7 Relativistic Nucleus-Nucleus Collisions and the QCD Matter Phase Diagram
369
Thus, in analyzing successive bins of the rapidity distributions in Fig. 7.32, the major
variation in the GC fit concerns the baryo-chemical potential μ B (y) which increases
from about 20 MeV (Fig. 7.26) at mid-rapidity, to about 150 MeV at y ≥ 3 while the
hadronization temperature stays constant, at T = 160 MeV. This interplay between
K − /K + , p/p and μ B is illustrated [128] in the right hand panel of Fig. 7.32, and
shown to be well accounted for by the GC statistical model [131].
These considerations imply that hadronization at RHIC (and LHC) energy occurs
local in y-space and late in time. The density distribution of net baryon number
results from the primordial pQCD shower evolution (c.f. Sect. 7.2.4), and is thus
fixed at formation time, t 0 ≤ 0.6 fm/c at RHIC. Hadronization of the bulk partonic
matter occurs later, at t ≥ 3 fm/c [86, 95], and transmits the local conditions in
rapidity space by preserving the local net baryon quantum number density. Most
importantly we conclude that hadronization occurs, not from a single longitudinally
boosted fireball but from a succession of “super-clusters”, of different partonic
composition depending on y, and decaying at different time due to the Lorentzboost that increases with y, in an “inside-outside” pattern (c.f. Fig. 7.18). We are
thus witnessing at hadronization a Hubble expanding system of local fireballs.
The detailed implications of this picture have not been analyzed yet. Note that a
central RHIC collision thus does not correspond to a single hadronization “point”
in the [T , μ] plane of Fig. 7.1 but samples {T , μ} along the QCD parton-hadron
coexistence line [132].
Throughout this chapter we have discussed hadronic freeze-out at high
√
s only
(top SPS to RHIC energy), because of the proximity of the chemical freeze-out
parameters [T , μ B ] to the QCD phase boundary from lattice QCD, which suggests
an overall picture of hadronization, to occur directly from a partonic cluster or
super-cluster. Our discussion of the GC statistical hadronization model has been
explicitly or implicitly based on the assumption that hadronic freeze-out coincides
with hadronization. However, the GC model has also been applied successfully
to hadro-chemical freeze-out at
√
s down to a few GeV [19, 107, 108] where it
is not expected that the dynamical evolution traverses the phase boundary at all,
but grand canonical multiplicity distributions, and their characteristic strangeness
enhancement pattern, are observed throughout. Toward lower
√
s, T decreases
while μ B increases, as is shown in Fig. 7.33 which presents a compilation of all
reported freeze-out parameters [108].
These points have also been included in the phase diagram of Fig. 7.1 which
shows that they are gradually branching away from the phase separation boundary
line that could recently be predicted by lattice QCD once new methods had been
developed to extend the theory to finite μ B [9, 10]. At
√
s ≥ 20 GeV we see that
c (QCD) ≈ H ≈ GC
(7.46)
where GC is the freeze-out density inferred from GC analysis [19, 107, 108].
In turn, the GC hadronic freeze-out points drop below the lattice QCD coexistence line at lower
√
s, implying that chemical freeze-out now occurs within the
hadronic expansion phase. This requires a model of freeze-out, now governed by
369
Thus, in analyzing successive bins of the rapidity distributions in Fig. 7.32, the major
variation in the GC fit concerns the baryo-chemical potential μ B (y) which increases
from about 20 MeV (Fig. 7.26) at mid-rapidity, to about 150 MeV at y ≥ 3 while the
hadronization temperature stays constant, at T = 160 MeV. This interplay between
K − /K + , p/p and μ B is illustrated [128] in the right hand panel of Fig. 7.32, and
shown to be well accounted for by the GC statistical model [131].
These considerations imply that hadronization at RHIC (and LHC) energy occurs
local in y-space and late in time. The density distribution of net baryon number
results from the primordial pQCD shower evolution (c.f. Sect. 7.2.4), and is thus
fixed at formation time, t 0 ≤ 0.6 fm/c at RHIC. Hadronization of the bulk partonic
matter occurs later, at t ≥ 3 fm/c [86, 95], and transmits the local conditions in
rapidity space by preserving the local net baryon quantum number density. Most
importantly we conclude that hadronization occurs, not from a single longitudinally
boosted fireball but from a succession of “super-clusters”, of different partonic
composition depending on y, and decaying at different time due to the Lorentzboost that increases with y, in an “inside-outside” pattern (c.f. Fig. 7.18). We are
thus witnessing at hadronization a Hubble expanding system of local fireballs.
The detailed implications of this picture have not been analyzed yet. Note that a
central RHIC collision thus does not correspond to a single hadronization “point”
in the [T , μ] plane of Fig. 7.1 but samples {T , μ} along the QCD parton-hadron
coexistence line [132].
Throughout this chapter we have discussed hadronic freeze-out at high
√
s only
(top SPS to RHIC energy), because of the proximity of the chemical freeze-out
parameters [T , μ B ] to the QCD phase boundary from lattice QCD, which suggests
an overall picture of hadronization, to occur directly from a partonic cluster or
super-cluster. Our discussion of the GC statistical hadronization model has been
explicitly or implicitly based on the assumption that hadronic freeze-out coincides
with hadronization. However, the GC model has also been applied successfully
to hadro-chemical freeze-out at
√
s down to a few GeV [19, 107, 108] where it
is not expected that the dynamical evolution traverses the phase boundary at all,
but grand canonical multiplicity distributions, and their characteristic strangeness
enhancement pattern, are observed throughout. Toward lower
√
s, T decreases
while μ B increases, as is shown in Fig. 7.33 which presents a compilation of all
reported freeze-out parameters [108].
These points have also been included in the phase diagram of Fig. 7.1 which
shows that they are gradually branching away from the phase separation boundary
line that could recently be predicted by lattice QCD once new methods had been
developed to extend the theory to finite μ B [9, 10]. At
√
s ≥ 20 GeV we see that
c (QCD) ≈ H ≈ GC
(7.46)
where GC is the freeze-out density inferred from GC analysis [19, 107, 108].
In turn, the GC hadronic freeze-out points drop below the lattice QCD coexistence line at lower
√
s, implying that chemical freeze-out now occurs within the
hadronic expansion phase. This requires a model of freeze-out, now governed by