Correlation between mean transverse momentum and anisotropic flow in heavy-ion collisions

The correlation between the mean transverse momentum of outgoing particles, (pt), and the magnitude of anisotropic flow, vn, has recently been measured in Pb+Pb collisions at the CERN Large Hadron Collider, as a function of the collision centrality. We confirm the previous observation that event-by-event hydrodynamics predicts a correlation between vn and (pt) that is similar to that measured in data. We show that the magnitude of this correlation can be directly predicted from the initial condition of the hydrodynamic calculation, for n=2,3, if one replaces vn by the corresponding initial-state anisotropy, ɛn, and (pt) by the total energy per unit rapidity of the fluid at the beginning of the hydrodynamic expansion.