Observation of transverse polarization and determination of psionic form factors of the Λ hyperon at s=3.773 GeV

Using a data sample of <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:math> collision data corresponding to an integrated luminosity of <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mn>20.3</c:mn><c:mtext> </c:mtext><c:mtext> </c:mtext><c:msup><c:mi>fb</c:mi><c:mrow><c:mo>−</c:mo><c:mn>1</c:mn></c:mrow></c:msup></c:math> collected by the BESIII detector at the BEPCII collider, we present an observation of transverse polarization and a complete determination of the psionic form factors of the <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi mathvariant="normal">Λ</e:mi></e:math> hyperon in <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"><h:msup><h:mi>e</h:mi><h:mo>+</h:mo></h:msup><h:msup><h:mi>e</h:mi><h:mo>−</h:mo></h:msup><h:mo stretchy="false">→</h:mo><h:mi mathvariant="normal">Λ</h:mi><h:mover accent="true"><h:mi mathvariant="normal">Λ</h:mi><h:mo stretchy="false">¯</h:mo></h:mover></h:math> decay with the entangled <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:mi mathvariant="normal">Λ</o:mi><o:mo>−</o:mo><o:mover accent="true"><o:mi mathvariant="normal">Λ</o:mi><o:mo stretchy="false">¯</o:mo></o:mover></o:math> pair at <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"><u:msqrt><u:mi>s</u:mi></u:msqrt><u:mo>=</u:mo><u:mn>3.773</u:mn><u:mtext> </u:mtext><u:mtext> </u:mtext><u:mi>GeV</u:mi></u:math>. The relative phase between the psionic form factors is determined to be <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"><w:mi mathvariant="normal">Δ</w:mi><w:mi mathvariant="normal">Φ</w:mi><w:mo>=</w:mo><w:mo stretchy="false">(</w:mo><w:mn>1.53</w:mn><w:mo>±</w:mo><w:mn>0.36</w:mn><w:mo>±</w:mo><w:mn>0.03</w:mn><w:mo stretchy="false">)</w:mo><w:mtext> </w:mtext><w:mtext> </w:mtext><w:mi>rad</w:mi></w:math> with a significance of 5.5 <cb:math xmlns:cb="http://www.w3.org/1998/Math/MathML" display="inline"><cb:mrow><cb:mi>σ</cb:mi></cb:mrow></cb:math> taking into account systematic uncertainty. This result indicates a nonzero phase between the transition amplitudes of the <eb:math xmlns:eb="http://www.w3.org/1998/Math/MathML" display="inline"><eb:mi mathvariant="normal">Λ</eb:mi><eb:mover accent="true"><eb:mi mathvariant="normal">Λ</eb:mi><eb:mo stretchy="false">¯</eb:mo></eb:mover></eb:math> helicity states. Additionally, we measure the angular distribution parameter and the modulus of the ratio between the psionic form factors to be <kb:math xmlns:kb="http://www.w3.org/1998/Math/MathML" display="inline"><kb:mi>η</kb:mi><kb:mo>=</kb:mo><kb:mn>0.86</kb:mn><kb:mo>±</kb:mo><kb:mn>0.05</kb:mn><kb:mo>±</kb:mo><kb:mn>0.03</kb:mn></kb:math> and <mb:math xmlns:mb="http://www.w3.org/1998/Math/MathML" display="inline"><mb:mrow><mb:mi>R</mb:mi><mb:mo stretchy="false">(</mb:mo><mb:mi>s</mb:mi><mb:mo stretchy="false">)</mb:mo><mb:mo>=</mb:mo><mb:mo stretchy="false">|</mb:mo><mb:msub><mb:mrow><mb:mi>G</mb:mi></mb:mrow><mb:mrow><mb:mi>E</mb:mi></mb:mrow></mb:msub><mb:mo stretchy="false">(</mb:mo><mb:mi>s</mb:mi><mb:mo stretchy="false">)</mb:mo><mb:mo>/</mb:mo><mb:msub><mb:mrow><mb:mi>G</mb:mi></mb:mrow><mb:mrow><mb:mi>M</mb:mi></mb:mrow></mb:msub><mb:mo stretchy="false">(</mb:mo><mb:mi>s</mb:mi><mb:mo stretchy="false">)</mb:mo><mb:mo stretchy="false">|</mb:mo><mb:mo>=</mb:mo><mb:mn>0.47</mb:mn><mb:mo>±</mb:mo><mb:mn>0.08</mb:mn><mb:mo>±</mb:mo><mb:mn>0.05</mb:mn></mb:mrow></mb:math>, where the first uncertainty is statistical and the second systematic.