Threshold effects as the origin of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>Y</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mn>4500</mml:mn> <mml:mo stretchy="false">)</mml:mo> </mml:math> observed in <mm

The BESIII Collaboration has recently observed a resonant structure <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>Y</a:mi> <a:mo stretchy="false">(</a:mo> <a:mn>4500</a:mn> <a:mo stretchy="false">)</a:mo> </a:math> in <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:msup> <e:mi>e</e:mi> <e:mo>+</e:mo> </e:msup> <e:msup> <e:mi>e</e:mi> <e:mo>−</e:mo> </e:msup> <e:mo stretchy="false">→</e:mo> <e:mi>J</e:mi> <e:mo>/</e:mo> <e:mi>ψ</e:mi> <e:msup> <e:mi>K</e:mi> <e:mo>+</e:mo> </e:msup> <e:msup> <e:mi>K</e:mi> <e:mo>−</e:mo> </e:msup> </e:math> , whose origin remains unresolved. In this study, we analyze the cross section line shape of <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"> <h:msup> <h:mi>e</h:mi> <h:mo>+</h:mo> </h:msup> <h:msup> <h:mi>e</h:mi> <h:mo>−</h:mo> </h:msup> <h:mo stretchy="false">→</h:mo> <h:mi>J</h:mi> <h:mo>/</h:mo> <h:mi>ψ</h:mi> <h:msup> <h:mi>K</h:mi> <h:mo>+</h:mo> </h:msup> <h:msup> <h:mi>K</h:mi> <h:mo>−</h:mo> </h:msup> </h:math> by taking into account the <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"> <k:mi>ψ</k:mi> <k:mo stretchy="false">(</k:mo> <k:mn>4415</k:mn> <k:mo stretchy="false">)</k:mo> </k:math> state and intermediate charmed meson loops. By treating <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"> <o:mi>ψ</o:mi> <o:mo stretchy="false">(</o:mo> <o:mn>4415</o:mn> <o:mo stretchy="false">)</o:mo> </o:math> as both a pure <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"> <s:mi>S</s:mi> </s:math> -wave state and <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"> <u:mi>S</u:mi> <u:mo>−</u:mo> <u:mi>D</u:mi> </u:math> mixed states, and introducing the <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"> <w:msubsup> <w:mi>Z</w:mi> <w:mrow> <w:mi>c</w:mi> <w:mi>s</w:mi> </w:mrow> <w:mrow> <w:mo stretchy="false">(</w:mo> <w:mo>′</w:mo> <w:mo stretchy="false">)</w:mo> </w:mrow> </w:msubsup> </w:math> resonance, we find that the <ab:math xmlns:ab="http://www.w3.org/1998/Math/MathML" display="inline"> <ab:mi>Y</ab:mi> <ab:mo stretchy="false">(</ab:mo> <ab:mn>4500</ab:mn> <ab:mo stretchy="false">)</ab:mo> </ab:math> peak at <eb:math xmlns:eb="http://www.w3.org/1998/Math/MathML" display="inline"> <eb:msqrt> <eb:mi>s</eb:mi> </eb:msqrt> <eb:mo>=</eb:mo> <eb:mn>4.5</eb:mn> <eb:mtext> </eb:mtext> <eb:mtext> </eb:mtext> <eb:mi>GeV</eb:mi> </eb:math> arises from the triangle singularity mechanism in the <gb:math xmlns:gb="http://www.w3.org/1998/Math/MathML" display="inline"> <gb:msubsup> <gb:mi>Z</gb:mi> <gb:mrow> <gb:mi>c</gb:mi> <gb:mi>s</gb:mi> </gb:mrow> <gb:mrow> <gb:mo stretchy="false">(</gb:mo> <gb:mo>′</gb:mo> <gb:mo stretchy="false">)</gb:mo> </gb:mrow> </gb:msubsup> </gb:math> -mediated rescattering processes, supporting its interpretation as a threshold effect rather than a conventional resonance.