| Summary: | We analyze possible singularities in the <inline-formula><math display="inline"><semantics><mrow><mi>J</mi><mo>/</mo><mi>ψ</mi><mo>Λ</mo></mrow></semantics></math></inline-formula> invariant mass distribution of the <inline-formula><math display="inline"><semantics><mrow><msubsup><mo>Ξ</mo><mi>b</mi><mo>−</mo></msubsup><mspace width="3.33333pt"></mspace><mo>→</mo><mspace width="3.33333pt"></mspace><msup><mi>K</mi><mo>−</mo></msup><mi>J</mi><mo>/</mo><mi>ψ</mi><mo>Λ</mo></mrow></semantics></math></inline-formula> process via triangle loop diagrams. Triangle singularities in the physical region are found in 18 different triangle loop diagrams. Among those with <inline-formula><math display="inline"><semantics><msup><mo>Ξ</mo><mo>*</mo></msup></semantics></math></inline-formula>-charmonium-<inline-formula><math display="inline"><semantics><mo>Λ</mo></semantics></math></inline-formula> intermediate states, the one from the <inline-formula><math display="inline"><semantics><mrow><msub><mi>χ</mi><mrow><mi>c</mi><mn>1</mn></mrow></msub><mo>Ξ</mo><mrow><mo>(</mo><mn>2120</mn><mo>)</mo></mrow><mo>Λ</mo></mrow></semantics></math></inline-formula> loop, which is located around 4628 MeV, is found the most likely to cause observable effects. One needs <i>S</i>- and <i>P</i>-waves in <inline-formula><math display="inline"><semantics><mrow><msub><mi>χ</mi><mrow><mi>c</mi><mn>1</mn></mrow></msub><mo>Λ</mo></mrow></semantics></math></inline-formula> and <inline-formula><math display="inline"><semantics><mrow><mi>J</mi><mo>/</mo><mi>ψ</mi><mo>Λ</mo></mrow></semantics></math></inline-formula> systems, respectively, when the quantum numbers of these systems are <inline-formula><math display="inline"><semantics><mrow><mn>1</mn><mo>/</mo><msup><mn>2</mn><mo>+</mo></msup></mrow></semantics></math></inline-formula> or <inline-formula><math display="inline"><semantics><mrow><mn>3</mn><mo>/</mo><msup><mn>2</mn><mo>+</mo></msup></mrow></semantics></math></inline-formula>. When the quantum numbers of the <inline-formula><math display="inline"><semantics><mrow><mo>Ξ</mo><mo>(</mo><mn>2120</mn><mo>)</mo></mrow></semantics></math></inline-formula> are <inline-formula><math display="inline"><semantics><mrow><msup><mi>J</mi><mi>P</mi></msup><mo>=</mo><mn>1</mn><mo>/</mo><msup><mn>2</mn><mo>+</mo></msup></mrow></semantics></math></inline-formula>, <inline-formula><math display="inline"><semantics><mrow><mn>1</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup></mrow></semantics></math></inline-formula> or <inline-formula><math display="inline"><semantics><mrow><mn>3</mn><mo>/</mo><msup><mn>2</mn><mo>+</mo></msup></mrow></semantics></math></inline-formula>, the peak structure should be sharper than the other <inline-formula><math display="inline"><semantics><msup><mi>J</mi><mi>P</mi></msup></semantics></math></inline-formula> choices. This suggests that although the whole strength is unknown, we should pay attention to the contributions from the <inline-formula><math display="inline"><semantics><msup><mo>Ξ</mo><mo>*</mo></msup></semantics></math></inline-formula>-charmonium-<inline-formula><math display="inline"><semantics><mo>Λ</mo></semantics></math></inline-formula> triangle diagram if structures are observed in the <inline-formula><math display="inline"><semantics><mrow><mi>J</mi><mo>/</mo><mi>ψ</mi><mo>Λ</mo></mrow></semantics></math></inline-formula> invariant mass spectrum experimentally. In addition, a few triangle diagrams with the <inline-formula><math display="inline"><semantics><mrow><msubsup><mi>D</mi><mrow><mi>s</mi><mn>1</mn></mrow><mo>*</mo></msubsup><mrow><mo>(</mo><mn>2700</mn><mo>)</mo></mrow></mrow></semantics></math></inline-formula> as one of the intermediate particles can also produce singularities in the <inline-formula><math display="inline"><semantics><mrow><mi>J</mi><mo>/</mo><mi>ψ</mi><mo>Λ</mo></mrow></semantics></math></inline-formula> distribution, but at higher energies above 4.9 GeV.
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