Analysis of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>D</mml:mi><mml:msup><mml:mi>D</mml:mi><mml:mo>*</mml:mo></mml:msup></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"

Numerous exotic hadrons with heavy quarks have been reported in the experiments. In such states, symmetries of heavy quarks are considered to play a significant role. In particular, the superflavor symmetry, or also called the heavy quark antidiquark symmetry is one of the interesting symmetries, which links a quark <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>Q</a:mi></a:math> to an antidiquark <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mover accent="true"><c:mi>Q</c:mi><c:mo stretchy="false">¯</c:mo></c:mover><c:mover accent="true"><c:mi>Q</c:mi><c:mo stretchy="false">¯</c:mo></c:mover></c:math> having the same color representation as <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mi>Q</i:mi></i:math>. In this paper, we study a <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mover accent="true"><k:mi>D</k:mi><k:mo stretchy="false">¯</k:mo></k:mover><k:msub><k:mi mathvariant="normal">Ξ</k:mi><k:mrow><k:mi>c</k:mi><k:mi>c</k:mi></k:mrow></k:msub></k:math> molecular state as a superflavor partner of the doubly charmed tetraquark <p:math xmlns:p="http://www.w3.org/1998/Math/MathML" display="inline"><p:msub><p:mi>T</p:mi><p:mrow><p:mi>c</p:mi><p:mi>c</p:mi></p:mrow></p:msub></p:math> reported by LHCb recently. <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> locating slightly below the <t:math xmlns:t="http://www.w3.org/1998/Math/MathML" display="inline"><t:mi>D</t:mi><t:msup><t:mi>D</t:mi><t:mo>*</t:mo></t:msup></t:math> threshold is a candidate of the hadronic molecule. Thus by replacing the singly charmed meson <v:math xmlns:v="http://www.w3.org/1998/Math/MathML" display="inline"><v:msup><v:mi>D</v:mi><v:mrow><v:mo stretchy="false">(</v:mo><v:mo>*</v:mo><v:mo stretchy="false">)</v:mo></v:mrow></v:msup></v:math> with the doubly charmed baryon <z:math xmlns:z="http://www.w3.org/1998/Math/MathML" display="inline"><z:msubsup><z:mi mathvariant="normal">Ξ</z:mi><z:mrow><z:mi>c</z:mi><z:mi>c</z:mi></z:mrow><z:mrow><z:mo stretchy="false">(</z:mo><z:mo>*</z:mo><z:mo stretchy="false">)</z:mo></z:mrow></z:msubsup></z:math>, superflavor symmetry predicts the existence of the <eb:math xmlns:eb="http://www.w3.org/1998/Math/MathML" display="inline"><eb:msup><eb:mover accent="true"><eb:mi>D</eb:mi><eb:mo stretchy="false">¯</eb:mo></eb:mover><eb:mrow><eb:mo stretchy="false">(</eb:mo><eb:mo>*</eb:mo><eb:mo stretchy="false">)</eb:mo></eb:mrow></eb:msup><eb:msubsup><eb:mi mathvariant="normal">Ξ</eb:mi><eb:mrow><eb:mi>c</eb:mi><eb:mi>c</eb:mi></eb:mrow><eb:mrow><eb:mo stretchy="false">(</eb:mo><eb:mo>*</eb:mo><eb:mo stretchy="false">)</eb:mo></eb:mrow></eb:msubsup></eb:math> bound state. We employ the one boson exchange model respecting with the heavy quark spin symmetry where the parameter is obtained to reproduce the <nb:math xmlns:nb="http://www.w3.org/1998/Math/MathML" display="inline"><nb:msub><nb:mi>T</nb:mi><nb:mrow><nb:mi>c</nb:mi><nb:mi>c</nb:mi></nb:mrow></nb:msub></nb:math> binding energy. We apply this model with superflavor symmetry to the <pb:math xmlns:pb="http://www.w3.org/1998/Math/MathML" display="inline"><pb:msup><pb:mover accent="true"><pb:mi>D</pb:mi><pb:mo stretchy="false">¯</pb:mo></pb:mover><pb:mrow><pb:mo stretchy="false">(</pb:mo><pb:mo>*</pb:mo><pb:mo stretchy="false">)</pb:mo></pb:mrow></pb:msup><pb:msubsup><pb:mi mathvariant="normal">Ξ</pb:mi><pb:mrow><pb:mi>c</pb:mi><pb:mi>c</pb:mi></pb:mrow><pb:mrow><pb:mo stretchy="false">(</pb:mo><pb:mo>*</pb:mo><pb:mo stretchy="false">)</pb:mo></pb:mrow></pb:msubsup></pb:math> molecule and predict a bound state with <yb:math xmlns:yb="http://www.w3.org/1998/Math/MathML" display="inline"><yb:mi>I</yb:mi><yb:mo stretchy="false">(</yb:mo><yb:msup><yb:mi>J</yb:mi><yb:mi>P</yb:mi></yb:msup><yb:mo stretchy="false">)</yb:mo><yb:mo>=</yb:mo><yb:mn>0</yb:mn><yb:mo stretchy="false">(</yb:mo><yb:msup><yb:mfrac><yb:mn>1</yb:mn><yb:mn>2</yb:mn></yb:mfrac><yb:mo>−</yb:mo></yb:msup><yb:mo stretchy="false">)</yb:mo></yb:math>. If the pentaquark state corresponding to <ec:math xmlns:ec="http://www.w3.org/1998/Math/MathML" display="inline"><ec:msup><ec:mover accent="true"><ec:mi>D</ec:mi><ec:mo stretchy="false">¯</ec:mo></ec:mover><ec:mrow><ec:mo stretchy="false">(</ec:mo><ec:mo>*</ec:mo><ec:mo stretchy="false">)</ec:mo></ec:mrow></ec:msup><ec:msubsup><ec:mi mathvariant="normal">Ξ</ec:mi><ec:mrow><ec:mi>c</ec:mi><ec:mi>c</ec:mi></ec:mrow><ec:mrow><ec:mo stretchy="false">(</ec:mo><ec:mo>*</ec:mo><ec:mo stretchy="false">)</ec:mo></ec:mrow></ec:msubsup></ec:math> molecular state is observed in future experiments as predicted in this work, it is more likely that <nc:math xmlns:nc="http://www.w3.org/1998/Math/MathML" display="inline"><nc:msub><nc:mi>T</nc:mi><nc:mrow><nc:mi>c</nc:mi><nc:mi>c</nc:mi></nc:mrow></nc:msub></nc:math> is a <pc:math xmlns:pc="http://www.w3.org/1998/Math/MathML" display="inline"><pc:mi>D</pc:mi><pc:msup><pc:mi>D</pc:mi><pc:mo>*</pc:mo></pc:msup></pc:math> molecular state. Published by the American Physical Society 2024