7 Relativistic Nucleus-Nucleus Collisions and the QCD Matter Phase Diagram
365
which is reproduced by the percolation model [120]. Also included is a prediction
for Cu+Cu at this energy which rises more steeply on the common N part scale
because the collision and energy density reached in central Cu+Cu collisions, at
N part ≈ 100, exceeds that in peripheral Au+Au collisions (at the same N part ) which
share a more prominent contribution from the dilute surface regions of the nuclear
density profile. We note, finally, that this deviation from universal N part scaling does
not contradict the observations of a perfect such scaling as far as overall charged
particle multiplicity densities are concerned (recall Fig. 7.12) which are dominated
by pions, not subject to size dependent canonical suppression.
7.3.3 Origin of Hadro-Chemical Equilibrium
The statistical hadronization model (SHM) is not a model of the QCD confinement
process leading to hadrons, which occurs once the dynamical cooling evolution
of the system arrives at T c . At this stage the partonic reaction volume, small in
elementary collisions but extended in A+A collisions, will decay (by whatever
elementary QCD process) to on-shell hadrons and resonances. This coherent
quantum mechanical decay results in a de-coherent quasi-classical, primordial onshell hadron-resonance population which, at the instant of its formation, lends
itself to a quasi-classical Gibbs ensemble description. Its detailed modalities
(canonical for small decaying systems, grand canonical for extended fireballs in
A+A collisions), and its derived parameters [T , μ B ] merely recast the conditions,
prevailing at hadronization. The success of SHM analysis thus implies that the
QCD hadronization process ends in statistical equilibrium concerning the hadronresonance species population.
In order to identify mechanisms in QCD hadronization that introduce the hadrochemical equilibrium we refer to jet hadronization in e + e − annihilation reactions,
which we showed in Fig. 7.17 to be well described by the canonical SHM. In di-jet
formation at LEP energy,
√
s = 92 GeV, we find a charged particle multiplicity
of about 10 per jet, and we estimate that, likewise, about 10 primordial partons
participate on either side of the back-to-back di-jet [85]. There is thus no chance for
either a partonic or hadronic, extensive rescattering toward chemical equilibrium.
However, in the jet hadronization models developed by Amati and Veneziano [83],
Webber [121] and Ellis and Geiger [85] the period of QCD DGLAP parton shower
evolution (and of perturbative QCD, in general) ends with local color neutralization,
by formation of spatial partonic singlet clusters. This QCD “color pre-confinement”
[83] process reminds of a coalescence mechanism, in which the momenta and the
initial virtual masses of the individual clustering partons get converted to internal,
invariant virtual mass of color neutral, spatially extended objects. Their mass
spectrum [121] extends from about 0.5 to 10 GeV. This cluster mass distribution,
shown in Fig. 7.31, represents the first stochastic element in this hadronization
model.
365
which is reproduced by the percolation model [120]. Also included is a prediction
for Cu+Cu at this energy which rises more steeply on the common N part scale
because the collision and energy density reached in central Cu+Cu collisions, at
N part ≈ 100, exceeds that in peripheral Au+Au collisions (at the same N part ) which
share a more prominent contribution from the dilute surface regions of the nuclear
density profile. We note, finally, that this deviation from universal N part scaling does
not contradict the observations of a perfect such scaling as far as overall charged
particle multiplicity densities are concerned (recall Fig. 7.12) which are dominated
by pions, not subject to size dependent canonical suppression.
7.3.3 Origin of Hadro-Chemical Equilibrium
The statistical hadronization model (SHM) is not a model of the QCD confinement
process leading to hadrons, which occurs once the dynamical cooling evolution
of the system arrives at T c . At this stage the partonic reaction volume, small in
elementary collisions but extended in A+A collisions, will decay (by whatever
elementary QCD process) to on-shell hadrons and resonances. This coherent
quantum mechanical decay results in a de-coherent quasi-classical, primordial onshell hadron-resonance population which, at the instant of its formation, lends
itself to a quasi-classical Gibbs ensemble description. Its detailed modalities
(canonical for small decaying systems, grand canonical for extended fireballs in
A+A collisions), and its derived parameters [T , μ B ] merely recast the conditions,
prevailing at hadronization. The success of SHM analysis thus implies that the
QCD hadronization process ends in statistical equilibrium concerning the hadronresonance species population.
In order to identify mechanisms in QCD hadronization that introduce the hadrochemical equilibrium we refer to jet hadronization in e + e − annihilation reactions,
which we showed in Fig. 7.17 to be well described by the canonical SHM. In di-jet
formation at LEP energy,
√
s = 92 GeV, we find a charged particle multiplicity
of about 10 per jet, and we estimate that, likewise, about 10 primordial partons
participate on either side of the back-to-back di-jet [85]. There is thus no chance for
either a partonic or hadronic, extensive rescattering toward chemical equilibrium.
However, in the jet hadronization models developed by Amati and Veneziano [83],
Webber [121] and Ellis and Geiger [85] the period of QCD DGLAP parton shower
evolution (and of perturbative QCD, in general) ends with local color neutralization,
by formation of spatial partonic singlet clusters. This QCD “color pre-confinement”
[83] process reminds of a coalescence mechanism, in which the momenta and the
initial virtual masses of the individual clustering partons get converted to internal,
invariant virtual mass of color neutral, spatially extended objects. Their mass
spectrum [121] extends from about 0.5 to 10 GeV. This cluster mass distribution,
shown in Fig. 7.31, represents the first stochastic element in this hadronization
model.