Fundamental tests of <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>

We systematically investigate tests of the parity <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>P</a:mi></a:math> and the combined parity and charge-conjugate <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> symmetries from differential angular distributions of <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>J</e:mi><e:mo>/</e:mo><e:mi>ψ</e:mi></e:math> decaying into the lowest-lying baryon pairs at BESIII and the next-generation super tau-charm facilities (STCFs). Large corrections from <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mi>Z</g:mi></g:math> and <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mi>W</i:mi></i:math> exchange induced parity-violating effects are found for <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mi>J</k:mi><k:mo>/</k:mo><k:mi>ψ</k:mi></k:math> decays with large logarithms resummed up to <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mi mathvariant="script">O</m:mi><m:mo stretchy="false">(</m:mo><m:msub><m:mi>α</m:mi><m:mi>s</m:mi></m:msub><m:mo stretchy="false">)</m:mo></m:math>. The parity-violating asymmetries on the production and the decay sides of <r:math xmlns:r="http://www.w3.org/1998/Math/MathML" display="inline"><r:mi>J</r:mi><r:mo>/</r:mo><r:mi>ψ</r:mi></r:math> are both estimated to be of <t:math xmlns:t="http://www.w3.org/1998/Math/MathML" display="inline"><t:mi mathvariant="script">O</t:mi><t:mo stretchy="false">(</t:mo><t:msup><t:mn>10</t:mn><t:mrow><t:mo>−</t:mo><t:mn>4</t:mn></t:mrow></t:msup><t:mo stretchy="false">)</t:mo></t:math>, thus barely observable with the 10 billion <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"><y:mi>J</y:mi><y:mo>/</y:mo><y:mi>ψ</y:mi></y:math> events currently collected at BESIII. Nevertheless, these asymmetries utilizing the current BESIII data already permit a measurement of the weak mixing angle with an absolute uncertainty <ab:math xmlns:ab="http://www.w3.org/1998/Math/MathML" display="inline"><ab:mi>δ</ab:mi><ab:msubsup><ab:mi>s</ab:mi><ab:mi>w</ab:mi><ab:mn>2</ab:mn></ab:msubsup><ab:mo>≈</ab:mo><ab:mn>0.09</ab:mn></ab:math>, corresponding to the first determination of <cb:math xmlns:cb="http://www.w3.org/1998/Math/MathML" display="inline"><cb:msubsup><cb:mi>s</cb:mi><cb:mi>w</cb:mi><cb:mn>2</cb:mn></cb:msubsup></cb:math> at the <eb:math xmlns:eb="http://www.w3.org/1998/Math/MathML" display="inline"><eb:mi>J</eb:mi><eb:mo>/</eb:mo><eb:mi>ψ</eb:mi></eb:math> threshold. In the future, STCFs are estimated to improve this bound by a factor of <gb:math xmlns:gb="http://www.w3.org/1998/Math/MathML" display="inline"><gb:mo>∼</gb:mo><gb:mn>20</gb:mn></gb:math> to <ib:math xmlns:ib="http://www.w3.org/1998/Math/MathML" display="inline"><ib:mi>δ</ib:mi><ib:msubsup><ib:mi>s</ib:mi><ib:mi>w</ib:mi><ib:mn>2</ib:mn></ib:msubsup><ib:mo>≈</ib:mo><ib:mn>0.005</ib:mn></ib:math> within one year based on luminosity rescaling. We also obtain the 95% confidence level upper bounds on the electric dipole moments of the octet baryons, which are of <kb:math xmlns:kb="http://www.w3.org/1998/Math/MathML" display="inline"><kb:mrow><kb:mi mathvariant="script">O</kb:mi><kb:mo stretchy="false">(</kb:mo><kb:msup><kb:mrow><kb:mn>10</kb:mn></kb:mrow><kb:mrow><kb:mo>−</kb:mo><kb:mn>18</kb:mn></kb:mrow></kb:msup><kb:mo stretchy="false">)</kb:mo><kb:mtext> </kb:mtext><kb:mtext> </kb:mtext><kb:mi>e</kb:mi><kb:mtext> </kb:mtext><kb:mi>cm</kb:mi></kb:mrow></kb:math> for BESIII and <pb:math xmlns:pb="http://www.w3.org/1998/Math/MathML" display="inline"><pb:mrow><pb:mi mathvariant="script">O</pb:mi><pb:mo stretchy="false">(</pb:mo><pb:msup><pb:mrow><pb:mn>10</pb:mn></pb:mrow><pb:mrow><pb:mo>−</pb:mo><pb:mn>19</pb:mn></pb:mrow></pb:msup><pb:mo stretchy="false">)</pb:mo><pb:mtext> </pb:mtext><pb:mtext> </pb:mtext><pb:mi>e</pb:mi><pb:mtext> </pb:mtext><pb:mi>cm</pb:mi></pb:mrow></pb:math> for STCFs. These bounds are improved by 2 to 3 orders of magnitude in comparison with the only existing one on <ub:math xmlns:ub="http://www.w3.org/1998/Math/MathML" display="inline"><ub:mi mathvariant="normal">Λ</ub:mi></ub:math> from Fermilab. The method discussed in this work also paves a way for a first and direct measurement of the <xb:math xmlns:xb="http://www.w3.org/1998/Math/MathML" display="inline"><xb:mi mathvariant="normal">Ξ</xb:mi></xb:math> and <ac:math xmlns:ac="http://www.w3.org/1998/Math/MathML" display="inline"><ac:mi mathvariant="normal">Σ</ac:mi></ac:math> electric dipole moments. Published by the American Physical Society 2024