Spectrum of the molecular tetraquarks: Unraveling the Tcs0(2900) and <…

This is the authors' abstract. We don't add key points for this paper.

We relate the interactions of the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:msup><a:mrow><a:mover accent="true"><a:mrow><a:mi>D</a:mi></a:mrow><a:mrow><a:mo stretchy="false">¯</a:mo></a:mrow></a:mover></a:mrow><a:mrow><a:mo stretchy="false">(</a:mo><a:mo>*</a:mo><a:mo stretchy="false">)</a:mo></a:mrow></a:msup><a:msup><a:mrow><a:mi>K</a:mi></a:mrow><a:mrow><a:mo>*</a:mo></a:mrow></a:msup></a:mrow></a:math> and <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mrow><g:msup><g:mrow><g:mi>D</g:mi></g:mrow><g:mrow><g:mo stretchy="false">(</g:mo><g:mo>*</g:mo><g:mo stretchy="false">)</g:mo></g:mrow></g:msup><g:msup><g:mrow><g:mi>K</g:mi></g:mrow><g:mrow><g:mo>*</g:mo></g:mrow></g:msup></g:mrow></g:math> systems to those of <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mrow><k:msup><k:mrow><k:mi>D</k:mi></k:mrow><k:mrow><k:mo stretchy="false">(</k:mo><k:mo>*</k:mo><k:mo stretchy="false">)</k:mo></k:mrow></k:msup><k:msup><k:mrow><k:mi>D</k:mi></k:mrow><k:mrow><k:mo stretchy="false">(</k:mo><k:mo>*</k:mo><k:mo stretchy="false">)</k:mo></k:mrow></k:msup></k:mrow></k:math> and <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"><q:mrow><q:msup><q:mrow><q:mi>D</q:mi></q:mrow><q:mrow><q:mo stretchy="false">(</q:mo><q:mo>*</q:mo><q:mo stretchy="false">)</q:mo></q:mrow></q:msup><q:msup><q:mrow><q:mover accent="true"><q:mrow><q:mi>D</q:mi></q:mrow><q:mrow><q:mo stretchy="false">¯</q:mo></q:mrow></q:mover></q:mrow><q:mrow><q:mo stretchy="false">(</q:mo><q:mo>*</q:mo><q:mo stretchy="false">)</q:mo></q:mrow></q:msup></q:mrow></q:math> respectively, considering the residual strong interactions at the near-threshold energy is too weak to excite the strange quarks inside the hadrons. We propose an effective model to describe the low-energy S-wave interactions that are undertaken by the light <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"><y:mi>u</y:mi></y:math>, <ab:math xmlns:ab="http://www.w3.org/1998/Math/MathML" display="inline"><ab:mi>d</ab:mi></ab:math> quarks between two separated heavy hadrons. We find that the existence of molecules in the heavy-(anti)heavy sectors will naturally lead to the emergence of molecular states in <cb:math xmlns:cb="http://www.w3.org/1998/Math/MathML" display="inline"><cb:mrow><cb:msup><cb:mrow><cb:mover accent="true"><cb:mrow><cb:mi>D</cb:mi></cb:mrow><cb:mrow><cb:mo stretchy="false">¯</cb:mo></cb:mrow></cb:mover></cb:mrow><cb:mrow><cb:mo stretchy="false">(</cb:mo><cb:mo>*</cb:mo><cb:mo stretchy="false">)</cb:mo></cb:mrow></cb:msup><cb:msup><cb:mrow><cb:mi>K</cb:mi></cb:mrow><cb:mrow><cb:mo>*</cb:mo></cb:mrow></cb:msup></cb:mrow></cb: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:mi>K</ib:mi></ib:mrow><ib:mrow><ib:mo>*</ib:mo></ib:mrow></ib:msup></ib:mrow></ib:math> systems. The recently observed <mb:math xmlns:mb="http://www.w3.org/1998/Math/MathML" display="inline"><mb:mrow><mb:msub><mb:mrow><mb:mi>T</mb:mi></mb:mrow><mb:mrow><mb:mi>c</mb:mi><mb:mi>s</mb:mi><mb:mn>0</mb:mn></mb:mrow></mb:msub><mb:mo stretchy="false">(</mb:mo><mb:mn>2900</mb:mn><mb:mo stretchy="false">)</mb:mo></mb:mrow></mb:math> and <qb:math xmlns:qb="http://www.w3.org/1998/Math/MathML" display="inline"><qb:mrow><qb:msubsup><qb:mrow><qb:mi>T</qb:mi></qb:mrow><qb:mrow><qb:mi>c</qb:mi><qb:mover accent="true"><qb:mrow><qb:mi>s</qb:mi></qb:mrow><qb:mrow><qb:mo stretchy="false">¯</qb:mo></qb:mrow></qb:mover><qb:mn>0</qb:mn></qb:mrow><qb:mrow><qb:mi>a</qb:mi></qb:mrow></qb:msubsup><qb:mo stretchy="false">(</qb:mo><qb:mn>2900</qb:mn><qb:mo stretchy="false">)</qb:mo></qb:mrow></qb:math> can be well identified as the <wb:math xmlns:wb="http://www.w3.org/1998/Math/MathML" display="inline"><wb:mn>0</wb:mn><wb:mo stretchy="false">(</wb:mo><wb:msup><wb:mn>0</wb:mn><wb:mo>+</wb:mo></wb:msup><wb:mo stretchy="false">)</wb:mo></wb:math> and <ac:math xmlns:ac="http://www.w3.org/1998/Math/MathML" display="inline"><ac:mn>1</ac:mn><ac:mo stretchy="false">(</ac:mo><ac:msup><ac:mn>0</ac:mn><ac:mo>+</ac:mo></ac:msup><ac:mo stretchy="false">)</ac:mo></ac:math> partners of <ec:math xmlns:ec="http://www.w3.org/1998/Math/MathML" display="inline"><ec:mrow><ec:msub><ec:mrow><ec:mi>T</ec:mi></ec:mrow><ec:mrow><ec:mi>c</ec:mi><ec:mi>c</ec:mi></ec:mrow></ec:msub><ec:mo stretchy="false">(</ec:mo><ec:mn>3875</ec:mn><ec:mo stretchy="false">)</ec:mo></ec:mrow></ec:math> and <ic:math xmlns:ic="http://www.w3.org/1998/Math/MathML" display="inline"><ic:mrow><ic:msub><ic:mrow><ic:mi>Z</ic:mi></ic:mrow><ic:mrow><ic:mi>c</ic:mi></ic:mrow></ic:msub><ic:mo stretchy="false">(</ic:mo><ic:mn>3900</ic:mn><ic:mo stretchy="false">)</ic:mo></ic:mrow></ic:math> in the charmed strange sector, respectively. We also predict their members under the (<mc:math xmlns:mc="http://www.w3.org/1998/Math/MathML" display="inline"><mc:mi>c</mc:mi></mc:math> and <oc:math xmlns:oc="http://www.w3.org/1998/Math/MathML" display="inline"><oc:mi>s</oc:mi></oc:math>) quark symmetry and SU(2) flavor symmetry. Most of them are very good molecule candidates, for example, (i) the <qc:math xmlns:qc="http://www.w3.org/1998/Math/MathML" display="inline"><qc:mn>0</qc:mn><qc:mo stretchy="false">(</qc:mo><qc:msup><qc:mn>1</qc:mn><qc:mo>+</qc:mo></qc:msup><qc:mo stretchy="false">)</qc:mo></qc:math> states in <uc:math xmlns:uc="http://www.w3.org/1998/Math/MathML" display="inline"><uc:msup><uc:mi>D</uc:mi><uc:mo>*</uc:mo></uc:msup><uc:msup><uc:mi>D</uc:mi><uc:mo>*</uc:mo></uc:msup></uc:math>, <wc:math xmlns:wc="http://www.w3.org/1998/Math/MathML" display="inline"><wc:mover accent="true"><wc:mi>D</wc:mi><wc:mo stretchy="false">¯</wc:mo></wc:mover><wc:msup><wc:mi>K</wc:mi><wc:mo>*</wc:mo></wc:msup></wc:math>, <ad:math xmlns:ad="http://www.w3.org/1998/Math/MathML" display="inline"><ad:msup><ad:mover accent="true"><ad:mi>D</ad:mi><ad:mo stretchy="false">¯</ad:mo></ad:mover><ad:mo>*</ad:mo></ad:msup><ad:msup><ad:mi>K</ad:mi><ad:mo>*</ad:mo></ad:msup></ad:math>; (ii) the <ed:math xmlns:ed="http://www.w3.org/1998/Math/MathML" display="inline"><ed:msup><ed:mn>0</ed:mn><ed:mrow><ed:mo stretchy="false">(</ed:mo><ed:mo>+</ed:mo><ed:mo stretchy="false">)</ed:mo></ed:mrow></ed:msup><ed:mo stretchy="false">(</ed:mo><ed:msup><ed:mn>2</ed:mn><ed:mrow><ed:mo>+</ed:mo><ed:mo stretchy="false">(</ed:mo><ed:mo>+</ed:mo><ed:mo stretchy="false">)</ed:mo></ed:mrow></ed:msup><ed:mo stretchy="false">)</ed:mo></ed:math> states in <md:math xmlns:md="http://www.w3.org/1998/Math/MathML" display="inline"><md:msup><md:mi>D</md:mi><md:mo>*</md:mo></md:msup><md:msup><md:mover accent="true"><md:mi>D</md:mi><md:mo stretchy="false">¯</md:mo></md:mover><md:mo>*</md:mo></md:msup></md:math>, <qd:math xmlns:qd="http://www.w3.org/1998/Math/MathML" display="inline"><qd:msup><qd:mover accent="true"><qd:mi>D</qd:mi><qd:mo stretchy="false">¯</qd:mo></qd:mover><qd:mo>*</qd:mo></qd:msup><qd:msup><qd:mi>K</qd:mi><qd:mo>*</qd:mo></qd:msup></qd:math>, <ud:math xmlns:ud="http://www.w3.org/1998/Math/MathML" display="inline"><ud:msup><ud:mi>D</ud:mi><ud:mo>*</ud:mo></ud:msup><ud:msup><ud:mi>K</ud:mi><ud:mo>*</ud:mo></ud:msup></ud:math>; (iii) the <wd:math xmlns:wd="http://www.w3.org/1998/Math/MathML" display="inline"><wd:msup><wd:mn>1</wd:mn><wd:mo>−</wd:mo></wd:msup><wd:mo stretchy="false">(</wd:mo><wd:msup><wd:mn>0</wd:mn><wd:mrow><wd:mo>+</wd:mo><wd:mo>+</wd:mo></wd:mrow></wd:msup><wd:mo stretchy="false">)</wd:mo></wd:math> state in <ae:math xmlns:ae="http://www.w3.org/1998/Math/MathML" display="inline"><ae:msup><ae:mi>D</ae:mi><ae:mo>*</ae:mo></ae:msup><ae:msup><ae:mover accent="true"><ae:mi>D</ae:mi><ae:mo stretchy="false">¯</ae:mo></ae:mover><ae:mo>*</ae:mo></ae:msup></ae:math> and <ee:math xmlns:ee="http://www.w3.org/1998/Math/MathML" display="inline"><ee:mn>1</ee:mn><ee:mo stretchy="false">(</ee:mo><ee:msup><ee:mn>1</ee:mn><ee:mo>+</ee:mo></ee:msup><ee:mo stretchy="false">)</ee:mo></ee:math> state in <ie:math xmlns:ie="http://www.w3.org/1998/Math/MathML" display="inline"><ie:msup><ie:mi>D</ie:mi><ie:mo>*</ie:mo></ie:msup><ie:msup><ie:mi>K</ie:mi><ie:mo>*</ie:mo></ie:msup></ie:math>. The <ke:math xmlns:ke="http://www.w3.org/1998/Math/MathML" display="inline"><ke:msup><ke:mn>0</ke:mn><ke:mo>+</ke:mo></ke:msup><ke:mo stretchy="false">(</ke:mo><ke:msup><ke:mn>0</ke:mn><ke:mrow><ke:mo>+</ke:mo><ke:mo>+</ke:mo></ke:mrow></ke:msup><ke:mo stretchy="false">)</ke:mo></ke:math> state in <oe:math xmlns:oe="http://www.w3.org/1998/Math/MathML" display="inline"><oe:mi>D</oe:mi><oe:mover accent="true"><oe:mi>D</oe:mi><oe:mo stretchy="false">¯</oe:mo></oe:mover></oe:math> and the <se:math xmlns:se="http://www.w3.org/1998/Math/MathML" display="inline"><se:mn>0</se:mn><se:mo stretchy="false">(</se:mo><se:msup><se:mn>1</se:mn><se:mo>+</se:mo></se:msup><se:mo stretchy="false">)</se:mo></se:math> state in <we:math xmlns:we="http://www.w3.org/1998/Math/MathML" display="inline"><we:mi>D</we:mi><we:msup><we:mi>K</we:mi><we:mo>*</we:mo></we:msup></we:math> might also exist as virtual states, and the <ye:math xmlns:ye="http://www.w3.org/1998/Math/MathML" display="inline"><ye:mn>0</ye:mn><ye:mo stretchy="false">(</ye:mo><ye:msup><ye:mn>1</ye:mn><ye:mo>+</ye:mo></ye:msup><ye:mo stretchy="false">)</ye:mo></ye:math> <cf:math xmlns:cf="http://www.w3.org/1998/Math/MathML" display="inline"><cf:mi>D</cf:mi><cf:msup><cf:mi>K</cf:mi><cf:mo>*</cf:mo></cf:msup></cf:math> can serve as a key to infer the existence of <ef:math xmlns:ef="http://www.w3.org/1998/Math/MathML" display="inline"><ef:msup><ef:mn>0</ef:mn><ef:mo>+</ef:mo></ef:msup><ef:mo stretchy="false">(</ef:mo><ef:msup><ef:mn>0</ef:mn><ef:mrow><ef:mo>+</ef:mo><ef:mo>+</ef:mo></ef:mrow></ef:msup><ef:mo stretchy="false">)</ef:mo></ef:math> <if:math xmlns:if="http://www.w3.org/1998/Math/MathML" display="inline"><if:mi>D</if:mi><if:mover accent="true"><if:mi>D</if:mi><if:mo stretchy="false">¯</if:mo></if:mover></if:math>. The <mf:math xmlns:mf="http://www.w3.org/1998/Math/MathML" display="inline"><mf:msub><mf:mi>D</mf:mi><mf:mi>s</mf:mi></mf:msub><mf:mi>π</mf:mi></mf:math> invariant mass spectrum of <of:math xmlns:of="http://www.w3.org/1998/Math/MathML" display="inline"><of:msubsup><of:mi>T</of:mi><of:mrow><of:mi>c</of:mi><of:mover accent="true"><of:mi>s</of:mi><of:mo stretchy="false">¯</of:mo></of:mover><of:mn>0</of:mn></of:mrow><of:mi>a</of:mi></of:msubsup><of:mo stretchy="false">(</of:mo><of:mn>2900</of:mn><of:mo stretchy="false">)</of:mo></of:math> is also studied within the coupled-channel approach, and the molecular interpretation of <uf:math xmlns:uf="http://www.w3.org/1998/Math/MathML" display="inline"><uf:msubsup><uf:mi>T</uf:mi><uf:mrow><uf:mi>c</uf:mi><uf:mover accent="true"><uf:mi>s</uf:mi><uf:mo stretchy="false">¯</uf:mo></uf:mover><uf:mn>0</uf:mn></uf:mrow><uf:mi>a</uf:mi></uf:msubsup><uf:mo stretchy="false">(</uf:mo><uf:mn>2900</uf:mn><uf:mo stretchy="false">)</uf:mo></uf:math> is consistent with the experimental data. Searching for the predicted states in experiments is crucial to discriminate the different pictures for interpreting these near-threshold exotica. Published by the American Physical Society 2024