The LHCb state $P_{\psi s}^\Lambda(4338)$ as a triangle singularity

We present a model for the <math altimg="si2.svg"><mi>J</mi><mo stretchy="false">/</mo><mi>ψ</mi><mspace width="0.2em"/><mi mathvariant="normal">Λ</mi></math> spectrum in <math altimg="si3.svg"><msup><mrow><mi>B</mi></mrow><mrow><mo linebreak="badbreak" linebreakstyle="after">−</mo></mrow></msup><mo stretchy="false">→</mo><mi>J</mi><mo stretchy="false">/</mo><mi>ψ</mi><mspace width="0.2em"/><mi mathvariant="normal">Λ</mi><mspace width="0.2em"/><mover accent="true"><mrow><mi>p</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover></math> decays, including the <math altimg="si1.svg"><msubsup><mrow><mi>P</mi></mrow><mrow><mi>ψ</mi><mi>s</mi></mrow><mrow><mi mathvariant="normal">Λ</mi></mrow></msubsup><mo stretchy="false">(</mo><mn>4338</mn><mo stretchy="false">)</mo></math> baryon recently observed by the LHCb collaboration. We assume production via triangle diagrams which couple to the final state via non-perturbative interactions which are constrained by heavy-quark and <math altimg="si4.svg"><mi>S</mi><msub><mrow><mi>U</mi></mrow><mrow><mn>3</mn></mrow></msub></math>-flavor symmetry. The bulk of the distribution is described by a triangle diagram with a color-favored electroweak vertex, while the sharp <math altimg="si1.svg"><msubsup><mrow><mi>P</mi></mrow><mrow><mi>ψ</mi><mi>s</mi></mrow><mrow><mi mathvariant="normal">Λ</mi></mrow></msubsup><mo stretchy="false">(</mo><mn>4338</mn><mo stretchy="false">)</mo></math> enhancement is due to the triangle singularity in another diagram featuring a <math altimg="si5.svg"><mn>1</mn><mo stretchy="false">/</mo><msup><mrow><mn>2</mn></mrow><mrow><mo linebreak="badbreak" linebreakstyle="after">−</mo></mrow></msup></math> baryon consistent with <math altimg="si6.svg"><msub><mrow><mi mathvariant="normal">Σ</mi></mrow><mrow><mi>c</mi></mrow></msub><mo stretchy="false">(</mo><mn>2800</mn><mo stretchy="false">)</mo></math>. We predict a comparable <math altimg="si1.svg"><msubsup><mrow><mi>P</mi></mrow><mrow><mi>ψ</mi><mi>s</mi></mrow><mrow><mi mathvariant="normal">Λ</mi></mrow></msubsup><mo stretchy="false">(</mo><mn>4338</mn><mo stretchy="false">)</mo></math> signal in <math altimg="si7.svg"><msub><mrow><mi>η</mi></mrow><mrow><mi>c</mi></mrow></msub><mspace width="0.2em"/><mi mathvariant="normal">Λ</mi></math>, and anticipate possible large isospin mixing effects through decays to <math altimg="si8.svg"><mi>J</mi><mo stretchy="false">/</mo><mi>ψ</mi><mspace width="0.2em"/><msup><mrow><mi mathvariant="normal">Σ</mi></mrow><mrow><mn>0</mn></mrow></msup></math> and <math altimg="si9.svg"><msub><mrow><mi>η</mi></mrow><mrow><mi>c</mi></mrow></msub><mspace width="0.2em"/><msup><mrow><mi mathvariant="normal">Σ</mi></mrow><mrow><mn>0</mn></mrow></msup></math>.