High-multiplicity pp and pA collisions: Hydrodynamics at its edge

With growing multiplicity, the pp and pA collisions enter the domain where the macroscopic description (thermodynamics and hydrodynamics) becomes applicable. We discuss this situation, first with simplified thought experiments, then with some idealized representative cases, and finally address the real data. For clarity, we do not do it numerically but analytically, using the Gubser solution. We found that the radial flow is expected to increase from central AA to central pA, while the elliptic flow decreases, with higher harmonics being comparable. We extensively study the magnitude and distribution of the viscous corrections, in Navier-Stokes and Israel-Stuart approximations, ending with higher gradient resummation proposed by Lublinsky and Shuryak. We found that those corrections grow from AA to pA to pp, but remain tractable even for pp.