Uncovering the mystery of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>X</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>3872</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math> with the coupled-channel dyna

The <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>X</a:mi><a:mo stretchy="false">(</a:mo><a:mn>3872</a:mn><a:mo stretchy="false">)</a:mo></a:math>, as the first and the most crucial member in the exotic charmoniumlike <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>X</e:mi><e:mi>Y</e:mi><e:mi>Z</e:mi></e:math> family, has been studied for a long time. However, its dynamical origin, whether stemming from a <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mi>D</g:mi><g:msup><g:mover accent="true"><g:mi>D</g:mi><g:mo stretchy="false">¯</g:mo></g:mover><g:mo>*</g:mo></g:msup></g:math> hadronic molecule or the first excited <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mi>P</k:mi></k:math>-wave charmonium <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:msub><m:mi>χ</m:mi><m:mrow><m:mi>c</m:mi><m:mn>1</m:mn></m:mrow></m:msub><m:mo stretchy="false">(</m:mo><m:mn>2</m:mn><m:mi>P</m:mi><m:mo stretchy="false">)</m:mo></m:math>, remains controversial. In this Letter, we demonstrate that the <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"><q:mi>X</q:mi><q:mo stretchy="false">(</q:mo><q:mn>3872</q:mn><q:mo stretchy="false">)</q:mo></q:math> definitely does not result from the mass shift of the higher bare <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"><u:msub><u:mi>χ</u:mi><u:mrow><u:mi>c</u:mi><u:mn>1</u:mn></u:mrow></u:msub><u:mo stretchy="false">(</u:mo><u:mn>2</u:mn><u:mi>P</u:mi><u:mo stretchy="false">)</u:mo></u:math> resonance pole in the coupled-channel dynamics involving a short-distance <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"><y:mi>c</y:mi><y:mover accent="true"><y:mi>c</y:mi><y:mo stretchy="false">¯</y:mo></y:mover></y:math> core and the long-distance <cb:math xmlns:cb="http://www.w3.org/1998/Math/MathML" display="inline"><cb:mi>D</cb:mi><cb:msup><cb:mover accent="true"><cb:mi>D</cb:mi><cb:mo stretchy="false">¯</cb:mo></cb:mover><cb:mo>*</cb:mo></cb:msup></cb:math> channels. Instead, it originates from either the <gb:math xmlns:gb="http://www.w3.org/1998/Math/MathML" display="inline"><gb:mi>D</gb:mi><gb:msup><gb:mover accent="true"><gb:mi>D</gb:mi><gb:mo stretchy="false">¯</gb:mo></gb:mover><gb:mo>*</gb:mo></gb:msup></gb:math> molecular pole or the shadow pole associated with the antiresonance of the <kb:math xmlns:kb="http://www.w3.org/1998/Math/MathML" display="inline"><kb:mi>P</kb:mi></kb:math>-wave charmonium, depending on the weak or strong coupling mode, respectively. To differentiate these origins and fully exploit the nature of <mb:math xmlns:mb="http://www.w3.org/1998/Math/MathML" display="inline"><mb:mi>X</mb:mi><mb:mo stretchy="false">(</mb:mo><mb:mn>3872</mb:mn><mb:mo stretchy="false">)</mb:mo></mb:math>, we conduct a comprehensive analysis in a couple-channel dynamics framework, including the isospin violation, the three-body <qb:math xmlns:qb="http://www.w3.org/1998/Math/MathML" display="inline"><qb:mi>D</qb:mi><qb:mover accent="true"><qb:mi>D</qb:mi><qb:mo stretchy="false">¯</qb:mo></qb:mover><qb:mi>π</qb:mi></qb:math> effect, the dynamical width of <ub:math xmlns:ub="http://www.w3.org/1998/Math/MathML" display="inline"><ub:msup><ub:mi>D</ub:mi><ub:mo>*</ub:mo></ub:msup></ub:math>, and nonopen-charm decays of the bare <wb:math xmlns:wb="http://www.w3.org/1998/Math/MathML" display="inline"><wb:msub><wb:mi>χ</wb:mi><wb:mrow><wb:mi>c</wb:mi><wb:mn>1</wb:mn></wb:mrow></wb:msub><wb:mo stretchy="false">(</wb:mo><wb:mn>2</wb:mn><wb:mi>P</wb:mi><wb:mo stretchy="false">)</wb:mo></wb:math>. Our findings highlight the pivotal role of the coupled-channel dynamics in explaining the disparity between the pole widths of <ac:math xmlns:ac="http://www.w3.org/1998/Math/MathML" display="inline"><ac:mi>X</ac:mi><ac:mo stretchy="false">(</ac:mo><ac:mn>3872</ac:mn><ac:mo stretchy="false">)</ac:mo></ac:math> and <ec:math xmlns:ec="http://www.w3.org/1998/Math/MathML" display="inline"><ec:msubsup><ec:mi>T</ec:mi><ec:mrow><ec:mi>c</ec:mi><ec:mi>c</ec:mi></ec:mrow><ec:mo>+</ec:mo></ec:msubsup></ec:math>, while also predicting a new resonance with <gc:math xmlns:gc="http://www.w3.org/1998/Math/MathML" display="inline"><gc:msup><gc:mi>J</gc:mi><gc:mrow><gc:mi>P</gc:mi><gc:mi>C</gc:mi></gc:mrow></gc:msup><gc:mo>=</gc:mo><gc:msup><gc:mn>1</gc:mn><gc:mrow><gc:mo>+</gc:mo><gc:mo>+</gc:mo></gc:mrow></gc:msup></gc:math> around 4.0 GeV. By matching the newly observed <ic:math xmlns:ic="http://www.w3.org/1998/Math/MathML" display="inline"><ic:msub><ic:mi>χ</ic:mi><ic:mrow><ic:mi>c</ic:mi><ic:mn>1</ic:mn></ic:mrow></ic:msub><ic:mo stretchy="false">(</ic:mo><ic:mn>4010</ic:mn><ic:mo stretchy="false">)</ic:mo></ic:math> by the LHCb Collaboration to our predicted resonance, we conclude that the <mc:math xmlns:mc="http://www.w3.org/1998/Math/MathML" display="inline"><mc:mi>X</mc:mi><mc:mo stretchy="false">(</mc:mo><mc:mn>3872</mc:mn><mc:mo stretchy="false">)</mc:mo></mc:math> most likely originates from the <qc:math xmlns:qc="http://www.w3.org/1998/Math/MathML" display="inline"><qc:mi>D</qc:mi><qc:msup><qc:mover accent="true"><qc:mi>D</qc:mi><qc:mo stretchy="false">¯</qc:mo></qc:mover><qc:mo>*</qc:mo></qc:msup></qc:math> pole with a confidence level exceeding 99.7%.