7 Relativistic Nucleus-Nucleus Collisions and the QCD Matter Phase Diagram
371
the expanding system is already in rapid flow once it traverses the phase boundary,
with an expansion time scale shorter than the formation time scale of mean field
phenomena. At lower energies, on the other hand, the system might not even dive
into the deconfined phase but spend a comparatively long time in its direct vicinity,
at the turning point between compression and re-expansion where all dynamical
time constants are large, and the hadron density is high, such that the inelastic
hadronic transmutation rate becomes high (particularly in collisions of more than
two hadronic reactants, with reaction rates [138] proportional to n ), and sufficiently
so for maintaining hadronic chemical equilibrium after it is first established at
maximum hadron density, in low
√
s systems that do not cross the phase boundary
at all.
The GC freeze-out parameters [T , μ] at various
√
s in Fig. 7.33 permit a
smooth interpolation in the T , μ plane [139], which, in turn, allows for GC model
predictions which are continuous in
√
s. Such a curve is shown in Fig. 7.28
compared to the 4π data points for the K + /π + multiplicity ratio in central collisions
Au+Au/Pb+Pb, at all
√
s investigated thus far. It exhibits a smooth maximum, due
to the interplay of T saturation and μ B fall-off to zero, but does not account for
the sharp peak structure seen in the data at
√
s ≈ 7 GeV and μ B ≈ 480 MeV.
This behavior is not a peculiarity of the K + channel only; it also is reflected in
an unusually high Wroblewski ratio (see Eq. (7.39)) obtained at
√
s = 7.6 GeV,
of λ s = 0.60 [19]. This sharp strangeness maximum is unexplained as of yet. It
implies that hadron formation at this
√
s reflects influences that are less prominent
above and below, and most attempts to understand the effect [141–143] are centered
at the assumption that at this particular
√
s the overall bulk dynamics will settle
directly at the phase boundary where, moreover, finite μ B lattice theory also expects
a QCD critical point [9–11]. This would cause a softest point to occur in the equation
of state, i.e. a minimum in the relation of expansion pressure vs. energy density,
slowing down the dynamical evolution [144, 145], and thus increasing the sensitivity
to expansion modes characteristic of a first order phase transition [143], which
occurs at μ B ≥ μ crit
B . Such conditions may modify the K/π ratio (Fig. 7.28) [143].
It thus appears that the interval from top AGS to lower SPS energy, 5 ≤
√
s ≤
10 GeV, promises highly interesting information regarding the QCD phase diagram
(Fig. 7.1) in the direct vicinity of the parton-hadron coexistence line. In particular,
the physics of a critical point of QCD matter deserves further study. Observable consequences also comprise so-called “critical fluctuations” [146, 147] of multiplicity
density, mean transverse momentum and hadron-chemical composition [148], the
latter in fact being observed near
√
s = 7 GeV in an event by event study of the
K/π ratio in central Pb+Pb collisions [149]. We shall return to critical point physics
in Sect. 7.7.
371
the expanding system is already in rapid flow once it traverses the phase boundary,
with an expansion time scale shorter than the formation time scale of mean field
phenomena. At lower energies, on the other hand, the system might not even dive
into the deconfined phase but spend a comparatively long time in its direct vicinity,
at the turning point between compression and re-expansion where all dynamical
time constants are large, and the hadron density is high, such that the inelastic
hadronic transmutation rate becomes high (particularly in collisions of more than
two hadronic reactants, with reaction rates [138] proportional to n ), and sufficiently
so for maintaining hadronic chemical equilibrium after it is first established at
maximum hadron density, in low
√
s systems that do not cross the phase boundary
at all.
The GC freeze-out parameters [T , μ] at various
√
s in Fig. 7.33 permit a
smooth interpolation in the T , μ plane [139], which, in turn, allows for GC model
predictions which are continuous in
√
s. Such a curve is shown in Fig. 7.28
compared to the 4π data points for the K + /π + multiplicity ratio in central collisions
Au+Au/Pb+Pb, at all
√
s investigated thus far. It exhibits a smooth maximum, due
to the interplay of T saturation and μ B fall-off to zero, but does not account for
the sharp peak structure seen in the data at
√
s ≈ 7 GeV and μ B ≈ 480 MeV.
This behavior is not a peculiarity of the K + channel only; it also is reflected in
an unusually high Wroblewski ratio (see Eq. (7.39)) obtained at
√
s = 7.6 GeV,
of λ s = 0.60 [19]. This sharp strangeness maximum is unexplained as of yet. It
implies that hadron formation at this
√
s reflects influences that are less prominent
above and below, and most attempts to understand the effect [141–143] are centered
at the assumption that at this particular
√
s the overall bulk dynamics will settle
directly at the phase boundary where, moreover, finite μ B lattice theory also expects
a QCD critical point [9–11]. This would cause a softest point to occur in the equation
of state, i.e. a minimum in the relation of expansion pressure vs. energy density,
slowing down the dynamical evolution [144, 145], and thus increasing the sensitivity
to expansion modes characteristic of a first order phase transition [143], which
occurs at μ B ≥ μ crit
B . Such conditions may modify the K/π ratio (Fig. 7.28) [143].
It thus appears that the interval from top AGS to lower SPS energy, 5 ≤
√
s ≤
10 GeV, promises highly interesting information regarding the QCD phase diagram
(Fig. 7.1) in the direct vicinity of the parton-hadron coexistence line. In particular,
the physics of a critical point of QCD matter deserves further study. Observable consequences also comprise so-called “critical fluctuations” [146, 147] of multiplicity
density, mean transverse momentum and hadron-chemical composition [148], the
latter in fact being observed near
√
s = 7 GeV in an event by event study of the
K/π ratio in central Pb+Pb collisions [149]. We shall return to critical point physics
in Sect. 7.7.