7 Relativistic Nucleus-Nucleus Collisions and the QCD Matter Phase Diagram
353
suggesting that primordial partonic flow begins to contribute significantly to radial
flow.
7.3 Hadronization and Hadronic Freeze-Out in A+A
Collisions
Within the course of the global expansion of the primordial reaction volume
the local flow “cells” will hit the parton-hadron phase boundary as their energy
density approaches crit ≈ 1 GeV/fm 3 . Hadronization will thus occur, not at
an instant over the entire interaction volume, but within a finite overall time
interval [86] that results from the spread of proper time at which individual cells,
or coherent clusters of such cells (as developed during expansion) arrive at the
phase boundary. However, irrespective of such a local-temporal occurrence, the
hadronization process (which is governed by non perturbative QCD at the low
Q 2 corresponding to bulk hadronization) universally results in a novel, global
equilibrium property that concerns the relative abundance of produced hadrons and
resonances. This so-called “hadrochemical equilibrium state” is directly observable,
in contrast to the stages of primordial parton equilibration that are only indirectly
assessed, via dynamical model studies.
This equilibrium population of species occurs both in elementary and nuclear
collisions [107]. We have seen in Fig. 7.17 a first illustration, by e + e − annihilation
data at
√
s = 91.2 GeV LEP energy, that are well reproduced by the partition
functions of the statistical hadronization model (SHM) in its canonical form [84].
The derived hadronization temperature, T H = 165 MeV, turns out to be universal to
all elementary and nuclear collision processes at
√
s ≥ 20 GeV, and it agrees with
the limiting temperature predicted by Hagedorn [38] to occur in any multi-hadronic
equilibrium system once the energy density approaches about 0.6 GeV/fm 3 . Thus,
the upper limit of hadronic equilibrium density corresponds, closely, to the lower
limit, crit = 0.6–1.0 GeV/fm 3 of partonic equilibrium matter, according to lattice
QCD [48]. In elementary collisions only about 20 partons or hadrons participate:
there should be no chance to approach thermodynamic equilibrium of species by
rescattering cascades, neither in the partonic nor in the hadronic phase. The fact that,
nevertheless, the hadron formation temperature T H coincides with the Hagedorn
limiting temperature and with the QCD confinement temperature, is a consequence
of the non-perturbative QCD hadronization process itself [85], which “gives birth”
to hadrons/resonances in canonical equilibrium, at high
√
s, as we shall see below.
This process also governs A+A collisions but, as it occurs here under conditions of
high energy density extended over considerable volume, the SHM description now
requires a grand canonical ensemble, with important consequences for production
of strange hadrons (strangeness enhancement).
The grand canonical order of hadron/resonance production in central A+A
collisions, and its characteristic strangeness enhancement shows that a state of
353
suggesting that primordial partonic flow begins to contribute significantly to radial
flow.
7.3 Hadronization and Hadronic Freeze-Out in A+A
Collisions
Within the course of the global expansion of the primordial reaction volume
the local flow “cells” will hit the parton-hadron phase boundary as their energy
density approaches crit ≈ 1 GeV/fm 3 . Hadronization will thus occur, not at
an instant over the entire interaction volume, but within a finite overall time
interval [86] that results from the spread of proper time at which individual cells,
or coherent clusters of such cells (as developed during expansion) arrive at the
phase boundary. However, irrespective of such a local-temporal occurrence, the
hadronization process (which is governed by non perturbative QCD at the low
Q 2 corresponding to bulk hadronization) universally results in a novel, global
equilibrium property that concerns the relative abundance of produced hadrons and
resonances. This so-called “hadrochemical equilibrium state” is directly observable,
in contrast to the stages of primordial parton equilibration that are only indirectly
assessed, via dynamical model studies.
This equilibrium population of species occurs both in elementary and nuclear
collisions [107]. We have seen in Fig. 7.17 a first illustration, by e + e − annihilation
data at
√
s = 91.2 GeV LEP energy, that are well reproduced by the partition
functions of the statistical hadronization model (SHM) in its canonical form [84].
The derived hadronization temperature, T H = 165 MeV, turns out to be universal to
all elementary and nuclear collision processes at
√
s ≥ 20 GeV, and it agrees with
the limiting temperature predicted by Hagedorn [38] to occur in any multi-hadronic
equilibrium system once the energy density approaches about 0.6 GeV/fm 3 . Thus,
the upper limit of hadronic equilibrium density corresponds, closely, to the lower
limit, crit = 0.6–1.0 GeV/fm 3 of partonic equilibrium matter, according to lattice
QCD [48]. In elementary collisions only about 20 partons or hadrons participate:
there should be no chance to approach thermodynamic equilibrium of species by
rescattering cascades, neither in the partonic nor in the hadronic phase. The fact that,
nevertheless, the hadron formation temperature T H coincides with the Hagedorn
limiting temperature and with the QCD confinement temperature, is a consequence
of the non-perturbative QCD hadronization process itself [85], which “gives birth”
to hadrons/resonances in canonical equilibrium, at high
√
s, as we shall see below.
This process also governs A+A collisions but, as it occurs here under conditions of
high energy density extended over considerable volume, the SHM description now
requires a grand canonical ensemble, with important consequences for production
of strange hadrons (strangeness enhancement).
The grand canonical order of hadron/resonance production in central A+A
collisions, and its characteristic strangeness enhancement shows that a state of