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

Abstract

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. Published by the American Physical Society 2024

Topics & Concepts