Distinguishing the compact versus molecular nature 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:mo stretchy="

A central question in exotic-hadron physics is their internal structure whether these states are loosely bound hadronic molecules or compact multiquark configurations. To shed light on this issue, we develop a model that incorporates mixing between hadronic-molecular and compact multiquark components. We then apply this framework to the specific case of the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <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:mn>3875</a:mn> <a:msup> <a:mo stretchy="false">)</a:mo> <a:mo>+</a:mo> </a:msup> </a:math> and analyze the peak structure in the <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:msup> <e:mi>D</e:mi> <e:mn>0</e:mn> </e:msup> <e:msup> <e:mi>D</e:mi> <e:mn>0</e:mn> </e:msup> <e:msup> <e:mi>π</e:mi> <e:mo>+</e:mo> </e:msup> </e:math> invariant-mass spectrum reported by LHCb. We find that the model admits three solutions of comparable fit quality that can account for the <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:msub> <g:mi>T</g:mi> <g:mrow> <g:mi>c</g:mi> <g:mi>c</g:mi> </g:mrow> </g:msub> <g:mo stretchy="false">(</g:mo> <g:mn>3875</g:mn> <g:msup> <g:mo stretchy="false">)</g:mo> <g:mo>+</g:mo> </g:msup> </g:math> . One solution corresponds to a predominantly compact tetraquark configuration. The other two solutions imply a molecular <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:mo stretchy="false">(</k:mo> <k:mn>3875</k:mn> <k:msup> <k:mo stretchy="false">)</k:mo> <k:mo>+</k:mo> </k:msup> </k:math> : (1) the <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"> <o:msub> <o:mi>T</o:mi> <o:mrow> <o:mi>c</o:mi> <o:mi>c</o:mi> </o:mrow> </o:msub> <o:mo stretchy="false">(</o:mo> <o:mn>3875</o:mn> <o:msup> <o:mo stretchy="false">)</o:mo> <o:mo>+</o:mo> </o:msup> </o:math> is a <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"> <s:msup> <s:mi>D</s:mi> <s:mrow> <s:mo>*</s:mo> <s:mo>+</s:mo> </s:mrow> </s:msup> <s:msup> <s:mi>D</s:mi> <s:mn>0</s:mn> </s:msup> </s:math> molecule and an additional <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"> <u:msup> <u:mi>D</u:mi> <u:mrow> <u:mo>*</u:mo> <u:mn>0</u:mn> </u:mrow> </u:msup> <u:msup> <u:mi>D</u:mi> <u:mo>+</u:mo> </u:msup> </u:math> molecular state appears; (2) the <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"> <w:msub> <w:mi>T</w:mi> <w:mrow> <w:mi>c</w:mi> <w:mi>c</w:mi> </w:mrow> </w:msub> <w:mo stretchy="false">(</w:mo> <w:mn>3875</w:mn> <w:msup> <w:mo stretchy="false">)</w:mo> <w:mo>+</w:mo> </w:msup> </w:math> is a <ab:math xmlns:ab="http://www.w3.org/1998/Math/MathML" display="inline"> <ab:msup> <ab:mi>D</ab:mi> <ab:mrow> <ab:mo>*</ab:mo> <ab:mn>0</ab:mn> </ab:mrow> </ab:msup> <ab:msup> <ab:mi>D</ab:mi> <ab:mo>+</ab:mo> </ab:msup> </ab:math> molecule and an additional <cb:math xmlns:cb="http://www.w3.org/1998/Math/MathML" display="inline"> <cb:msup> <cb:mi>D</cb:mi> <cb:mrow> <cb:mo>*</cb:mo> <cb:mo>+</cb:mo> </cb:mrow> </cb:msup> <cb:msup> <cb:mi>D</cb:mi> <cb:mn>0</cb:mn> </cb:msup> </cb:math> molecular state is found below the <eb:math xmlns:eb="http://www.w3.org/1998/Math/MathML" display="inline"> <eb:msup> <eb:mi>D</eb:mi> <eb:mn>0</eb:mn> </eb:msup> <eb:msup> <eb:mi>D</eb:mi> <eb:mn>0</eb:mn> </eb:msup> <eb:msup> <eb:mi>π</eb:mi> <eb:mo>+</eb:mo> </eb:msup> </eb:math> threshold. These molecular states are not simple <gb:math xmlns:gb="http://www.w3.org/1998/Math/MathML" display="inline"> <gb:mi>I</gb:mi> <gb:mo>=</gb:mo> <gb:mn>0</gb:mn> </gb:math> states, but mixtures of <ib:math xmlns:ib="http://www.w3.org/1998/Math/MathML" display="inline"> <ib:mi>I</ib:mi> <ib:mo>=</ib:mo> <ib:mn>0</ib:mn> </ib:math> and <kb:math xmlns:kb="http://www.w3.org/1998/Math/MathML" display="inline"> <kb:mi>I</kb:mi> <kb:mo>=</kb:mo> <kb:mn>1</kb:mn> </kb:math> states. We show that all three scenarios are also consistent with the experimentally observed near-threshold <mb:math xmlns:mb="http://www.w3.org/1998/Math/MathML" display="inline"> <mb:msup> <mb:mi>D</mb:mi> <mb:mn>0</mb:mn> </mb:msup> <mb:msup> <mb:mi>D</mb:mi> <mb:mn>0</mb:mn> </mb:msup> </mb:math> and <ob:math xmlns:ob="http://www.w3.org/1998/Math/MathML" display="inline"> <ob:msup> <ob:mi>D</ob:mi> <ob:mn>0</ob:mn> </ob:msup> <ob:msup> <ob:mi>D</ob:mi> <ob:mo>+</ob:mo> </ob:msup> </ob:math> invariant-mass distributions.