Deciphering the nature of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>X</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mn>2300</mml:mn> <mml:mo stretchy="false">)</mml:mo> </mml:math> with the PACIAE model

Inspired by the BESIII newest observation of an axial-vector particle <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>X</a:mi> <a:mo stretchy="false">(</a:mo> <a:mn>2300</a:mn> <a:mo stretchy="false">)</a:mo> </a:math> in the <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:mi>ψ</e:mi> <e:mo stretchy="false">(</e:mo> <e:mn>3686</e:mn> <e:mo stretchy="false">)</e:mo> <e:mo stretchy="false">→</e:mo> <e:mi>ϕ</e:mi> <e:mi>η</e:mi> <e:msup> <e:mi>η</e:mi> <e:mo>′</e:mo> </e:msup> </e:math> process [M. Ablikim (BESIII Collaboration), ], we simulate its production in <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"> <j:msup> <j:mi>e</j:mi> <j:mo>+</j:mo> </j:msup> <j:msup> <j:mi>e</j:mi> <j:mo>−</j:mo> </j:msup> </j:math> collisions at <l:math xmlns:l="http://www.w3.org/1998/Math/MathML" display="inline"> <l:msqrt> <l:mi>s</l:mi> </l:msqrt> <l:mo>=</l:mo> <l:mn>4.95</l:mn> <l:mtext> </l:mtext> <l:mtext> </l:mtext> <l:mi>GeV</l:mi> </l:math> using the parton and hadron cascade model PACIAE 4.0. In this model, the final partonic state (FPS) and the final hadronic state (FHS) are simulated and recorded sequentially. While previous interpretations have described the <n:math xmlns:n="http://www.w3.org/1998/Math/MathML" display="inline"> <n:mi>X</n:mi> <n:mo stretchy="false">(</n:mo> <n:mn>2300</n:mn> <n:mo stretchy="false">)</n:mo> </n:math> as an excited strangeonium state or an <r:math xmlns:r="http://www.w3.org/1998/Math/MathML" display="inline"> <r:mi>s</r:mi> <r:mi>s</r:mi> <r:mover accent="true"> <r:mi>s</r:mi> <r:mo stretchy="false">¯</r:mo> </r:mover> <r:mover accent="true"> <r:mi>s</r:mi> <r:mo stretchy="false">¯</r:mo> </r:mover> </r:math> tetraquark state, it is noted that the <x:math xmlns:x="http://www.w3.org/1998/Math/MathML" display="inline"> <x:mi>U</x:mi> <x:mo stretchy="false">(</x:mo> <x:mn>1</x:mn> <x:mo stretchy="false">)</x:mo> </x:math> anomaly coupling permits nonstrange quarks to couple to a vector <bb:math xmlns:bb="http://www.w3.org/1998/Math/MathML" display="inline"> <bb:mi>s</bb:mi> <bb:mover accent="true"> <bb:mi>s</bb:mi> <bb:mo stretchy="false">¯</bb:mo> </bb:mover> </bb:math> component via soft-gluon interactions. This motivates us to propose, for the first time, that the <fb:math xmlns:fb="http://www.w3.org/1998/Math/MathML" display="inline"> <fb:mi>X</fb:mi> <fb:mo stretchy="false">(</fb:mo> <fb:mn>2300</fb:mn> <fb:mo stretchy="false">)</fb:mo> </fb:math> could also be a <jb:math xmlns:jb="http://www.w3.org/1998/Math/MathML" display="inline"> <jb:mi>q</jb:mi> <jb:mover accent="true"> <jb:mi>q</jb:mi> <jb:mo stretchy="false">¯</jb:mo> </jb:mover> <jb:mi>s</jb:mi> <jb:mover accent="true"> <jb:mi>s</jb:mi> <jb:mo stretchy="false">¯</jb:mo> </jb:mover> </jb:math> ( <pb:math xmlns:pb="http://www.w3.org/1998/Math/MathML" display="inline"> <pb:mi>q</pb:mi> <pb:mo>=</pb:mo> <pb:mi>u</pb:mi> <pb:mo>/</pb:mo> <pb:mi>d</pb:mi> </pb:math> ) state. Furthermore, we suggest another novel possibility that the <rb:math xmlns:rb="http://www.w3.org/1998/Math/MathML" display="inline"> <rb:mi>X</rb:mi> <rb:mo stretchy="false">(</rb:mo> <rb:mn>2300</rb:mn> <rb:mo stretchy="false">)</rb:mo> </rb:math> may be a hadro-strangeonium state, i.e., a bound system of a strangeonium and a light hadron. The excited strangeonium candidate is formed by coalescing an <vb:math xmlns:vb="http://www.w3.org/1998/Math/MathML" display="inline"> <vb:mi>s</vb:mi> <vb:mover accent="true"> <vb:mi>s</vb:mi> <vb:mo stretchy="false">¯</vb:mo> </vb:mover> </vb:math> quark pair in the FPS with the quantum statistical mechanics inspired dynamically constrained phase-space coalescence (DCPC) model. The tetraquark candidates of <zb:math xmlns:zb="http://www.w3.org/1998/Math/MathML" display="inline"> <zb:mi>q</zb:mi> <zb:mover accent="true"> <zb:mi>q</zb:mi> <zb:mo stretchy="false">¯</zb:mo> </zb:mover> <zb:mi>s</zb:mi> <zb:mover accent="true"> <zb:mi>s</zb:mi> <zb:mo stretchy="false">¯</zb:mo> </zb:mover> </zb:math> and <fc:math xmlns:fc="http://www.w3.org/1998/Math/MathML" display="inline"> <fc:mi>s</fc:mi> <fc:mi>s</fc:mi> <fc:mover accent="true"> <fc:mi>s</fc:mi> <fc:mo stretchy="false">¯</fc:mo> </fc:mover> <fc:mover accent="true"> <fc:mi>s</fc:mi> <fc:mo stretchy="false">¯</fc:mo> </fc:mover> </fc:math> are similarly produced by coalescing four constituent quarks in the FPS. In contrast, a hadro-strangeonium candidate emerges from the recombination of the constituent mesons <lc:math xmlns:lc="http://www.w3.org/1998/Math/MathML" display="inline"> <lc:mi>ϕ</lc:mi> </lc:math> and <nc:math xmlns:nc="http://www.w3.org/1998/Math/MathML" display="inline"> <nc:msup> <nc:mi>η</nc:mi> <nc:mo>′</nc:mo> </nc:msup> <nc:mo>/</nc:mo> <nc:mi>η</nc:mi> </nc:math> in the FHS. We then calculate the <pc:math xmlns:pc="http://www.w3.org/1998/Math/MathML" display="inline"> <pc:mi>X</pc:mi> <pc:mo stretchy="false">(</pc:mo> <pc:mn>2300</pc:mn> <pc:mo stretchy="false">)</pc:mo> </pc:math> ’s orbital angular momentum quantum number in its rest frame and perform the spectral classification for each of the above candidates. Given its quantum numbers <tc:math xmlns:tc="http://www.w3.org/1998/Math/MathML" display="inline"> <tc:msup> <tc:mi>J</tc:mi> <tc:mrow> <tc:mi>P</tc:mi> <tc:mi>C</tc:mi> </tc:mrow> </tc:msup> <tc:mo>=</tc:mo> <tc:msup> <tc:mn>1</tc:mn> <tc:mrow> <tc:mo>+</tc:mo> <tc:mo>−</tc:mo> </tc:mrow> </tc:msup> </tc:math> , the <vc:math xmlns:vc="http://www.w3.org/1998/Math/MathML" display="inline"> <vc:mi>X</vc:mi> <vc:mo stretchy="false">(</vc:mo> <vc:mn>2300</vc:mn> <vc:mo stretchy="false">)</vc:mo> </vc:math> is identified as a <zc:math xmlns:zc="http://www.w3.org/1998/Math/MathML" display="inline">