Multiplicity dependent <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:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>ψ</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>2</mml:mn><mml:mi>S</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math> production at forward and backward rapidity in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>p</mml:mi><mml:mo>+</mml:mo><mml:mi>p</mml:mi></mml:math> collisions at <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msqrt><mml:mi>s</mml:mi></mml:msqrt><mml:mo>=</mml:mo><mml:mn>200</mml:mn><mml:mtext> </mml:mtext><mml:mtext> </mml:mtext><mml:mi>GeV</mml:mi></mml:math>

Recent measurements of <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:math> production as a function of event charged-particle multiplicity at the collision energies of both the Large Hadron Collider (LHC) and the Relativistic Heavy Ion Collider (RHIC) show enhanced <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>J</c:mi><c:mo>/</c:mo><c:mi>ψ</c:mi></c:math> production yields with increasing multiplicity. One potential explanation for this type of dependence is multiparton interactions (MPI). We present the first study of potential autocorrelations at RHIC energies and forward and backward rapidity of self-normalized <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>J</e:mi><e:mo>/</e:mo><e:mi>ψ</e:mi></e:math> yields and <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mi>ψ</g:mi><g:mo stretchy="false">(</g:mo><g:mn>2</g:mn><g:mi>S</g:mi><g:mo stretchy="false">)</g:mo></g:math> to <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mi>J</k:mi><k:mo>/</k:mo><k:mi>ψ</k:mi></k:math> ratio, as a function of self-normalized multiplicity in <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mi>p</m:mi><m:mo>+</m:mo><m:mi>p</m:mi></m:math> collisions. In addition, detailed studies tuned to RHIC energies were performed to investigate the MPI impacts. We find that the PHENIX data at RHIC are consistent with recent LHC measurements and can only be described by calculations that include MPI effects. The forward and backward <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>2</o:mn><o:mi>S</o:mi><o:mo stretchy="false">)</o:mo></o:math> to <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:mi>J</s:mi><s:mo>/</s:mo><s:mi>ψ</s:mi></s:math> ratio is found to be less dependent on the charged-particle multiplicity.