Prescaling and Far-from-Equilibrium Hydrodynamics in the Quark-Gluon Plasma

Prescaling is a far-from-equilibrium phenomenon which describes the rapid establishment of a universal scaling form of distributions much before the universal values of their scaling exponents are realized. We consider the example of the spatiotemporal evolution of the quark-gluon plasma explored in heavy-ion collisions at sufficiently high energies. Solving QCD kinetic theory with elastic and inelastic processes, we demonstrate that the gluon and quark distributions very quickly adapt a self-similar scaling form, which is independent of initial condition details and system parameters. The dynamics in the prescaling regime is then fully encoded in a few time-dependent scaling exponents, whose slow evolution gives rise to far-from-equilibrium hydrodynamic behavior.

Figure 1

Pressure anisotropy $P_L/P_T$ for a longitudinally expanding QCD plasma with overoccupied gluon initial state.

Figure 2

Time-dependent scaling exponents from multiple sets of integral moments for gluon density parameter ${\sigma }_0=0.1$.

Figure 3

The same as Fig. 2, but for ${\sigma }_0=0.6$.

Figure 4

Left: Gluon distribution rescaled with ${\tau }^{-\alpha }$ versus transverse momentum for the full QCD collision kernels (solid) and with elastic scatterings only (dashed). Right: The same distribution, but rescaled with a time-dependent scaling exponent.

Figure 5

Left: Gluon distribution versus longitudinal momentum ${\tau }^{\gamma }{p}_z$. Right: Same, but with time-dependent exponents.

Figure 6

Left: Fermion distribution versus longitudinal momentum ${\tau }^{\gamma }{p}_z$. Right: Same, but rescaled using the time-dependent gluon scaling exponents employed also in Fig. 2.