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 $\ensuremath{\lambda}$ and ${\mathrm{\ensuremath{\Delta}}}_{s}$ to characterize the evolution. $\ensuremath{\lambda}$ compares the microscopic relaxation time (away from the critical point) to the expansion rate $\ensuremath{\lambda}\ensuremath{\equiv}{\ensuremath{\tau}}_{0}/{\ensuremath{\tau}}_{Q}$, and ${\mathrm{\ensuremath{\Delta}}}_{s}$ compares the baryon to entropy ratio, $n/s$, to its critical value, ${\mathrm{\ensuremath{\Delta}}}_{s}\ensuremath{\equiv}(n/s\ensuremath{-}{n}_{c}/{s}_{c})/({n}_{c}/{s}_{c})$. We determine how the evolution of critical hydrodynamic fluctuations depends parametrically on $\ensuremath{\lambda}$ and ${\mathrm{\ensuremath{\Delta}}}_{s}$. 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.