Exploring the Efimov effect in the D*D*D* system

The emergence of the Efimov effect in the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msup><a:mi>D</a:mi><a:mo>*</a:mo></a:msup><a:msup><a:mi>D</a:mi><a:mo>*</a:mo></a:msup><a:msup><a:mi>D</a:mi><a:mo>*</a:mo></a:msup></a:math> system is explored under the assumption that the heavy partner of the <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:msubsup><c:mi>T</c:mi><c:mrow><c:mi>c</c:mi><c:mi>c</c:mi></c:mrow><c:mo>+</c:mo></c:msubsup></c:math> exists as a <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:msup><e:mi>D</e:mi><e:mo>*</e:mo></e:msup><e:msup><e:mi>D</e:mi><e:mo>*</e:mo></e:msup></e:math> molecule with <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mrow><g:mo stretchy="false">(</g:mo><g:mi>I</g:mi><g:mo stretchy="false">)</g:mo><g:msup><g:mrow><g:mi>J</g:mi></g:mrow><g:mrow><g:mi>P</g:mi></g:mrow></g:msup><g:mo>=</g:mo><g:mo stretchy="false">(</g:mo><g:mn>0</g:mn><g:mo stretchy="false">)</g:mo><g:msup><g:mrow><g:mn>1</g:mn></g:mrow><g:mrow><g:mo>+</g:mo></g:mrow></g:msup></g:mrow></g:math>. The three-to-three relativistic scattering amplitude is obtained from the ladder amplitude formalism, built from an energy-dependent contact two-body potential where the molecular component of the <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:msubsup><m:mi>T</m:mi><m:mrow><m:mi>c</m:mi><m:mi>c</m:mi></m:mrow><m:mo>*</m:mo></m:msubsup></m:math> state can be varied. We find that <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:mrow><o:mo stretchy="false">(</o:mo><o:mi>I</o:mi><o:mo stretchy="false">)</o:mo><o:msup><o:mrow><o:mi>J</o:mi></o:mrow><o:mrow><o:mi>P</o:mi></o:mrow></o:msup><o:mo>=</o:mo><o:mo stretchy="false">(</o:mo><o:mfrac><o:mrow><o:mn>1</o:mn></o:mrow><o:mrow><o:mn>2</o:mn></o:mrow></o:mfrac><o:mo stretchy="false">)</o:mo><o:msup><o:mrow><o:mn>0</o:mn></o:mrow><o:mrow><o:mo>−</o:mo></o:mrow></o:msup></o:mrow></o:math> three-body bound states can be formed, with properties that suggest that the Efimov effect can be realized for reasonable values of the molecular probability and binding energy of the <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"><u:msubsup><u:mi>T</u:mi><u:mrow><u:mi>c</u:mi><u:mi>c</u:mi></u:mrow><u:mo>*</u:mo></u:msubsup></u:math>.