7 Relativistic Nucleus-Nucleus Collisions and the QCD Matter Phase Diagram
431
model building. We mention here, in particular, investigations of the AdS/CFT
correspondence method [307] with respect to primordial equilibration [308]. Collective flow then transports the density distribution toward decoupling; this stage
is analyzed under the general idea to follow the Fourier components n of the
primordial energy density distribution eccentricity as they get delivered to observation in the form of spatial flow anisotropics quantified [309] by their Fourier
harmonics decomposition coefficients v n (see ref. [310] and bibliography therein).
Strictly speaking, the hydro-phase does not directly “deliver” the observables of
viscous, anisotropic flow to observation. This phase ends at hadronization because
the mean free path in the ensuing hadron-resonance(HR) expansion stage is too long
for hydrodynamics to apply. One thus introduces a transition from hydro to HR gas
by means of a hadronization model that translates hydro matter flow into hadronresonance propagation (by the Cooper-Frye formalism [311]). The latter is then
described by a hadron transport model acting as an “afterburner” [312, 313]. Such
so-called hybrid models thus consist of three stages that incorporate stage specific
dynamical models for initialization, hydro flow and hadron-resonance afterburning.
This allows for a very wide variety of theoretical choices concerning the overall
dynamics. Add to this that the experimental data from RHIC and LHC can be
analyzed with various techniques, delivering the flow coefficients v n (reaction plane
method, cumulant method etc.). Thus an almost excessive wealth of data to model
comparisons have been undertaken, with the highest focus on elliptical flow v 2 .
Data exist for up to v 6 . In general v 1 —directed flow—and v 2 are predominantly
related to impact geometry variations of mass 200 collisions, creating anisotropic
primordial energy density gradients. Whereas v 3 , in particular, appears to be
more dependent on the primordial energy density profile and its even by event
fluctuations, potentially related to Colour Glass Condensate(CGC) formation [314].
Very briefly summarizing the results one observes an anticorrelation between the
initialization-, and the hydro flow-effects. The specific shear viscosity η/s (that
quantifies the speed with which the system approaches equilibrium) is tantalizingly
close to the Kovtun, Son and Stariets [315] minimum of 1/4π, throughout, but
its deduced value at RHIC goes up with changing the initialization model from a
“trivial” Glauber trajectory choice, to a CGC model, as is illustrated in Fig. 7.72 with
RHIC STAR data [314] for v 2 vs. theory [315]. Employing the Glauber initialization
one deduces η/s to be near 0.08 (the KSS limit) whereas the CGC model requires
twice the shear velocity, about 0.16. The Glauber initial fireball is wider, spatially,
than the one from the CGC model. That ambiguity has not finally been settled yet,
it persists at the LHC, where the specific viscosity is slightly larger. The overall
present result, within the CGC type of hybrid dynamical models, is given by Eskola
and coworkers [316] and illustrated in Fig. 7.73. Similar results for η/s have been
given by other theory groups [313, 317]. In summary, an unambiguous conclusion
about the QGP state as a near ideal liquid has been arrived at, whereas the existence
of the CGC still remains to be finally established.
431
model building. We mention here, in particular, investigations of the AdS/CFT
correspondence method [307] with respect to primordial equilibration [308]. Collective flow then transports the density distribution toward decoupling; this stage
is analyzed under the general idea to follow the Fourier components n of the
primordial energy density distribution eccentricity as they get delivered to observation in the form of spatial flow anisotropics quantified [309] by their Fourier
harmonics decomposition coefficients v n (see ref. [310] and bibliography therein).
Strictly speaking, the hydro-phase does not directly “deliver” the observables of
viscous, anisotropic flow to observation. This phase ends at hadronization because
the mean free path in the ensuing hadron-resonance(HR) expansion stage is too long
for hydrodynamics to apply. One thus introduces a transition from hydro to HR gas
by means of a hadronization model that translates hydro matter flow into hadronresonance propagation (by the Cooper-Frye formalism [311]). The latter is then
described by a hadron transport model acting as an “afterburner” [312, 313]. Such
so-called hybrid models thus consist of three stages that incorporate stage specific
dynamical models for initialization, hydro flow and hadron-resonance afterburning.
This allows for a very wide variety of theoretical choices concerning the overall
dynamics. Add to this that the experimental data from RHIC and LHC can be
analyzed with various techniques, delivering the flow coefficients v n (reaction plane
method, cumulant method etc.). Thus an almost excessive wealth of data to model
comparisons have been undertaken, with the highest focus on elliptical flow v 2 .
Data exist for up to v 6 . In general v 1 —directed flow—and v 2 are predominantly
related to impact geometry variations of mass 200 collisions, creating anisotropic
primordial energy density gradients. Whereas v 3 , in particular, appears to be
more dependent on the primordial energy density profile and its even by event
fluctuations, potentially related to Colour Glass Condensate(CGC) formation [314].
Very briefly summarizing the results one observes an anticorrelation between the
initialization-, and the hydro flow-effects. The specific shear viscosity η/s (that
quantifies the speed with which the system approaches equilibrium) is tantalizingly
close to the Kovtun, Son and Stariets [315] minimum of 1/4π, throughout, but
its deduced value at RHIC goes up with changing the initialization model from a
“trivial” Glauber trajectory choice, to a CGC model, as is illustrated in Fig. 7.72 with
RHIC STAR data [314] for v 2 vs. theory [315]. Employing the Glauber initialization
one deduces η/s to be near 0.08 (the KSS limit) whereas the CGC model requires
twice the shear velocity, about 0.16. The Glauber initial fireball is wider, spatially,
than the one from the CGC model. That ambiguity has not finally been settled yet,
it persists at the LHC, where the specific viscosity is slightly larger. The overall
present result, within the CGC type of hybrid dynamical models, is given by Eskola
and coworkers [316] and illustrated in Fig. 7.73. Similar results for η/s have been
given by other theory groups [313, 317]. In summary, an unambiguous conclusion
about the QGP state as a near ideal liquid has been arrived at, whereas the existence
of the CGC still remains to be finally established.