Fully heavy tetraquark states and their evidences in LHC observations

Stimulated by the exciting progress on the observations of the fully charmed tetraquarks at LHC, we carry out a combined analysis of the mass spectra and fall-apart decays of the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mn>1</a:mn><a:mi>S</a:mi></a:mrow></a:math>-, <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mn>2</c:mn><c:mi>S</c:mi></c:math>-, and <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mn>1</e:mn><e:mi>P</e:mi></e:math>-wave <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mi>c</g:mi><g:mi>c</g:mi><g:mover accent="true"><g:mi>c</g:mi><g:mo stretchy="false">¯</g:mo></g:mover><g:mover accent="true"><g:mi>c</g:mi><g:mo stretchy="false">¯</g:mo></g:mover></g:math> states in a nonrelativistic quark model. It is found that the <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mi>X</m:mi><m:mo stretchy="false">(</m:mo><m:mn>6600</m:mn><m:mo stretchy="false">)</m:mo></m:math> structure observed in the di-<q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"><q:mi>J</q:mi><q:mo>/</q:mo><q:mi>ψ</q:mi></q:math> invariant mass spectrum can be explained by the <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:mn>1</s:mn><s:mi>S</s:mi></s:math>-wave state <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"><u:msub><u:mi>T</u:mi><u:mrow><u:mo stretchy="false">(</u:mo><u:mn>4</u:mn><u:mi>c</u:mi><u:mo stretchy="false">)</u:mo><u:msup><u:mn>0</u:mn><u:mrow><u:mo>+</u:mo><u:mo>+</u:mo></u:mrow></u:msup></u:mrow></u:msub><u:mo stretchy="false">(</u:mo><u:mn>6550</u:mn><u:mo stretchy="false">)</u:mo></u:math>. This structure may also bear some feed-down effects from the higher <ab:math xmlns:ab="http://www.w3.org/1998/Math/MathML" display="inline"><ab:mn>2</ab:mn><ab:mi>S</ab:mi></ab:math> and/or <cb:math xmlns:cb="http://www.w3.org/1998/Math/MathML" display="inline"><cb:mn>1</cb:mn><cb:mi>P</cb:mi></cb:math> tetraquark states. The <eb:math xmlns:eb="http://www.w3.org/1998/Math/MathML" display="inline"><eb:mi>X</eb:mi><eb:mo stretchy="false">(</eb:mo><eb:mn>6900</eb:mn><eb:mo stretchy="false">)</eb:mo></eb:math> structure observed in both the di-<ib:math xmlns:ib="http://www.w3.org/1998/Math/MathML" display="inline"><ib:mi>J</ib:mi><ib:mo>/</ib:mo><ib:mi>ψ</ib:mi></ib:math> and <kb:math xmlns:kb="http://www.w3.org/1998/Math/MathML" display="inline"><kb:mi>J</kb:mi><kb:mo>/</kb:mo><kb:mi>ψ</kb:mi><kb:mi>ψ</kb:mi><kb:mo stretchy="false">(</kb:mo><kb:mn>2</kb:mn><kb:mi>S</kb:mi><kb:mo stretchy="false">)</kb:mo></kb:math> channels can be naturally explained by the <ob:math xmlns:ob="http://www.w3.org/1998/Math/MathML" display="inline"><ob:mn>2</ob:mn><ob:mi>S</ob:mi></ob:math>-wave state <qb:math xmlns:qb="http://www.w3.org/1998/Math/MathML" display="inline"><qb:msub><qb:mi>T</qb:mi><qb:mrow><qb:mo stretchy="false">(</qb:mo><qb:mn>4</qb:mn><qb:mi>c</qb:mi><qb:mo stretchy="false">)</qb:mo><qb:msup><qb:mn>0</qb:mn><qb:mrow><qb:mo>+</qb:mo><qb:mo>+</qb:mo></qb:mrow></qb:msup></qb:mrow></qb:msub><qb:mo stretchy="false">(</qb:mo><qb:mn>6957</qb:mn><qb:mo stretchy="false">)</qb:mo></qb:math>. The small shoulder structure around 6.2–6.4 GeV observed at CMS and ATLAS may be due to the feed-down effects from some <wb:math xmlns:wb="http://www.w3.org/1998/Math/MathML" display="inline"><wb:mn>1</wb:mn><wb:mi>P</wb:mi></wb:math>-wave states with <yb:math xmlns:yb="http://www.w3.org/1998/Math/MathML" display="inline"><yb:mi>C</yb:mi><yb:mo>=</yb:mo><yb:mo>−</yb:mo><yb:mn>1</yb:mn></yb:math> and/or some <ac:math xmlns:ac="http://www.w3.org/1998/Math/MathML" display="inline"><ac:mn>2</ac:mn><ac:mi>S</ac:mi></ac:math>-wave states with <cc:math xmlns:cc="http://www.w3.org/1998/Math/MathML" display="inline"><cc:msup><cc:mi>J</cc:mi><cc:mrow><cc:mi>P</cc:mi><cc:mi>C</cc:mi></cc:mrow></cc:msup><cc:mo>=</cc:mo><cc:msup><cc:mn>0</cc:mn><cc:mrow><cc:mo>+</cc:mo><cc:mo>+</cc:mo></cc:mrow></cc:msup></cc:math>. Other decay channels are implied in such a scenario and they can be investigated by future experimental analyses. Considering the large discovery potential at LHC, we also present predictions for the <ec:math xmlns:ec="http://www.w3.org/1998/Math/MathML" display="inline"><ec:mi>b</ec:mi><ec:mi>b</ec:mi><ec:mover accent="true"><ec:mi>b</ec:mi><ec:mo stretchy="false">¯</ec:mo></ec:mover><ec:mover accent="true"><ec:mi>b</ec:mi><ec:mo stretchy="false">¯</ec:mo></ec:mover></ec:math> states which can be searched for in the future. Published by the American Physical Society 2024