Structure of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>c</mml:mi><mml:mi>c</mml:mi><mml:mover accent="true"><mml:mrow><mml:mi>c</mml:mi></mml:mrow><mml:mrow><mml:mo stretchy="false">¯</mml:mo></mml:mr

Motivated by recent experimental evidence for apparent <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>c</a:mi><a:mi>c</a:mi><a:mover accent="true"><a:mi>c</a:mi><a:mo stretchy="false">¯</a:mo></a:mover><a:mover accent="true"><a:mi>c</a:mi><a:mo stretchy="false">¯</a:mo></a:mover></a:math> states by LHCb, CMS and ATLAS, we consider how the mass spectrum and decays of such states can be used to discriminate among their possible theoretical interpretations, with a particular focus on identifying whether quarks or diquarks are the most relevant degrees of freedom. Our preferred scenario is that <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mi>X</g:mi><g:mo stretchy="false">(</g:mo><g:mn>6600</g:mn><g:mo stretchy="false">)</g:mo></g:math> and its apparent partner state <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mi>X</k:mi><k:mo stretchy="false">(</k:mo><k:mn>6400</k:mn><k:mo stretchy="false">)</k:mo></k:math> are the tensor <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:mo stretchy="false">(</o:mo><o:msup><o:mn>2</o:mn><o:mrow><o:mo>+</o:mo><o:mo>+</o:mo></o:mrow></o:msup><o:mo stretchy="false">)</o:mo></o:math> and scalar <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:mo stretchy="false">(</s:mo><s:msup><s:mn>0</s:mn><s:mrow><s:mo>+</s:mo><s:mo>+</s:mo></s:mrow></s:msup><s:mo stretchy="false">)</s:mo></s:math> states of an S-wave multiplet of <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"><w:mi>c</w:mi><w:mi>c</w:mi><w:mover accent="true"><w:mi>c</w:mi><w:mo stretchy="false">¯</w:mo></w:mover><w:mover accent="true"><w:mi>c</w:mi><w:mo stretchy="false">¯</w:mo></w:mover></w:math> states. Using tetraquark mass relations which are independent of (or only weakly dependent on) model parameters, we give predictions for the masses of additional partner states with axial and scalar quantum numbers. Additionally, we give predictions for relations among decay branching fractions to <cb:math xmlns:cb="http://www.w3.org/1998/Math/MathML" display="inline"><cb:mi>J</cb:mi><cb:mo>/</cb:mo><cb:mi>ψ</cb:mi><cb:mi>J</cb:mi><cb:mo>/</cb:mo><cb:mi>ψ</cb:mi></cb:math>, <eb:math xmlns:eb="http://www.w3.org/1998/Math/MathML" display="inline"><eb:mi>J</eb:mi><eb:mo>/</eb:mo><eb:mi>ψ</eb:mi><eb:msub><eb:mi>η</eb:mi><eb:mi>c</eb:mi></eb:msub></eb:math>, <gb:math xmlns:gb="http://www.w3.org/1998/Math/MathML" display="inline"><gb:msub><gb:mi>η</gb:mi><gb:mi>c</gb:mi></gb:msub><gb:msub><gb:mi>η</gb:mi><gb:mi>c</gb:mi></gb:msub></gb:math>, and <ib:math xmlns:ib="http://www.w3.org/1998/Math/MathML" display="inline"><ib:mrow><ib:msup><ib:mrow><ib:mi>D</ib:mi></ib:mrow><ib:mrow><ib:mo stretchy="false">(</ib:mo><ib:mo>*</ib:mo><ib:mo stretchy="false">)</ib:mo></ib:mrow></ib:msup><ib:msup><ib:mrow><ib:mover accent="true"><ib:mrow><ib:mi>D</ib:mi></ib:mrow><ib:mrow><ib:mo stretchy="false">¯</ib:mo></ib:mrow></ib:mover></ib:mrow><ib:mrow><ib:mo stretchy="false">(</ib:mo><ib:mo>*</ib:mo><ib:mo stretchy="false">)</ib:mo></ib:mrow></ib:msup></ib:mrow></ib:math> channels. The scenario we consider is consistent with existing experimental data on <qb:math xmlns:qb="http://www.w3.org/1998/Math/MathML" display="inline"><qb:mi>J</qb:mi><qb:mo>/</qb:mo><qb:mi>ψ</qb:mi><qb:mi>J</qb:mi><qb:mo>/</qb:mo><qb:mi>ψ</qb:mi></qb:math>, and our predictions for partner states and their decays can be confronted with future experimental data, to discriminate between quark and diquark models. Published by the American Physical Society 2024