Transits of the QCD Critical Point

Abstract

We analyze the evolution of hydrodynamic fluctuations in a heavy ion collision as the system passes close to the QCD critical point. We introduce two small dimensionless parameters $λ$ and $Δ_s$ to characterize the evolution. $λ$ compares the microscopic relaxation time (away from the critical point) to the expansion rate $λ\equiv τ_0/τ_Q$, and $Δ_s$ compares the baryon to entropy ratio, $n/s$, to its critical value, $Δ_s\equiv (n/s - n_c/s_c)/(n_c/s_c)$. We determine how the evolution of critical hydrodynamic fluctuations depends parametrically on $λ$ and $Δ_s$. Finally, we use this parametric reasoning to estimate the critical fluctuations and correlation length for a heavy ion collision, and to give guidance to the experimental search for the QCD critical point.