Decoding the structure near the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msup> <mml:mi>π</mml:mi> <mml:mo>+</mml:mo> </mml:msup> <mml:msup> <mml:mi>π</mml:mi> <mml:mo>−</mml:mo> </mml:msup> </mml:math> mass thre

In light of recent high-precision data taken by the BESIII Collaboration, we reconsider the dipion transition <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>ψ</a:mi> <a:mo stretchy="false">(</a:mo> <a:mn>3686</a:mn> <a:mo stretchy="false">)</a:mo> <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> . The strong pion-pion final-state interactions are taken into account model independently by using dispersion theory. We find that we can reproduce the substructure near the <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"> <f:msup> <f:mi>π</f:mi> <f:mo>+</f:mo> </f:msup> <f:msup> <f:mi>π</f:mi> <f:mo>−</f:mo> </f:msup> </f:math> threshold observed experimentally without introducing an extra resonance state. While a helicity-flip amplitude plays an important role for the formation of the dip in the invariant-mass distribution, the virtual exchange of the charmoniumlike exotic <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"> <h:msub> <h:mi>Z</h:mi> <h:mi>c</h:mi> </h:msub> <h:mo stretchy="false">(</h:mo> <h:mn>3900</h:mn> <h:mo stretchy="false">)</h:mo> </h:math> state improves the fit quality only slightly.