Roles of a0(980) and a0(1710</…

Motivated by the BESIII amplitude analysis of the single Cabibbo-suppressed process <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msup><a:mi>D</a:mi><a:mo>+</a:mo></a:msup><a:mo stretchy="false">→</a:mo><a:msup><a:mi>π</a:mi><a:mn>0</a:mn></a:msup><a:msup><a:mi>π</a:mi><a:mo>+</a:mo></a:msup><a:mi>η</a:mi></a:math>, we investigate this reaction by taking into account the contributions from 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>, <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"><h:mi>ρ</h:mi></h:math>, and <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"><j:msub><j:mi>a</j:mi><j:mn>0</j:mn></j:msub><j:mo stretchy="false">(</j:mo><j:mn>1710</j:mn><j:mo stretchy="false">)</j:mo></j:math>, where the scalar meson <n:math xmlns:n="http://www.w3.org/1998/Math/MathML" display="inline"><n:msub><n:mi>a</n:mi><n:mn>0</n:mn></n:msub><n:mo stretchy="false">(</n:mo><n:mn>980</n:mn><n:mo stretchy="false">)</n:mo></n:math> could be dynamically generated from the <r:math xmlns:r="http://www.w3.org/1998/Math/MathML" display="inline"><r:mi>S</r:mi></r:math>-wave pseudoscalar meson-pseudoscalar meson interaction within the chiral unitary approach. Our theoretical predictions for the <t:math xmlns:t="http://www.w3.org/1998/Math/MathML" display="inline"><t:msup><t:mi>π</t:mi><t:mn>0</t:mn></t:msup><t:mi>η</t:mi></t:math>, <v:math xmlns:v="http://www.w3.org/1998/Math/MathML" display="inline"><v:msup><v:mi>π</v:mi><v:mo>+</v:mo></v:msup><v:mi>η</v:mi></v:math>, and <x:math xmlns:x="http://www.w3.org/1998/Math/MathML" display="inline"><x:msup><x:mi>π</x:mi><x:mo>+</x:mo></x:msup><x:msup><x:mi>π</x:mi><x:mn>0</x:mn></x:msup></x:math> invariant mass distributions are in agreement with the BESIII measurements, especially the clear peaks around 1 GeV in the <z:math xmlns:z="http://www.w3.org/1998/Math/MathML" display="inline"><z:msup><z:mi>π</z:mi><z:mn>0</z:mn></z:msup><z:mi>η</z:mi></z:math> and <bb:math xmlns:bb="http://www.w3.org/1998/Math/MathML" display="inline"><bb:msup><bb:mi>π</bb:mi><bb:mo>+</bb:mo></bb:msup><bb:mi>η</bb:mi></bb:math> invariant mass distributions could be associated with the dynamically generated state <db:math xmlns:db="http://www.w3.org/1998/Math/MathML" display="inline"><db:msub><db:mi>a</db:mi><db:mn>0</db:mn></db:msub><db:mo stretchy="false">(</db:mo><db:mn>980</db:mn><db:mo stretchy="false">)</db:mo></db:math>. Furthermore, we demonstrate that the intermediate <hb:math xmlns:hb="http://www.w3.org/1998/Math/MathML" display="inline"><hb:msub><hb:mi>a</hb:mi><hb:mn>0</hb:mn></hb:msub><hb:mo stretchy="false">(</hb:mo><hb:mn>1710</hb:mn><hb:mo stretchy="false">)</hb:mo></hb:math> is also necessary to describe the enhancement structure around 1.6–1.7 GeV in the <lb:math xmlns:lb="http://www.w3.org/1998/Math/MathML" display="inline"><lb:msup><lb:mi>π</lb:mi><lb:mrow><lb:mn>0</lb:mn><lb:mo>/</lb:mo><lb:mo>+</lb:mo></lb:mrow></lb:msup><lb:mi>η</lb:mi></lb:math> invariant mass distribution. More precise experimental measurements of this process could provide deeper insights into the nature of the scalar mesons <nb:math xmlns:nb="http://www.w3.org/1998/Math/MathML" display="inline"><nb:msub><nb:mi>a</nb:mi><nb:mn>0</nb:mn></nb:msub><nb:mo stretchy="false">(</nb:mo><nb:mn>980</nb:mn><nb:mo stretchy="false">)</nb:mo></nb:math> and <rb:math xmlns:rb="http://www.w3.org/1998/Math/MathML" display="inline"><rb:msub><rb:mi>a</rb:mi><rb:mn>0</rb:mn></rb:msub><rb:mo stretchy="false">(</rb:mo><rb:mn>1710</rb:mn><rb:mo stretchy="false">)</rb:mo></rb:math>.