How does the X(3872) show up in e+e− collisions: Dip versus peak

We demonstrate that the dip observed near the total energy of 3872 MeV in the recent cross section data from the BESIII Collaboration for <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msup><a:mi>e</a:mi><a:mo>+</a:mo></a:msup><a:msup><a:mi>e</a:mi><a:mo>−</a:mo></a:msup><a:mo stretchy="false">→</a:mo><a:mi>J</a:mi><a:mo>/</a:mo><a:mi>ψ</a:mi><a:msup><a:mi>π</a:mi><a:mo>+</a:mo></a:msup><a:msup><a:mi>π</a:mi><a:mo>−</a:mo></a:msup></a:math> admits a natural explanation as a coupled-channel effect: it is a consequence of unitarity and a strong <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"><d:mi>S</d:mi></d:math>-wave <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"><f:mi>D</f:mi><f:msup><f:mover accent="true"><f:mi>D</f:mi><f:mo stretchy="false">¯</f:mo></f:mover><f:mo>*</f:mo></f:msup></f:math> attraction that generates the state <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"><j:mi>X</j:mi><j:mo stretchy="false">(</j:mo><j:mn>3872</j:mn><j:mo stretchy="false">)</j:mo></j:math>. We anticipate the appearance of a similar dip in the <n:math xmlns:n="http://www.w3.org/1998/Math/MathML" display="inline"><n:msup><n:mi>e</n:mi><n:mo>+</n:mo></n:msup><n:msup><n:mi>e</n:mi><n:mo>−</n:mo></n:msup><n:mo stretchy="false">→</n:mo><n:mi>J</n:mi><n:mo>/</n:mo><n:mi>ψ</n:mi><n:msup><n:mi>π</n:mi><n:mo>+</n:mo></n:msup><n:msup><n:mi>π</n:mi><n:mo>−</n:mo></n:msup><n:msup><n:mi>π</n:mi><n:mn>0</n:mn></n:msup></n:math> final state near the <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"><q:msup><q:mi>D</q:mi><q:mo>*</q:mo></q:msup><q:msup><q:mover accent="true"><q:mi>D</q:mi><q:mo stretchy="false">¯</q:mo></q:mover><q:mo>*</q:mo></q:msup></q:math> threshold driven by the same general mechanism, then to be interpreted as a signature of the predicted spin-2 partner of the <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"><u:mi>X</u:mi><u:mo stretchy="false">(</u:mo><u:mn>3872</u:mn><u:mo stretchy="false">)</u:mo></u:math>. Published by the American Physical Society 2024