| Summary: | JLab has recently found indications of the possible existence of a <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>Σ</mo><mi>N</mi><mi>N</mi></mrow></semantics></math></inline-formula> resonance at <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mn>3.14</mn><mo>±</mo><mn>0.84</mn><mo>)</mo><mo>−</mo><mi>i</mi><mo>(</mo><mn>2.28</mn><mo>±</mo><mn>1.2</mn><mo>)</mo></mrow></semantics></math></inline-formula> MeV. In the past, using models that exploit symmetries between the two-baryon sector with and without strangeness, hyperon–nucleon interactions that reproduce the experimental data of the strangeness <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>−</mo><mn>1</mn></mrow></semantics></math></inline-formula> sector have been derived. We make use of these interactions to review the existing Faddeev studies of the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>Λ</mo><mi>N</mi><mi>N</mi><mo>−</mo><mo>Σ</mo><mi>N</mi><mi>N</mi></mrow></semantics></math></inline-formula> system that show theoretical evidence of a <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mrow><mo>(</mo><mi>I</mi><mo>,</mo><msup><mi>J</mi><mi>P</mi></msup><mo>)</mo></mrow><mo>=</mo><mrow><mo>(</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>/</mo><msup><mn>2</mn><mo>+</mo></msup><mo>)</mo></mrow></mrow></semantics></math></inline-formula><inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>Σ</mo><mi>N</mi><mi>N</mi></mrow></semantics></math></inline-formula> quasibound state near the threshold. The calculated position of the pole is at 2.92<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mspace width="0.166667em"></mspace><mo>−</mo><mi>i</mi><mspace width="0.166667em"></mspace></mrow></semantics></math></inline-formula>2.17 MeV, which is in reasonable agreement with the experimental findings.
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