7 Relativistic Nucleus-Nucleus Collisions and the QCD Matter Phase Diagram
409
cannot be unambiguously disentangled from the deconfinement transition effects at
T c ” [256].
We may be looking at the wrong domain of [T , μ B ] space: too high
√
s and, thus,
too high T , too low μ B . Already at top SPS energy the medium is dominated by the
deconfinement, not by the chiral QCD transition. After hadronization the medium
is still at T close to T c but the density drops off within a few fm/c, not allowing for
an equilibrium mean field state of chirally restored hadrons. It is thus perhaps not
surprising that the data are seen to be dominated by simple broadening and lack of
structure: perhaps that is all that happens to hadrons at T c .
The chiral restoration transition should thus be studied at higher μ B and lower
T such that the dynamics achieves high baryon densities but still merely touches
the critical (deconfinement) temperature. In fact, at μ B → 1 GeV and T <
100 MeV the chiral transition should be of first order [259]. Here, in fact, the
chiral condensate mass plays the role of the order parameter (in analogy to the
magnetization in a spin system), which approaches zero as T → T c . We might thus
speculate that, unlike at top SPS to LHC energy (where deconfinement dominates),
the chiral QCD first order phase transition will dominate the phenomena occurring
near the hadron-parton borderline, in the vicinity of
√
s = 4–6 GeV [142]. This
requires a new experimental program, with low energy running at the SPS [260], at
RHIC [261] and at the GSI FAIR project [262].
7.7 Fluctuation and Correlation Signals
Fluctuation and correlation signals in A+A collisions can be evaluated in single
events, due to the high multiplicity of produced particles. Depending on the physics
context we may be interested to see either a small, or a large nonstatistical fluctuation effect. For example in view of the universality of hadronization (Sect. 7.3)
we would have difficulty with an event by event pion to baryon ratio (essentially
μ
−1
B ) fluctuating by, say, 50%. Conversely, searching for critical fluctuations in the
vicinity of a predicted critical point of QCD [146, 147] we would be frustrated
if event-wise p T , d N/d y (low p T pion) [263] or strange to non-strange ratios
like K/π [148, 264] would not exhibit any significant fluctuation beyond statistics.
Overall, event by event fluctuation observables also carry a message concerning
the robustness of our assumptions about equilibrium attainment. It turns out that
equilibrium properties are not, merely, central limit consequences of ensemble
averaging. Rather to the contrary, each A ≈ 200 central collision event at
√
s ≥
10 GeV appears to offer, to the dynamical evolution of bulk properties, a sufficiently
complete macroscopic limit. Such that we can view the event-wise bulk dynamics
as “self analyzing”.
409
cannot be unambiguously disentangled from the deconfinement transition effects at
T c ” [256].
We may be looking at the wrong domain of [T , μ B ] space: too high
√
s and, thus,
too high T , too low μ B . Already at top SPS energy the medium is dominated by the
deconfinement, not by the chiral QCD transition. After hadronization the medium
is still at T close to T c but the density drops off within a few fm/c, not allowing for
an equilibrium mean field state of chirally restored hadrons. It is thus perhaps not
surprising that the data are seen to be dominated by simple broadening and lack of
structure: perhaps that is all that happens to hadrons at T c .
The chiral restoration transition should thus be studied at higher μ B and lower
T such that the dynamics achieves high baryon densities but still merely touches
the critical (deconfinement) temperature. In fact, at μ B → 1 GeV and T <
100 MeV the chiral transition should be of first order [259]. Here, in fact, the
chiral condensate mass plays the role of the order parameter (in analogy to the
magnetization in a spin system), which approaches zero as T → T c . We might thus
speculate that, unlike at top SPS to LHC energy (where deconfinement dominates),
the chiral QCD first order phase transition will dominate the phenomena occurring
near the hadron-parton borderline, in the vicinity of
√
s = 4–6 GeV [142]. This
requires a new experimental program, with low energy running at the SPS [260], at
RHIC [261] and at the GSI FAIR project [262].
7.7 Fluctuation and Correlation Signals
Fluctuation and correlation signals in A+A collisions can be evaluated in single
events, due to the high multiplicity of produced particles. Depending on the physics
context we may be interested to see either a small, or a large nonstatistical fluctuation effect. For example in view of the universality of hadronization (Sect. 7.3)
we would have difficulty with an event by event pion to baryon ratio (essentially
μ
−1
B ) fluctuating by, say, 50%. Conversely, searching for critical fluctuations in the
vicinity of a predicted critical point of QCD [146, 147] we would be frustrated
if event-wise p T , d N/d y (low p T pion) [263] or strange to non-strange ratios
like K/π [148, 264] would not exhibit any significant fluctuation beyond statistics.
Overall, event by event fluctuation observables also carry a message concerning
the robustness of our assumptions about equilibrium attainment. It turns out that
equilibrium properties are not, merely, central limit consequences of ensemble
averaging. Rather to the contrary, each A ≈ 200 central collision event at
√
s ≥
10 GeV appears to offer, to the dynamical evolution of bulk properties, a sufficiently
complete macroscopic limit. Such that we can view the event-wise bulk dynamics
as “self analyzing”.