Analysis of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mi>c</mml:mi><mml:mi>c</mml:mi></mml:mrow></mml:msub></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mi>b</mml:mi><mml:mi>b</mml:mi></mml:mrow></mml:msub></mml:math> based on the hadronic molecular model and their spin multiplets

Abstract

<a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msup><a:mrow><a:msub><a:mi>T</a:mi><a:mrow><a:mi>c</a:mi><a:mi>c</a:mi></a:mrow></a:msub><a:mo stretchy="false">(</a:mo><a:mi>c</a:mi><a:mi>c</a:mi><a:mover accent="true"><a:mi>u</a:mi><a:mo stretchy="false">¯</a:mo></a:mover><a:mover accent="true"><a:mi>d</a:mi><a:mo stretchy="false">¯</a:mo></a:mover><a:mo stretchy="false">)</a:mo></a:mrow><a:mo>+</a:mo></a:msup></a:math> has been reported by the LHCb experiment in 2022. The analysis using the Breit-Wigner parametrization found the small binding energy, 0.273 MeV, which is measured from the threshold of <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:msup><i:mi>D</i:mi><i:mrow><i:mo>*</i:mo><i:mo>+</i:mo></i:mrow></i:msup><i:msup><i:mi>D</i:mi><i:mn>0</i:mn></i:msup></i:math>. In this paper, we consider <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:msub><k:mi>T</k:mi><k:mrow><k:mi>c</k:mi><k:mi>c</k:mi></k:mrow></k:msub></k:math> as a <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mi>D</m:mi><m:msup><m:mi>D</m:mi><m:mo>*</m:mo></m:msup></m:math> hadronic molecule as a deuteronlike state. The one-boson exchange model is employed as for the heavy meson interactions, where we determine the cutoff parameter <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:mi mathvariant="normal">Λ</o:mi></o:math> to reproduce the reported binding energy of <r:math xmlns:r="http://www.w3.org/1998/Math/MathML" display="inline"><r:msub><r:mi>T</r:mi><r:mrow><r:mi>c</r:mi><r:mi>c</r:mi></r:mrow></r:msub></r:math> with <t:math xmlns:t="http://www.w3.org/1998/Math/MathML" display="inline"><t:mi>I</t:mi><t:mo stretchy="false">(</t:mo><t:msup><t:mi>J</t:mi><t:mi>P</t:mi></t:msup><t:mo stretchy="false">)</t:mo><t:mo>=</t:mo><t:mn>0</t:mn><t:mo stretchy="false">(</t:mo><t:msup><t:mn>1</t:mn><t:mo>+</t:mo></t:msup><t:mo stretchy="false">)</t:mo></t:math>. We discuss the properties of the bound state and also search for <z:math xmlns:z="http://www.w3.org/1998/Math/MathML" display="inline"><z:msub><z:mi>T</z:mi><z:mrow><z:mi>c</z:mi><z:mi>c</z:mi></z:mrow></z:msub></z:math> with quantum numbers other than <bb:math xmlns:bb="http://www.w3.org/1998/Math/MathML" display="inline"><bb:mn>0</bb:mn><bb:mo stretchy="false">(</bb:mo><bb:msup><bb:mn>1</bb:mn><bb:mo>+</bb:mo></bb:msup><bb:mo stretchy="false">)</bb:mo></bb:math>. Furthermore, we analyze <fb:math xmlns:fb="http://www.w3.org/1998/Math/MathML" display="inline"><fb:msub><fb:mi>T</fb:mi><fb:mrow><fb:mi>b</fb:mi><fb:mi>b</fb:mi></fb:mrow></fb:msub></fb:math> as a bottom counterpart of <hb:math xmlns:hb="http://www.w3.org/1998/Math/MathML" display="inline"><hb:msub><hb:mi>T</hb:mi><hb:mrow><hb:mi>c</hb:mi><hb:mi>c</hb:mi></hb:mrow></hb:msub></hb:math>, which involves two bottom quarks, and obtain several bound states. Finally, we consider the light-cloud basis for wave functions of the doubly heavy tetraquarks in the heavy quark limit. Using the basis, we find the spin multiplets of their bound states, indicating the spin structures of diquarks in <jb:math xmlns:jb="http://www.w3.org/1998/Math/MathML" display="inline"><jb:msub><jb:mi>T</jb:mi><jb:mrow><jb:mi>c</jb:mi><jb:mi>c</jb:mi></jb:mrow></jb:msub></jb:math> and <lb:math xmlns:lb="http://www.w3.org/1998/Math/MathML" display="inline"><lb:msub><lb:mi>T</lb:mi><lb:mrow><lb:mi>b</lb:mi><lb:mi>b</lb:mi></lb:mrow></lb:msub></lb:math> with the finite quark masses. Published by the American Physical Society 2024

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