Dispersive analysis of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>J</mml:mi> <mml:mo>/</mml:mo> <mml:mi>ψ</mml:mi> <mml:mo stretchy="false">→</mml:mo> <mml:msup> <mml:mi>π</mml:mi> <mml:mn>0</mml:mn> </mml:

Motivated by the discrepancies noted recently between the theoretical predictions of the electromagnetic <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>J</a:mi> <a:mo>/</a:mo> <a:mi>ψ</a:mi> <a:mo stretchy="false">→</a:mo> <a:msup> <a:mi>π</a:mi> <a:mn>0</a:mn> </a:msup> <a:msup> <a:mi>γ</a:mi> <a:mo>*</a:mo> </a:msup> </a:math> transition form factor and the BESIII data, we reanalyze this transition form factor using the dispersive Khuri-Treiman equations, with final-state interactions in both the direct channel and the crossed channels properly considered. This improved framework incorporates <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"> <d:mi>ρ</d:mi> <d:mi>–</d:mi> <d:mi>ω</d:mi> </d:math> mixing effects. The effect of four-pion states is evaluated through a dispersively improved vector-meson-dominance model. From this information, we propose a two-parameter fit that provides an excellent description of the BESIII data over the broad energy range from 0 to 2.8 GeV. We demonstrate that the <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"> <f:mi>ρ</f:mi> <f:msup> <f:mi>π</f:mi> <f:mn>0</f:mn> </f:msup> </f:math> decay mode of the <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"> <h:mi>J</h:mi> <h:mo>/</h:mo> <h:mi>ψ</h:mi> </h:math> is dominated by strong interaction, while the <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"> <j:mi>ω</j:mi> <j:msup> <j:mi>π</j:mi> <j:mn>0</j:mn> </j:msup> </j:math> mode is dominated by one-photon exchange. From this, we extract the relative phase between the strong and the one-virtual-photon (electromagnetic) modes in hadronic decays of <l:math xmlns:l="http://www.w3.org/1998/Math/MathML" display="inline"> <l:mi>J</l:mi> <l:mo>/</l:mo> <l:mi>ψ</l:mi> </l:math> as <n:math xmlns:n="http://www.w3.org/1998/Math/MathML" display="inline"> <n:mo stretchy="false">(</n:mo> <n:mn>62</n:mn> <n:mo>±</n:mo> <n:mn>21</n:mn> <n:mo stretchy="false">)</n:mo> <n:mo>°</n:mo> </n:math> . This could provide useful information in understanding the long-standing <r:math xmlns:r="http://www.w3.org/1998/Math/MathML" display="inline"> <r:mi>ρ</r:mi> <r:mi>π</r:mi> </r:math> puzzle in <t:math xmlns:t="http://www.w3.org/1998/Math/MathML" display="inline"> <t:mi>J</t:mi> <t:mo>/</t:mo> <t:mi>ψ</t:mi> </t:math> decays.