<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msub> <mml:mi>a</mml:mi> <mml:mn>0</mml:mn> </mml:msub> <mml:mo stretchy="false">(</mml:mo> <mml:mn>980</mml:mn> <mml:mo stretchy="false">)</mml:mo> </mml:math> productio

We study the <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:mi>ϕ</a:mi> <a:mi>η</a:mi> <a:msup> <a:mi>π</a:mi> <a:mn>0</a:mn> </a:msup> </a:math> reaction measured recently by the BESIII Collaboration with high precision, paying attention to three important aspects: (1) the production of the <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"> <d:msub> <d:mi>a</d:mi> <d:mn>0</d:mn> </d:msub> <d:mo stretchy="false">(</d:mo> <d:mn>980</d:mn> <d:mo stretchy="false">)</d:mo> </d:math> in the <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"> <h:msup> <h:mi>π</h:mi> <h:mn>0</h:mn> </h:msup> <h:mi>η</h:mi> </h:math> mass distributions, with the typical narrow width observed in isospin violating processes; (2) the origin of two peaks in the <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"> <j:mi>ϕ</j:mi> <j:msup> <j:mi>π</j:mi> <j:mn>0</j:mn> </j:msup> </j:math> mass distributions that were branded as “non- <l:math xmlns:l="http://www.w3.org/1998/Math/MathML" display="inline"> <l:mi>ϕ</l:mi> </l:math> ” contribution in the experimental analysis; (3) the existence of two triangle mechanisms developing a triangle singularity at the same energy where the non- <n:math xmlns:n="http://www.w3.org/1998/Math/MathML" display="inline"> <n:mi>ϕ</n:mi> </n:math> contribution peaks in the experiment. However, we also show that the strength of these peaks is very small relative to the observed ones, a feature that is tied to the experimental technique used to identify the <p:math xmlns:p="http://www.w3.org/1998/Math/MathML" display="inline"> <p:mi>ϕ</p:mi> </p:math> looking at <r:math xmlns:r="http://www.w3.org/1998/Math/MathML" display="inline"> <r:msup> <r:mi>K</r:mi> <r:mo>+</r:mo> </r:msup> <r:msup> <r:mi>K</r:mi> <r:mo>−</r:mo> </r:msup> </r:math> in a narrow window of invariant mass around the <t:math xmlns:t="http://www.w3.org/1998/Math/MathML" display="inline"> <t:mi>ϕ</t:mi> </t:math> mass. We suggest that these triangle singularities could be observed with other methods to identify the <v:math xmlns:v="http://www.w3.org/1998/Math/MathML" display="inline"> <v:mi>ϕ</v:mi> </v:math> .