Multiplicity, Transverse Momentum and Pseudorapidity Dependence of Freeze-Out Parameters for Open-Charm Hadrons in Hadronic Collisions at LHC Energy

Heavy quarks (charm and beauty) act as better probes in understanding the formation and evolution of the QCD medium in the ultra-relativistic heavy-ion collisions because of their heavy mass and large relaxation time compared to QGP (quark-gluon plasma) lifetime. Possible thermalization of charm quarks is observed in small systems like proton+proton (pp) collisions by studying charm-hadrons, namely \(\mathrm D^{0}\) and \(\Lambda _{c}^{+}\) . With this enthusiasm, we have studied the freeze-out scenarios of \(\mathrm D^{0}\) and \(\Lambda _{c}^{+}\) in a pp collisions at \(\sqrt{s}\) = 13 TeV using a pQCD-based framework called PYTHIA8. In this work, the production dynamics of open-charm hadrons are studied as a function of event multiplicity ( \(\frac{dN_{ch}}{d\eta }\) ), transverse momentum spectra ( \(p_{T}\) ) and pseudorapidity ( \(\eta \) ). The \(p_{T}\) -spectra are analyzed with thermodynamically consistent non-extensive Tsallis distribution function. The effective temperature (T) and non-extensive parameter (q) have been studied as a function of charged-particle multiplicity, transverse momentum, and pseudorapidity. We observed that T increases with ( \(\frac{dN_{ch}}{d\eta }\) ) and decreases with ( \(\eta \) ) while the non-extensive parameter increases for both the cases, when we consider heavy-flavors. Further, it is observed that the behaviour of T and q with transverse momentum depends explicitly on the final state charged-particle multiplicity. Along with these two parameters T and q, a correlation between these initial state effects and final state effects is observed through the number of multi-partonic interactions ( \(n_{MPI}\) ) and Knudsen number. Possible thermalization in small collision systems and applicability of hydrodynamics are explored.