X(2370) glueball-like particle productions in e+e− collisions at the BESIII energy and in pp collisions at the LHC energy with the PACIAE model

Inspired by the BESIII newest observation of X(2370) glueball-like particle, we search its productions in both <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msup><a:mi>e</a:mi><a:mo>+</a:mo></a:msup><a:msup><a:mi>e</a:mi><a:mo>−</a:mo></a:msup></a:math> collisions at <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:msqrt><c:mi>s</c:mi></c:msqrt><c:mo>=</c:mo><c:mn>4.95</c:mn><c:mtext> </c:mtext><c:mtext> </c:mtext><c:mi>GeV</c:mi></c:math> and proton-proton (pp) collisions at <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:msqrt><e:mi>s</e:mi></e:msqrt><e:mo>=</e:mo><e:mn>13</e:mn><e:mtext> </e:mtext><e:mtext> </e:mtext><e:mi>TeV</e:mi></e:math> with a parton and hadron cascade model PACIAE. In this model, the final partonic state (FPS) and the final hadronic state (FHS) are consecutively simulated and recorded. The X(2370) glueball- or tetraquark-state is then, respectively, recombined by two gluons or four quarks <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mi>s</g:mi><g:mi>s</g:mi><g:mover accent="true"><g:mi>s</g:mi><g:mo stretchy="false">¯</g:mo></g:mover><g:mover accent="true"><g:mi>s</g:mi><g:mo stretchy="false">¯</g:mo></g:mover></g:math> in the FPS using the quantum statistical mechanics inspired dynamically constrained phase-space coalescence (DCPC) model. The X(2370) molecular-state is recombined by the baryon-antibaryon of <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mrow><m:mi mathvariant="normal">Λ</m:mi><m:mtext>−</m:mtext><m:mover accent="true"><m:mrow><m:mi mathvariant="normal">Λ</m:mi></m:mrow><m:mrow><m:mo stretchy="false">¯</m:mo></m:mrow></m:mover></m:mrow></m:math> or <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:mrow><s:mi mathvariant="normal">Σ</s:mi><s:mtext>−</s:mtext><s:mover accent="true"><s:mrow><s:mi mathvariant="normal">Σ</s:mi></s:mrow><s:mrow><s:mo stretchy="false">¯</s:mo></s:mrow></s:mover></s:mrow></s:math>, or by three mesons of <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"><y:msup><y:mi>π</y:mi><y:mo>+</y:mo></y:msup><y:msup><y:mi>π</y:mi><y:mo>−</y:mo></y:msup><y:msup><y:mi>η</y:mi><y:mo>′</y:mo></y:msup></y:math>, <ab:math xmlns:ab="http://www.w3.org/1998/Math/MathML" display="inline"><ab:msup><ab:mi>K</ab:mi><ab:mo>+</ab:mo></ab:msup><ab:msup><ab:mi>K</ab:mi><ab:mo>−</ab:mo></ab:msup><ab:msup><ab:mi>η</ab:mi><ab:mo>′</ab:mo></ab:msup></ab:math>, or <cb:math xmlns:cb="http://www.w3.org/1998/Math/MathML" display="inline"><cb:msubsup><cb:mi>K</cb:mi><cb:mi>S</cb:mi><cb:mn>0</cb:mn></cb:msubsup><cb:msubsup><cb:mi>K</cb:mi><cb:mi>S</cb:mi><cb:mn>0</cb:mn></cb:msubsup><cb:msup><cb:mi>η</cb:mi><cb:mo>′</cb:mo></cb:msup></cb:math> in the FHS using DCPC model. In both <eb:math xmlns:eb="http://www.w3.org/1998/Math/MathML" display="inline"><eb:msup><eb:mi>e</eb:mi><eb:mo>+</eb:mo></eb:msup><eb:msup><eb:mi>e</eb:mi><eb:mo>−</eb:mo></eb:msup></eb:math> and pp collisions, significant discrepancies in the yields, the transverse momentum spectra and the rapidity distributions among the X(2370) glueball-, tetraquark-, and molecular-state are observed. These discrepancies are proposed as valuable criteria identifying the X(2370) different states from each other. Our results not only support the BESIII observation of glueball-like particle X(2370) production in <gb:math xmlns:gb="http://www.w3.org/1998/Math/MathML" display="inline"><gb:msup><gb:mi>e</gb:mi><gb:mo>+</gb:mo></gb:msup><gb:msup><gb:mi>e</gb:mi><gb:mo>−</gb:mo></gb:msup></gb:math> collisions, but also serve as a prediction for the X(2370) production in pp collisions. We strongly suggest the experimental measurement of the X(2370) glueball-like particle production in pp collisions at the LHC energies.