Precision CP Symmetry Test and Polarization Analysis in Σ+ Decays

A stringent test of <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mi>C</a:mi><a:mi>P</a:mi></a:mrow></a:math> symmetry in hyperon decays is performed using <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mrow><c:mn>1.0</c:mn><c:mo>×</c:mo><c:msup><c:mrow><c:mn>10</c:mn></c:mrow><c:mrow><c:mn>10</c:mn></c:mrow></c:msup><c:mtext> </c:mtext><c:mtext> </c:mtext><c:mi>J</c:mi><c:mo>/</c:mo><c:mi>ψ</c:mi></c:mrow></c:math> events and <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mn>2.7</e:mn><e:mo>×</e:mo><e:msup><e:mn>10</e:mn><e:mn>9</e:mn></e:msup><e:mtext> </e:mtext><e:mtext> </e:mtext><e:mi>ψ</e:mi><e:mo stretchy="false">(</e:mo><e:mn>3686</e:mn><e:mo stretchy="false">)</e:mo></e:math> events collected by the BESIII experiment. The <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mi>C</i:mi><i:mi>P</i:mi></i:math> asymmetry in the two-body nonleptonic weak decays <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:msup><k:mi mathvariant="normal">Σ</k:mi><k:mo>+</k:mo></k:msup><k:mo stretchy="false">→</k:mo><k:mi>p</k:mi><k:msup><k:mi>π</k:mi><k:mn>0</k:mn></k:msup></k:math> and <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:msup><o:mover accent="true"><o:mi mathvariant="normal">Σ</o:mi><o:mo stretchy="false">¯</o:mo></o:mover><o:mo>−</o:mo></o:msup><o:mo stretchy="false">→</o:mo><o:mover accent="true"><o:mi>p</o:mi><o:mo stretchy="false">¯</o:mo></o:mover><o:msup><o:mi>π</o:mi><o:mn>0</o:mn></o:msup></o:math> is determined to be <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"><w:mrow><w:msub><w:mrow><w:mi>A</w:mi></w:mrow><w:mrow><w:mi>C</w:mi><w:mi>P</w:mi></w:mrow></w:msub><w:mo>=</w:mo><w:mo>−</w:mo><w:mn>0.0118</w:mn><w:mo>±</w:mo><w:mn>0.0083</w:mn><w:mo stretchy="false">(</w:mo><w:mrow><w:mi>stat</w:mi></w:mrow><w:mo stretchy="false">)</w:mo><w:mo>±</w:mo><w:mn>0.0028</w:mn><w:mo stretchy="false">(</w:mo><w:mrow><w:mi>syst</w:mi></w:mrow><w:mo stretchy="false">)</w:mo></w:mrow></w:math>, consistent with <cb:math xmlns:cb="http://www.w3.org/1998/Math/MathML" display="inline"><cb:mi>C</cb:mi><cb:mi>P</cb:mi></cb:math> conservation. The average decay parameter <eb:math xmlns:eb="http://www.w3.org/1998/Math/MathML" display="inline"><eb:mrow><eb:mrow><eb:mo stretchy="false">⟨</eb:mo><eb:msub><eb:mrow><eb:mi>α</eb:mi></eb:mrow><eb:mrow><eb:mn>0</eb:mn></eb:mrow></eb:msub><eb:mo stretchy="false">⟩</eb:mo></eb:mrow><eb:mo>=</eb:mo><eb:mo>−</eb:mo><eb:mn>0.9869</eb:mn><eb:mo>±</eb:mo><eb:mn>0.0011</eb:mn><eb:mo stretchy="false">(</eb:mo><eb:mrow><eb:mi>stat</eb:mi></eb:mrow><eb:mo stretchy="false">)</eb:mo><eb:mo>±</eb:mo><eb:mn>0.0016</eb:mn><eb:mo stretchy="false">(</eb:mo><eb:mrow><eb:mi>syst</eb:mi></eb:mrow><eb:mo stretchy="false">)</eb:mo></eb:mrow></eb:math> represents the most precise measurement in the baryon sector to date. A model-independent analysis of the hyperon polarization is performed for the first time at <mb:math xmlns:mb="http://www.w3.org/1998/Math/MathML" display="inline"><mb:mi>J</mb:mi><mb:mo>/</mb:mo><mb:mi>ψ</mb:mi></mb:math> and <ob:math xmlns:ob="http://www.w3.org/1998/Math/MathML" display="inline"><ob:mi>ψ</ob:mi><ob:mo stretchy="false">(</ob:mo><ob:mn>3686</ob:mn><ob:mo stretchy="false">)</ob:mo></ob:math> resonances, revealing a clear sign reversal and offering new insight into SU(3) symmetry breaking and baryon internal structure. These results provide the most stringent constraints on <sb:math xmlns:sb="http://www.w3.org/1998/Math/MathML" display="inline"><sb:mi>C</sb:mi><sb:mi>P</sb:mi></sb:math> violation in <ub:math xmlns:ub="http://www.w3.org/1998/Math/MathML" display="inline"><ub:mi mathvariant="normal">Σ</ub:mi></ub:math> decays and establish a benchmark for future precision studies.