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In inelastic $p+p$ collisions, the interacting objects are quarks and gluons(partons). It is believed that there are multiple interactions between thepartons in a single $p+p$ event. Recent studies of multiplicity dependence ofparticle production in $p+p$ collisions have gathered considerable interest inthe scientific community. According to several theoretical calculations,multiple gluon participation in hadronic collisions is the cause ofhigh-multiplicity events. If the interaction is hard enough (large $p_{\rm T}$transfer), the semi-hard processes of multiple interactions of partons mightalso lead to production of heavy particles like J/$\psi$. At the LHC, anapproximately linear increase of the relative J/$\psi$ yield with chargedparticle multiplicity is observed in $p+p$ collisions. In the present work, wehave studied the contribution of quarks and gluons to the multiplicitydependence of J/$\psi$ production using pQCD inspired event generator, PYTHIA8tune 4C, in $p+p$ collisions at $\sqrt{s} =$13 TeV by investigating relativeJ/$\psi$ yield and relative $\langle p_{\rm T} \rangle$ of J/$\psi$ as afunction of charged particle multiplicity for different hard-QCD processes. Wehave estimated a newly defined ratio, $r_{pp} = {\langle p_{\rm T}^{2}\rangle}_{i}/{\langle p_{\rm T}^{2} \rangle}_{\rm MB}$, to understand J/$\psi$production in high-multiplicity $p+p$ collisions. For the first time we attemptto study the nuclear modification factor like observables ($R_{\rm pp}$ and$R_{\rm cp}$) to understand the QCD medium formed in high-multiplicity $p+p$collisions.

Multiplicity Dependence of J/$\psi$ Production and QCD Dynamics in $p+p$ Collisions at $\sqrt{s}$ = 13 TeV