Unveiling the <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>1710</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math> nature in the process <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:mover accent="true"><mml:mi>K</mml:mi><mml:mo stretchy="false">¯</mml:mo></mml:mover><mml:mn>0</mml:mn></mml:msup><mml:msup><mml:mi>K</mml:mi><mml:mo>+</mml:mo></mml:msup><mml:msup><mml:mi>ρ</mml:mi><mml:mo>−</mml:mo></mml:msup></mml:math>

Abstract

We have investigated the process <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:mover accent="true"><a:mi>K</a:mi><a:mo stretchy="false">¯</a:mo></a:mover><a:mn>0</a:mn></a:msup><a:msup><a:mi>K</a:mi><a:mo>+</a:mo></a:msup><a:msup><a:mi>ρ</a:mi><a:mo>−</a:mo></a:msup></a:math> by taking into account the <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"><f:mi>S</f:mi></f:math>-wave <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"><h:msup><h:mi>K</h:mi><h:mo>*</h:mo></h:msup><h:msup><h:mover accent="true"><h:mi>K</h:mi><h:mo stretchy="false">¯</h:mo></h:mover><h:mo>*</h:mo></h:msup></h:math>, <l:math xmlns:l="http://www.w3.org/1998/Math/MathML" display="inline"><l:mi>ρ</l:mi><l:mi>ω</l:mi></l:math>, and <n:math xmlns:n="http://www.w3.org/1998/Math/MathML" display="inline"><n:mi>ρ</n:mi><n:mi>ϕ</n:mi></n:math> final-state interactions, where the scalar meson <p:math xmlns:p="http://www.w3.org/1998/Math/MathML" display="inline"><p:msub><p:mi>a</p:mi><p:mn>0</p:mn></p:msub><p:mo stretchy="false">(</p:mo><p:mn>1710</p:mn><p:mo stretchy="false">)</p:mo></p:math> is generated. In addition, we also take into account the contributions from the scalar <t:math xmlns:t="http://www.w3.org/1998/Math/MathML" display="inline"><t:msub><t:mi>a</t:mi><t:mn>0</t:mn></t:msub><t:mo stretchy="false">(</t:mo><t:mn>980</t:mn><t:mo stretchy="false">)</t:mo><t:mo stretchy="false">(</t:mo><t:mo stretchy="false">→</t:mo><t:msup><t:mover accent="true"><t:mi>K</t:mi><t:mo stretchy="false">¯</t:mo></t:mover><t:mn>0</t:mn></t:msup><t:msup><t:mi>K</t:mi><t:mo>+</t:mo></t:msup><t:mo stretchy="false">)</t:mo></t:math> and the intermediate resonances <cb:math xmlns:cb="http://www.w3.org/1998/Math/MathML" display="inline"><cb:mrow><cb:msub><cb:mrow><cb:mi>K</cb:mi></cb:mrow><cb:mrow><cb:mn>1</cb:mn></cb:mrow></cb:msub><cb:mo stretchy="false">(</cb:mo><cb:mn>1270</cb:mn><cb:msup><cb:mrow><cb:mo stretchy="false">)</cb:mo></cb:mrow><cb:mrow><cb:mo>−</cb:mo></cb:mrow></cb:msup><cb:mo stretchy="false">(</cb:mo><cb:mo stretchy="false">→</cb:mo><cb:msup><cb:mrow><cb:mover accent="true"><cb:mrow><cb:mi>K</cb:mi></cb:mrow><cb:mrow><cb:mo stretchy="false">¯</cb:mo></cb:mrow></cb:mover></cb:mrow><cb:mrow><cb:mn>0</cb:mn></cb:mrow></cb:msup><cb:msup><cb:mrow><cb:mi>ρ</cb:mi></cb:mrow><cb:mrow><cb:mo>−</cb:mo></cb:mrow></cb:msup><cb:mo stretchy="false">)</cb:mo></cb:mrow></cb:math> and <lb:math xmlns:lb="http://www.w3.org/1998/Math/MathML" display="inline"><lb:msub><lb:mi>K</lb:mi><lb:mn>1</lb:mn></lb:msub><lb:mo stretchy="false">(</lb:mo><lb:mn>1270</lb:mn><lb:msup><lb:mo stretchy="false">)</lb:mo><lb:mn>0</lb:mn></lb:msup><lb:mo stretchy="false">(</lb:mo><lb:mo stretchy="false">→</lb:mo><lb:msup><lb:mi>K</lb:mi><lb:mo>+</lb:mo></lb:msup><lb:msup><lb:mi>ρ</lb:mi><lb:mo>−</lb:mo></lb:msup><lb:mo stretchy="false">)</lb:mo></lb:math>. Our results show that, in the <sb:math xmlns:sb="http://www.w3.org/1998/Math/MathML" display="inline"><sb:msup><sb:mover accent="true"><sb:mi>K</sb:mi><sb:mo stretchy="false">¯</sb:mo></sb:mover><sb:mn>0</sb:mn></sb:msup><sb:msup><sb:mi>K</sb:mi><sb:mo>+</sb:mo></sb:msup></sb:math> invariant mass distribution, a clear peak structure around 1.8 GeV appears, which could be associated with the scalar <wb:math xmlns:wb="http://www.w3.org/1998/Math/MathML" display="inline"><wb:msub><wb:mi>a</wb:mi><wb:mn>0</wb:mn></wb:msub><wb:mo stretchy="false">(</wb:mo><wb:mn>1710</wb:mn><wb:mo stretchy="false">)</wb:mo></wb:math>, however, no significant structure of the <ac:math xmlns:ac="http://www.w3.org/1998/Math/MathML" display="inline"><ac:msub><ac:mi>a</ac:mi><ac:mn>0</ac:mn></ac:msub><ac:mo stretchy="false">(</ac:mo><ac:mn>980</ac:mn><ac:mo stretchy="false">)</ac:mo></ac:math> is observed. On the other hand, one can find clear peaks of the <ec:math xmlns:ec="http://www.w3.org/1998/Math/MathML" display="inline"><ec:msub><ec:mi>K</ec:mi><ec:mn>1</ec:mn></ec:msub><ec:mo stretchy="false">(</ec:mo><ec:mn>1270</ec:mn><ec:mo stretchy="false">)</ec:mo></ec:math> in the <ic:math xmlns:ic="http://www.w3.org/1998/Math/MathML" display="inline"><ic:msup><ic:mover accent="true"><ic:mi>K</ic:mi><ic:mo stretchy="false">¯</ic:mo></ic:mover><ic:mn>0</ic:mn></ic:msup><ic:msup><ic:mi>ρ</ic:mi><ic:mo>−</ic:mo></ic:msup></ic:math> and <mc:math xmlns:mc="http://www.w3.org/1998/Math/MathML" display="inline"><mc:msup><mc:mi>K</mc:mi><mc:mo>+</mc:mo></mc:msup><mc:msup><mc:mi>ρ</mc:mi><mc:mo>−</mc:mo></mc:msup></mc:math> invariant mass distributions. The future precise measurement of this process by the BESIII and Belle II Collaborations and the planned Super Tau-Charm Facility in the future could shed light on the nature of <oc:math xmlns:oc="http://www.w3.org/1998/Math/MathML" display="inline"><oc:msub><oc:mi>a</oc:mi><oc:mn>0</oc:mn></oc:msub><oc:mo stretchy="false">(</oc:mo><oc:mn>1710</oc:mn><oc:mo stretchy="false">)</oc:mo></oc:math>. Published by the American Physical Society 2024

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