Relativistic diffusion and heavy-ion collisions

We study first- and second-order theories of relativistic diffusion coupled to hydrodynamics under the approximation, valid at midrapidity in the BNL Relativistic Heavy Ion Collider (RHIC) and the CERN Large Hadron Collider (LHC), that conserved number densities are much smaller than the entropy density. We identify experimentally accessible quantities of interest and show that the first- and second-order theories may lead to radically different evolutions of these quantities. In the first-order theory the memory of the initial state is almost completely washed out, whereas in the second-order theory it is possible that freeze-out occurs at a time when transient dynamics is still on and the memory of the initial state remains. There are observational consequences that we touch upon. In the first-order theory, and for initial conditions when the second-order theory mimics the first-order theory, one may be able to put a bound on the diffusion constant.</p>.