi> </a:math> ) and charge conjugation-parity ( <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mi>C</c:mi> <c:mi>P</c:mi> </c:math> ) violation in the 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 superhigh 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 <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:mi>P</e:mi> </e:math> -violating parameters and subsequently obtain the expected sensitivity of the <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:mi>C</g:mi> <g:mi>P</g:mi> </g:math> -violating parameters in charmed baryon decays of <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:msubsup> <i:mi mathvariant="normal">Λ</i:mi> <i:mi>c</i:mi> <i:mo>+</i:mo> </i:msubsup> <i:mo stretchy="false">→</i:mo> <i:mi>p</i:mi> <i:msup> <i:mi>π</i:mi> <i:mn>0</i:mn> </i:msup> </i:math> , <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"> <m:mi>p</m:mi> <m:mi>η</m:mi> </m:math> , <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"> <o:mi mathvariant="normal">Λ</o:mi> <o:msup> <o:mi>K</o:mi> <o:mo>+</o:mo> </o:msup> </o:math> , <r:math xmlns:r="http://www.w3.org/1998/Math/MathML" display="inline"> <r:msup> <r:mi mathvariant="normal">Σ</r:mi> <r:mn>0</r:mn> </r:msup> <r:msup> <r:mi>K</r:mi> <r:mo>+</r:mo> </r:msup> </r:math> , and <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"> <u:msup> <u:mi mathvariant="normal">Σ</u:mi> <u:mo>+</u:mo> </u:msup> <u:msubsup> <u:mi>K</u:mi> <u:mi>S</u:mi> <u:mn>0</u:mn> </u:msubsup> </u:math> , 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 <x:math xmlns:x="http://www.w3.org/1998/Math/MathML" display="inline"> <x:mi>P</x:mi> </x:math> and <z:math xmlns:z="http://www.w3.org/1998/Math/MathML" display="inline"> <z:mi>C</z:mi> <z:mi>P</z:mi> </z:math> violation.