Heavy multiquark systems as clusters of smaller units: A diffusion Monte Carlo calculation

Multiquark systems appear less frequently than mesons and baryons despite the enormous worldwide experimental effort that has been made during the last two decades. In this work, we propose a possible explanation for that fact, restricting ourselves to the case of sets including only <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>c</a:mi></a:math> and <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mover accent="true"><c:mi>c</c:mi><c:mo stretchy="false">¯</c:mo></c:mover></c:math> quarks. We show that those multiquarks can be thought as different combinations of smaller units that associate together to produce colorless assemblies with a definite value of the total spin. For instance, for the <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mi>c</g:mi><g:mi>c</g:mi><g:mi>c</g:mi><g:mi>c</g:mi><g:mi>c</g:mi><g:mi>c</g:mi></g:math> hexaquark with spin <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mi>S</i:mi><i:mo>=</i:mo><i:mn>0</i:mn></i:math>, we have three possibilities; a set of six undistinguishable <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mi>c</k:mi></k:math> quarks, an association of two <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mi>c</m:mi><m:mi>c</m:mi><m:mi>c</m:mi></m:math> baryons, or a set of three <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:mi>c</o:mi><o:mi>c</o:mi></o:math> diquarks close together. This means we can have three different values for the mass of an open-charm hexaquark with <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"><q:mi>S</q:mi><q:mo>=</q:mo><q:mn>0</q:mn></q:math>. Using the diffusion Monte Carlo method, we calculate all possible combinations compatible with tetraquark <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:mi>c</s:mi><s:mi>c</s:mi><s:mover accent="true"><s:mi>c</s:mi><s:mo stretchy="false">¯</s:mo></s:mover><s:mover accent="true"><s:mi>c</s:mi><s:mo stretchy="false">¯</s:mo></s:mover></s:math>, pentaquark <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"><y:mi>c</y:mi><y:mi>c</y:mi><y:mi>c</y:mi><y:mi>c</y:mi><y:mover accent="true"><y:mi>c</y:mi><y:mo stretchy="false">¯</y:mo></y:mover></y:math>, open-charm <cb:math xmlns:cb="http://www.w3.org/1998/Math/MathML" display="inline"><cb:mi>c</cb:mi><cb:mi>c</cb:mi><cb:mi>c</cb:mi><cb:mi>c</cb:mi><cb:mi>c</cb:mi><cb:mi>c</cb:mi></cb:math>, and hidden-charm <eb:math xmlns:eb="http://www.w3.org/1998/Math/MathML" display="inline"><eb:mi>c</eb:mi><eb:mi>c</eb:mi><eb:mi>c</eb:mi><eb:mover accent="true"><eb:mi>c</eb:mi><eb:mo stretchy="false">¯</eb:mo></eb:mover><eb:mover accent="true"><eb:mi>c</eb:mi><eb:mo stretchy="false">¯</eb:mo></eb:mover><eb:mover accent="true"><eb:mi>c</eb:mi><eb:mo stretchy="false">¯</eb:mo></eb:mover></eb:math> hexaquark structures with the minimum value of total spin (<mb:math xmlns:mb="http://www.w3.org/1998/Math/MathML" display="inline"><mb:mi>S</mb:mi><mb:mo>=</mb:mo><mb:mn>0</mb:mn></mb:math> or <ob:math xmlns:ob="http://www.w3.org/1998/Math/MathML" display="inline"><ob:mi>S</ob:mi><ob:mo>=</ob:mo><ob:mn>1</ob:mn><ob:mo>/</ob:mo><ob:mn>2</ob:mn></ob:math>). We consider compact structures with radial wave functions including pair interactions between all the quarks in the cluster. We find that, in all cases, the mass of the multiquark decreases with the number of small units that conform the set of quarks. For instance, an open charm hexaquark made up of three diquarks has a smaller mass than a set of six <qb:math xmlns:qb="http://www.w3.org/1998/Math/MathML" display="inline"><qb:mi>c</qb:mi></qb:math> undistinguishable units. When the pieces that conform the multiquark are themselves colorless with a definite value of the total spin, the cluster splits into those smaller units that separate infinitely from each other.