Role of the triangle singularity in the isospin breaking process J/ψ→ΛΛ¯π and the possible evidence of…

In this study, the impact of triangle singularity is investigated in the isospin breaking process <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>J</a:mi><a:mo>/</a:mo><a:mi>ψ</a:mi><a:mo stretchy="false">→</a:mo><a:mi mathvariant="normal">Λ</a:mi><a:mover accent="true"><a:mi mathvariant="normal">Λ</a:mi><a:mo stretchy="false">¯</a:mo></a:mover><a:mi>π</a:mi></a:math>. The triangle singularity is found to play a significant role in the process, resulting in the creation of a resonancelike structure around 1.4 GeV in the <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"><h:mi mathvariant="normal">Λ</h:mi><h:mi>π</h:mi><h:mo stretchy="false">(</h:mo><h:mover accent="true"><h:mi mathvariant="normal">Λ</h:mi><h:mo stretchy="false">¯</h:mo></h:mover><h:mi>π</h:mi><h:mo stretchy="false">)</h:mo></h:math> invariant mass spectrum. To amplify the impact of this triangle singularity, the presence of two <p:math xmlns:p="http://www.w3.org/1998/Math/MathML" display="inline"><p:mrow><p:msup><p:mrow><p:mi mathvariant="normal">Σ</p:mi></p:mrow><p:mrow><p:mo>*</p:mo></p:mrow></p:msup><p:mo stretchy="false">(</p:mo><p:msup><p:mrow><p:mfrac><p:mrow><p:mn>1</p:mn></p:mrow><p:mrow><p:mn>2</p:mn></p:mrow></p:mfrac></p:mrow><p:mrow><p:mo>−</p:mo></p:mrow></p:msup><p:mo stretchy="false">)</p:mo></p:mrow></p:math> states around 1.4 GeV and 1.6 GeV is essential, yet these states have not been definitively identified in the current baryon spectrum. We recommend that experiments, particularly the Beijing Spectrometer and the future Super Tau-Charm Factory, investigate the process <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"><u:mi>J</u:mi><u:mo>/</u:mo><u:mi>ψ</u:mi><u:mo stretchy="false">→</u:mo><u:mi mathvariant="normal">Λ</u:mi><u:mover accent="true"><u:mi mathvariant="normal">Λ</u:mi><u:mo stretchy="false">¯</u:mo></u:mover><u:mi>π</u:mi></u:math> to offer direct evidence for our predicted triangle singularity and additional evidence regarding the <bb:math xmlns:bb="http://www.w3.org/1998/Math/MathML" display="inline"><bb:mi mathvariant="normal">Σ</bb:mi><bb:mo stretchy="false">(</bb:mo><bb:msup><bb:mfrac><bb:mn>1</bb:mn><bb:mn>2</bb:mn></bb:mfrac><bb:mo>−</bb:mo></bb:msup><bb:mo stretchy="false">)</bb:mo></bb:math> states.