$J/\psi$ Production Dynamics: Event shape, Multiplicity and Rapidity dependence in Proton+Proton Collisions at LHC energies using PYTHIA8

High-multiplicity pp collisions at the Large Hadron Collider (LHC) energies have created special importance in view of the Underlying Event (UE) observables. The recent results of LHC, such as long range angular correlation, flow-like patterns, strangeness enhancement etc. in high multiplicity events are not yet completely understood. In the same direction, the understanding of multiplicity dependence of J/$\psi$ production is highly necessary. Transverse spherocity, which is an event shape variable, helps to investigate the particle production by isolating the hard and the soft components. In the present study, we have investigated the multiplicity dependence of J/$\psi$ production at mid-rapidity and forward rapidity through the transverse spherocity analysis and tried to understand the role of jets by separating the isotropic and jetty events from the minimum bias collisions. We have analyzed the J/$\psi$ production at the mid-rapidity and forward rapidities via dielectron and dimuon channels, respectively using 4C tuned PYTHIA8 event generator. The analysis has been performed in two different center-of-mass energies: $\sqrt{s}$ = 5.02 and 13 TeV, to see the energy dependence of jet contribution to the multiplicity dependence study of J/$\psi$ production. Furthermore, we have studied the production dynamics through the dependence of thermodynamic parameters on event multiplicity and transverse spherocity.