Transverse momentum structure of pair correlations as a signature of collective behavior in small collision systems
We perform 3+1D viscous hydrodynamic calculations of proton-lead and lead-lead collisions at top LHC energy. We show that existing data from high-multiplicity p-Pb events can be well described in hydrodynamics, suggesting that collective flow is plausible as a correct description of these collisions. However, a more stringent test of the presence of hydrodynamic behavior can be made by studying the detailed momentum dependence of two-particle correlations. We define a relevant observable, $r_n$, and make predictions for its value and centrality dependence if hydrodynamics is a valid description. This will provide a non-trivial confirmation of the nature of the correlations seen in small collision systems, and potentially to determine where the hydrodynamic description, if valid anywhere, stops being valid. Lastly, we probe what can be learned from this observable, finding that it is insensitive to viscosity, but sensitive to aspects of the initial state of the system that other observables are insensitive to, such as the transverse length scale of the fluctuations in the initial stages of the collision.