Polarization analysis in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:msup> <mml:mrow> <mml:mi>e</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> </mml:mrow> </mml:msup> <mml:msup> <mml:mrow> <mml:mi>e<

We present a comprehensive polarization analysis for the process <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:msup> <a:mi>e</a:mi> <a:mo>+</a:mo> </a:msup> <a:msup> <a:mi>e</a:mi> <a:mo>−</a:mo> </a:msup> <a:mo stretchy="false">→</a:mo> <a:mi>J</a:mi> <a:mo>/</a:mo> <a:mi>ψ</a:mi> <a:mo stretchy="false">→</a:mo> </a:math> baryon-antibaryon pairs <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:msub> <e:mi>B</e:mi> <e:mn>1</e:mn> </e:msub> <e:msub> <e:mover accent="true"> <e:mi>B</e:mi> <e:mo stretchy="false">¯</e:mo> </e:mover> <e:mn>2</e:mn> </e:msub> </e:math> . All possible helicity amplitudes for <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:msup> <i:mi>e</i:mi> <i:mo>+</i:mo> </i:msup> <i:msup> <i:mi>e</i:mi> <i:mo>−</i:mo> </i:msup> <i:mo stretchy="false">→</i:mo> <i:mi>J</i:mi> <i:mo>/</i:mo> <i:mi>ψ</i:mi> </i:math> and <l:math xmlns:l="http://www.w3.org/1998/Math/MathML" display="inline"> <l:mi>J</l:mi> <l:mo>/</l:mo> <l:mi>ψ</l:mi> <l:mo stretchy="false">→</l:mo> <l:msub> <l:mi>B</l:mi> <l:mn>1</l:mn> </l:msub> <l:msub> <l:mover accent="true"> <l:mi>B</l:mi> <l:mo stretchy="false">¯</l:mo> </l:mover> <l:mn>2</l:mn> </l:msub> </l:math> are provided, along with their transformation properties under parity and <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"> <q:mi>C</q:mi> <q:mi>P</q:mi> </q:math> operations. Taking full account of beam polarization, we analyze the polarization of the <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"> <s:mi>J</s:mi> <s:mo>/</s:mo> <s:mi>ψ</s:mi> </s:math> produced in <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"> <u:msup> <u:mi>e</u:mi> <u:mo>+</u:mo> </u:msup> <u:msup> <u:mi>e</u:mi> <u:mo>−</u:mo> </u:msup> </u:math> annihilation and show that all eight independent polarization components can be nonzero. By introducing a polarization transfer matrix, we propose a novel method to compute the polarization transfer in the decay <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"> <w:mi>J</w:mi> <w:mo>/</w:mo> <w:mi>ψ</w:mi> <w:mo stretchy="false">→</w:mo> <w:msub> <w:mi>B</w:mi> <w:mn>1</w:mn> </w:msub> <w:msub> <w:mover accent="true"> <w:mi>B</w:mi> <w:mo stretchy="false">¯</w:mo> </w:mover> <w:mn>2</w:mn> </w:msub> </w:math> . Considering both hadronic and radiative baryon decay models, we derive the joint angular distribution of the final-state particles. Focusing on the process <bb:math xmlns:bb="http://www.w3.org/1998/Math/MathML" display="inline"> <bb:mi>J</bb:mi> <bb:mo>/</bb:mo> <bb:mi>ψ</bb:mi> <bb:mo stretchy="false">→</bb:mo> <bb:mi mathvariant="normal">Λ</bb:mi> <bb:msup> <bb:mover accent="true"> <bb:mi mathvariant="normal">Σ</bb:mi> <bb:mo stretchy="false">¯</bb:mo> </bb:mover> <bb:mn>0</bb:mn> </bb:msup> </bb:math> , we provide statistical uncertainty estimates for probing <ib:math xmlns:ib="http://www.w3.org/1998/Math/MathML" display="inline"> <ib:mi>C</ib:mi> <ib:mi>P</ib:mi> </ib:math> violation in associated production of different baryons. This work establishes a complete framework for studying the parity and <kb:math xmlns:kb="http://www.w3.org/1998/Math/MathML" display="inline"> <kb:mi>C</kb:mi> <kb:mi>P</kb:mi> </kb:math> violations present in baryon productions and decays within the helicity formalism.