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 ∆ s to characterize the evolution. λ compares the microscopic relaxation time (away from the critical point) to the expansion rate λ ≡ τ 0 /τ Q , and ∆ s compares the baryon to entropy ratio, n/s, to its critical value, ∆ s ≡ (n/s − n c /s c )/(n c /s c ). We determine how the evolution of critical hydrodynamic fluctuations depends parametrically on λ and ∆ 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.

Critical behavior of the bulk viscosity in QCD

“…Note that in the present work we have only considered the Fourier transform of the equilibrium response. A more complete treatment in an expanding system would be based on computing the response from the real time correlation functions of the order parameter in an expanding medium [20,23]. Also note that we focused on the leading critical enhancement in the bulk viscosity.…”

“…(21) and (28). For typical values of the diffusion constant t 0 T is of order one; we have used t 0 1.8 fm from [23]. The coefficient 3/(32π) ∼ 3 · 10 −2 is a loop factor.…”

“…In a heavy ion collision the growth of the correlation length is limited by the failure of the evolution to go precisely through the critical point, and by the finite time available for the correlation length to reach its equilibrium value [23,36]. The recent study [23] concludes that the second effect dominates, and that ξ/ξ 0 is limited by ξ KZ /ξ 0 where ξ KZ is the Kibble-Zurek scale. Akamatsu et al [23] estimate that ξ KZ /ξ 0 ∼ 1.33, so that the critical bulk viscosity in equ.…”

“…The recent study [23] concludes that the second effect dominates, and that ξ/ξ 0 is limited by ξ KZ /ξ 0 where ξ KZ is the Kibble-Zurek scale. Akamatsu et al [23] estimate that ξ KZ /ξ 0 ∼ 1.33, so that the critical bulk viscosity in equ. (40) does not become large.…”

“…Recently, a number of authors have investigated the dynamic evolution of fluctuations in an expanding QCD medium. This includes studies of non-critical correlation functions [18][19][20], simulations of critical stochastic diffusion in an expanding medium [21], and deterministic frameworks for the evolution of two-point [22][23][24] or higher n-point functions [25] near a critical point.…”