Poles and poltergeists in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi>e</mml:mi></mml:mrow><mml:mrow><mml:mo>+</mml:mo></mml:mrow></mml:msup><mml:msup><mml:mrow><mml:mi>e</mml:mi></mml:mrow><mml:mrow><mml:mo>−</mml:mo></mml:mrow></mml:msup><mml:mo stretchy="false">→</mml:mo><mml:mi>D</mml:mi><mml:mover accent="true"><mml:mrow><mml:mi>D</mml:mi></mml:mrow><mml:mrow><mml:mo stretchy="false">¯</mml:mo></mml:mrow></mml:mover></mml:mrow></mml:math> data

Abstract

A recent report of <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>D</a:mi><a:mover accent="true"><a:mi>D</a:mi><a:mo stretchy="false">¯</a:mo></a:mover></a:math> events by the BESIII collaboration suggests the presence of a structure <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"><f:mi>R</f:mi></f:math> at 3900 MeV. We argue that this structure, called <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"><h:mi>G</h:mi><h:mo stretchy="false">(</h:mo><h:mn>3900</h:mn><h:mo stretchy="false">)</h:mo></h:math> in the past, is not in fact due to a new <l:math xmlns:l="http://www.w3.org/1998/Math/MathML" display="inline"><l:mi>c</l:mi><l:mover accent="true"><l:mi>c</l:mi><l:mo stretchy="false">¯</l:mo></l:mover></l:math> resonance but rather naturally emerges due to a combination of interference between nearby resonances and the opening of the <p:math xmlns:p="http://www.w3.org/1998/Math/MathML" display="inline"><p:msup><p:mi>D</p:mi><p:mo>*</p:mo></p:msup><p:mover accent="true"><p:mi>D</p:mi><p:mo stretchy="false">¯</p:mo></p:mover></p:math> channel. We further find that the appearance of this structure does not require suppression because of a radial node in the <t:math xmlns:t="http://www.w3.org/1998/Math/MathML" display="inline"><t:mi>ψ</t:mi><t:mo stretchy="false">(</t:mo><t:mn>4040</t:mn><t:mo stretchy="false">)</t:mo></t:math> wave function, although a node improves fit quality. The measured <x:math xmlns:x="http://www.w3.org/1998/Math/MathML" display="inline"><x:msup><x:mi>e</x:mi><x:mo>+</x:mo></x:msup><x:msup><x:mi>e</x:mi><x:mo>−</x:mo></x:msup></x:math> coupling of <z:math xmlns:z="http://www.w3.org/1998/Math/MathML" display="inline"><z:mi>ψ</z:mi><z:mo stretchy="false">(</z:mo><z:mn>4040</z:mn><z:mo stretchy="false">)</z:mo></z:math> is found to be substantially smaller than previously estimated. In addition, we report new corrections to the measured cross section <db:math xmlns:db="http://www.w3.org/1998/Math/MathML" display="inline"><db:mi>σ</db:mi><db:mo stretchy="false">(</db:mo><db:msup><db:mi>e</db:mi><db:mo>+</db:mo></db:msup><db:msup><db:mi>e</db:mi><db:mo>−</db:mo></db:msup><db:mo stretchy="false">→</db:mo><db:mi>D</db:mi><db:mover accent="true"><db:mi>D</db:mi><db:mo stretchy="false">¯</db:mo></db:mover><db:mo stretchy="false">)</db:mo></db:math> at energies near <kb:math xmlns:kb="http://www.w3.org/1998/Math/MathML" display="inline"><kb:mi>ψ</kb:mi><kb:mo stretchy="false">(</kb:mo><kb:mn>3770</kb:mn><kb:mo stretchy="false">)</kb:mo></kb:math>. Published by the American Physical Society 2024

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