Hidden-flavor four-quark states in the charm and bottom region

We discuss the spectrum and the internal composition of ground and excited four-quark states in the charm and bottom energy region. To this end we extend previous calculations within the framework of the relativistic four-body Faddeev-Yakubovsky equation to include quantum numbers with <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msup><a:mi>J</a:mi><a:mrow><a:mi>P</a:mi><a:mi>C</a:mi></a:mrow></a:msup><a:mo>=</a:mo><a:msup><a:mn>0</a:mn><a:mrow><a:mo>+</a:mo><a:mo>+</a:mo></a:mrow></a:msup><a:mo>,</a:mo><a:msup><a:mn>0</a:mn><a:mrow><a:mo>−</a:mo><a:mo>+</a:mo></a:mrow></a:msup><a:mo>,</a:mo><a:msup><a:mn>1</a:mn><a:mrow><a:mo>−</a:mo><a:mo>−</a:mo></a:mrow></a:msup><a:mo>,</a:mo><a:msup><a:mn>1</a:mn><a:mrow><a:mo>+</a:mo><a:mo>−</a:mo></a:mrow></a:msup></a:math> and <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:msup><c:mn>1</c:mn><c:mrow><c:mo>+</c:mo><c:mo>+</c:mo></c:mrow></c:msup></c:math> and study their internal composition in terms of heavy-light meson pairs, hadroquarkonia and diquark-antidiquark clusters. We observe similar patterns in the charm and bottom energy region with different compositions of the four-quark states depending on <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:msup><e:mi>J</e:mi><e:mrow><e:mi>P</e:mi><e:mi>C</e:mi></e:mrow></e:msup></e:math> quantum numbers. Most notably, we find that all states with <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mi>C</g:mi><g:mo>·</g:mo><g:mi>P</g:mi><g:mo>=</g:mo><g:mo>+</g:mo><g:mn>1</g:mn></g:math> are dominated by heavy-light meson contributions, whereas for axial-vector states with <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:msup><i:mi>J</i:mi><i:mrow><i:mi>P</i:mi><i:mi>C</i:mi></i:mrow></i:msup><i:mo>=</i:mo><i:msup><i:mn>1</i:mn><i:mrow><i:mo>+</i:mo><i:mo>−</i:mo></i:mrow></i:msup></i:math> including the <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:msub><k:mi>Z</k:mi><k:mi>c</k:mi></k:msub><k:mo stretchy="false">(</k:mo><k:mn>3900</k:mn><k:mo stretchy="false">)</k:mo></k:math> we find a much more complicated picture depending on the flavor content. We systematically compare our results for the spectrum with existing experimental results and provide predictions for future analyses.