Measurements of J/<i>ψ</i> Production vs. Event Multiplicity in Forward Rapidity in <i>p</i> + <i>p</i> Collisions in the PHENIX Experiment

<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow></semantics></math></inline-formula>, a charmonium bound state made of a charm and an anti-charm quark, was discovered in the 1970s and confirmed the quark model. Because the mass of charm quarks is significantly above the quantum chromodynamics (QCD) scale <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi mathvariant="sans-serif">Λ</mi><mrow><mi>Q</mi><mi>C</mi><mi>D</mi></mrow></msub></semantics></math></inline-formula>, charmonia are considered excellent probes to test perturbative quantum chromodynamics (pQCD) calculations. In recent decades, they have been studied extensively at different high-energy colliders. However, their production mechanisms, which involve multiple scales, are still not very well understood. Recently, in high-multiplicity <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>p</mi><mo>+</mo><mi>p</mi></mrow></semantics></math></inline-formula> collisions at RHIC and at the LHC, a significant enhancement of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow></semantics></math></inline-formula> production yield has been observed, which suggests a strong contribution of multi-parton interaction (MPI). This is different from the traditional pQCD picture, where charm quark pairs are produced from a single hard scattering between partons in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>p</mi><mo>+</mo><mi>p</mi></mrow></semantics></math></inline-formula> collisions. In this work, we will report the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow></semantics></math></inline-formula> normalized production yield as a function of normalized charged particle multiplicity over a board range of rapidity and event multiplicity in the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>J</mi><mo>/</mo><mi>ψ</mi><mo>→</mo><msup><mi>μ</mi><mo>+</mo></msup><msup><mi>μ</mi><mo>−</mo></msup></mrow></semantics></math></inline-formula> channel with PHENIX Run 15 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>p</mi><mo>+</mo><mi>p</mi></mrow></semantics></math></inline-formula> data at <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msqrt><mi>s</mi></msqrt><mo>=</mo><mn>200</mn></mrow></semantics></math></inline-formula> GeV. The results are compared with PYTHIA 8 simulations with the MPI option turned on and off. Finally, the outlooks of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow></semantics></math></inline-formula> in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>p</mi><mo>+</mo><mi>A</mi><mi>u</mi></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>A</mi><mi>u</mi><mo>+</mo><mi>p</mi></mrow></semantics></math></inline-formula> collisions, along with color glass condensate (CGC) predictions and the multiplicity-dependent <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>ψ</mi><mo>(</mo><mn>2</mn><mi>S</mi><mo>)</mo><mo>/</mo><mi>J</mi><mo>/</mo><mi>ψ</mi></mrow></semantics></math></inline-formula> ratio in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>p</mi><mo>+</mo><mi>p</mi></mrow></semantics></math></inline-formula> data, will be briefly discussed.