Recently, there has been much activity in the study of dynamic condensed matter sys- tems under extreme conditions. This work bears even greater similarity to our study of spatial anisotropies in heavy-ion collisions.
The study of condensed matter systems under extreme pressure has a long history; re- cently, using diamond anvils, pressures of up to 0.1 TPa (106 atm) can be achieved under static conditions in the laboratory, resulting in a surprising diversity of new materials [McMi02]. Exploring even more extreme conditions – 10 TPa or larger – requires explosive generation of a transient system such as are done at the National Ignition Facility [Lind04] or in table-top experiments in which sub-ps laser pulses gener- ate “micro-explosions” under the surface of Sapphire crystals [Juod06] crystals or fused silica [Merm09].
The study of these micro-explosions parallels strikingly the study of femtoexplosions in heavy-ion collisions. In the initial state, the matter is in the charge-confined (atomic) state. Upon rapid deposition of extreme energy density (1017J/m3), a charge-deconfined plasma is generated within a few fs, at temperatures of 105− 106 K. The plasma expands
rapidly (∼ ps), cooling as it does so, and returns to charge-confined degrees of freedom. Plasma hydrodynamics and two-component “blast-wave” pictures [Hall07] are used to describe and understand the source evolution [Juod06].
With huge changes in physical scales and “color charge” replacing “electric charge,” the above describes the situation with RHIC collisions rather well, down to the blast-wave parameterizations [Reti04]. In both cases, too, the final-state anisotropy carries impor-
10.1. Anisotropic shapes as a probe of three strongly-coupled systems 85
tant physical information. The anisotropic final-state geometry of a micro-explosion is measured directly by a scanning electron microscope; c.f. figure 10.2. In a heavy-ion experiment, it is the final-state momenta that are directly measured, and azimuthally- sensitive two-particle intensity interferometry must be used to measure the coordinate- space geometry.
Since the first proof-of-principle micro-explosion experiments, there has been consider- able activity to extract the equation of state of the matter – the plasma state, phase transitions, etc. The approach taken is essentially identical to the one proposed at RHIC: to measure the final-state anisotropy as the initial energy of the system is varied, and compare the results to transport calculations with different EoS.
10.1.3. Anisotropic shape evolution in hot QCD matter
The case on which we shall focus henceforth is the anisotropic evolution of the hot matter generated in the overlap zone of two colliding heavy nuclei; this is indicated in the right panels of figure 10.1. Here, we introduce the anisotropies of interest and the physics driv- ing their evolution. The situation with heavy-ion collisions bears more resemblance to that of the micro-explosions of section 10.1.2 than to the cold atoms discussed in 10.1.1, since the experimenter cannot freely choose the time to measure the system anisotropy. When particles decouple from the medium created in a heavy-ion collision, they are said to “freeze-out.” Only the final state of the system – after it has expanded and frozen out – is available for examination; its temporal evolution must be modeled.
The anisotropy of the hot zone in a heavy-ion collision has two sources. Firstly, the beam direction (ˆz) is clearly special; both in momentum- and coordinate-space, the hot source is extended in ˆz. Collisions at finite impact parameter break the remaining symmetry in the azimuthal variable around the beam direction. The so-called reaction plane is the plane spanned by the impact parameter (oriented in the ˆx-direction in this work) and the beam direction. Figure 10.2 shows a plausible if simplistic sketch of the hot matter produced in a non-central heavy-ion collision, containing the minimal set of possible anisotropies– different length scales in each direction, and a tilt of the source away from the beam axis.
Of particular interest is the transverse eccentricity of the source, mentioned already in section 10.1.1. This eccentricity may be quantified by ≡ σ2y− σ2
x / σ2y+ σ2x, where
σx,y are characteristic scales of the system in and out of the reaction plane, respectively,
and will be discussed in more detail shortly. As discussed there, and seen in figure 10.1, the final state eccentricity is determined by both the anisotropic pressure gradient and the system lifetime; increasing either or both of these results in a lower (possibly nega- tive) .
The other major feature of the freeze-out distribution is the tilt of its major axis, relative to the beam direction. Such tilts are ubiquitously produced in three-dimensional sim-
86 Chapter 10. Shape analysis of strongly-interacting systems
ulations of heavy-ion collisions. At low energies (√sN N ≈ 4 GeV), θs ≈ 30◦ [Lisa00a];
its sign discriminated between competing explanations of momentum-space anisotropies for charged pions [Lisa00c].
Generic expectations for the collision energy dependence of freeze-out shapes seem straightforward. The eccentricity, , is affected by pressure and timescale. One ex- pects both the lifetime and the energy density of the system to increase with increasing √
sN N. Thus – if the relationship between pressure and energy density (the EoS) re-
mains fixed – it is natural to expect to decrease monotonically with√sN N. The tilt is a
manifestly non-boost-invariant aspect of the QGP created in the collision. Directed flow measurements at all energies confirm that the dynamics of heavy-ion collisions are never, strictly speaking, boost invariant. Even the hope that the system is “essentially” boost- invariant at midrapidity may be easily shattered if a finite tilt angle is measured there. Nevertheless, due to the increased elongation of dynamics along the beam direction, it is natural to expect a monotonic decrease of θs with
√
sN N as well.