Applicability of Hydrodynamics in Hadronic Phase of Heavy-Ion Collisions

The hadronic phase and its dynamics in relativistic heavy-ion collisions are topics of immense discussion. The hadronic phase contains various massive hadrons with an abundance of the lightest hadron, i.e., $\pi$-mesons (pions). In this paper, we consider that pions are in thermal equilibrium in the hadronic phase and use second-order viscous hydrodynamics for a medium of massive pions to obtain its expansion to the boundary of the kinetic freeze-out. We achieve the kinetic freeze-out boundary with the Knudsen number $Kn>1$ limit. When this condition is met, hydrodynamics expansion breaks down, and the mean free path becomes sufficiently large in comparison with the system size so that the particle yields are preserved. Further, we investigate the effect of the massive fluid on the resonance particle yields, including re-scattering and regeneration, along with the natural decay widths of the resonances. The resonances can play an essential role in determining the characteristics of the hadronic phase as they have sufficiently small lifetimes, which may be comparable to the hadronic phase lifetime. In the current study, we predict the hadronic phase lifetime, which is further used to determine the $K^*(892)^0/K$, $\phi(1020)/K$, and $\rho(770)^0/\pi$ yield ratios at the kinetic freeze-out. We calculate these ratios as a function of charged particle multiplicity and transverse momentum and compare the findings with experimental data. Our calculations qualitatively agree with the experimental data, indicating a possible hydrodynamical evolution of the hadronic phase.