Doubly heavy tetraquark states in the constituent quark model using diffusion Monte Carlo method

We use the diffusion Monte Carlo (DMC) method to calculate the doubly heavy tetraquark <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:msub><a:mrow><a:mi>T</a:mi></a:mrow><a:mrow><a:mi>c</a:mi><a:mi>c</a:mi></a:mrow></a:msub></a:mrow></a:math> system in two kinds of constituent quark models, the pure constituent quark model AL1/AP1 and the chiral constituent quark model. When the discrete configurations are complete and no spatial clustering is predetermined, the AL1/AP1 model gives an energy of <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mrow><c:msub><c:mrow><c:mi>T</c:mi></c:mrow><c:mrow><c:mi>c</c:mi><c:mi>c</c:mi></c:mrow></c:msub></c:mrow></c:math> close to the <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>D</e:mi><e:msup><e:mi>D</e:mi><e:mo>*</e:mo></e:msup></e:math> threshold, and the chiral constituent quark model yields a deeply bound state. We further calculate all doubly heavy tetraquark systems with <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:msup><g:mi>J</g:mi><g:mi>P</g:mi></g:msup><g:mo>=</g:mo><g:msup><g:mn>0</g:mn><g:mo>+</g:mo></g:msup><g:mo>,</g:mo><g:msup><g:mn>1</g:mn><g:mo>+</g:mo></g:msup><g:mo>,</g:mo><g:msup><g:mn>2</g:mn><g:mo>+</g:mo></g:msup></g:math>, and provide the binding energies of systems with bound states. The <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mi>I</i:mi><i:mo stretchy="false">(</i:mo><i:msup><i:mi>J</i:mi><i:mi>P</i:mi></i:msup><i:mo stretchy="false">)</i:mo><i:mo>=</i:mo><i:mn>0</i:mn><i:mo stretchy="false">(</i:mo><i:msup><i:mn>0</i:mn><i:mo>+</i:mo></i:msup><i:mo stretchy="false">)</i:mo></i:math> <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:mi>b</o:mi><o:mi>c</o:mi><o:mover accent="true"><o:mi>n</o:mi><o:mo stretchy="false">¯</o:mo></o:mover><o:mover accent="true"><o:mi>n</o:mi><o:mo stretchy="false">¯</o:mo></o:mover></o:math>, <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"><u:mn>0</u:mn><u:mo stretchy="false">(</u:mo><u:msup><u:mn>1</u:mn><u:mo>+</u:mo></u:msup><u:mo stretchy="false">)</u:mo></u:math> <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"><y:mi>b</y:mi><y:mi>b</y:mi><y:mover accent="true"><y:mi>n</y:mi><y:mo stretchy="false">¯</y:mo></y:mover><y:mover accent="true"><y:mi>n</y:mi><y:mo stretchy="false">¯</y:mo></y:mover></y:math>, <eb:math xmlns:eb="http://www.w3.org/1998/Math/MathML" display="inline"><eb:mn>0</eb:mn><eb:mo stretchy="false">(</eb:mo><eb:msup><eb:mn>1</eb:mn><eb:mo>+</eb:mo></eb:msup><eb:mo stretchy="false">)</eb:mo></eb:math> <ib:math xmlns:ib="http://www.w3.org/1998/Math/MathML" display="inline"><ib:mi>b</ib:mi><ib:mi>c</ib:mi><ib:mover accent="true"><ib:mi>n</ib:mi><ib:mo stretchy="false">¯</ib:mo></ib:mover><ib:mover accent="true"><ib:mi>n</ib:mi><ib:mo stretchy="false">¯</ib:mo></ib:mover></ib:math>, <ob:math xmlns:ob="http://www.w3.org/1998/Math/MathML" display="inline"><ob:mfrac><ob:mn>1</ob:mn><ob:mn>2</ob:mn></ob:mfrac><ob:mo stretchy="false">(</ob:mo><ob:msup><ob:mn>1</ob:mn><ob:mo>+</ob:mo></ob:msup><ob:mo stretchy="false">)</ob:mo></ob:math> <sb:math xmlns:sb="http://www.w3.org/1998/Math/MathML" display="inline"><sb:mi>b</sb:mi><sb:mi>b</sb:mi><sb:mover accent="true"><sb:mi>s</sb:mi><sb:mo stretchy="false">¯</sb:mo></sb:mover><sb:mover accent="true"><sb:mi>n</sb:mi><sb:mo stretchy="false">¯</sb:mo></sb:mover></sb:math> systems have bound states in all three models. Since the DMC method has almost no restriction on the spatial part, the resulting bound states have greater binding energies than those obtained in previous works.