340
R. Stock
absent in e + e − annihilation at similar
√
s where τ 0 ≈ 0.1 fm/c marks the end
of the primordial pQCD partonic shower evolution [83] during which the initially
created qq pair, of “virtually” Q =
√
s/2 each, multiplies in the course of the
QCD DGLAP evolution in perturbative vacuum, giving rise to daughter partons of
far lower virtuality, of a few GeV. In A+A collisions this shower era should last
longer, due to the interpenetrational spread of primordial collision time. It should
be over by about 0.25 fm/c. The shower partons in e + e − annihilation are localized
within back to back cone geometry reflecting the directions of the primordial quark
pair. The eventually observed “jet” signal, created by an initial Q 2 of 10 4 GeV 2 , is
established by then. Upon a slow-down of the dynamical evolution time scale to τ ≈
1 fm/c the shower partons fragment further, acquiring transverse momentum and yet
lower virtuality, then to enter a non perturbative QCD phase of color neutralization
during which hadron-like singlet parton clusters are formed. Their net initial pQCD
virtuality, in pQCD vacuum, is recast in terms of non-perturbative vacuum hadron
mass. The evolution ends with on-shell, observed jet-hadrons after about 3 fm/c of
overall reaction time.
Remarkably, even in this, somehow most elementary process of QCD evolution,
an aspect of equilibrium formation is observed, not in the narrowly focused final
dijet momentum topology but in the relative production rates of the various created
hadronic species. This so-called “hadrochemical” equilibrium among the hadronic
species is documented in Fig. 7.17. The hadron multiplicities per e + e − annihilation
event at
√
s = 91.2 GeV [38] are confronted with a Hagedorn [38] canonical
statistical Gibbs ensemble prediction [84] which reveals that the apparent species
equilibrium was fixed at a temperature of T = 165 MeV, which turns out to be the
universal hadronization temperature of all elementary and nuclear collisions at high
√
s (Hagedorns limiting temperature of the hadronic phase of matter). We shall
return to this topic in Sect. 7.3 but note, for now, that reactions with as few as 20
charged particles exhibit such statistical equilibrium properties, a pre-requisite for
application of thermodynamic or hydrodynamic concepts.
What happens with parton (and hadron) dynamics in A+A collisions after τ 0 ?
There will not be a QCD evolution in vacuum (which would be over after 3 fm/c)
as the transverse radius of the interacting system is large. It may grow to about
twice the nuclear radius, i.e. to about 15 fm before interactions cease; i.e. the system
needs about 15 fm/c to decouple. This simple fact is the key to our expectation that
the expansive evolution of the initial high energy density deposited in a cylinder
of considerable diameter (about 10 fm), may create certain equilibrium properties
that allow us to treat the contained particles and energy in terms of thermodynamic
phases of matter, such as a partonic QGP liquid, or a hadronic liquid or gas, etc.
Such that the expansion dynamics makes contact to the phase diagram illustrated in
Fig. 7.1. This expectation turns out to be justified as we shall describe in Sects. 7.3
and 7.4. What results for the evolution after τ 0 in a central A+A collision is sketched
in Fig. 7.18 by means of a schematic 2-dimensional light cone diagram, which is
entered by the two reactant nuclei along z = t trajectories where z is the beam
direction and Lorentz contraction has been taken to an extreme, such that there
R. Stock
absent in e + e − annihilation at similar
√
s where τ 0 ≈ 0.1 fm/c marks the end
of the primordial pQCD partonic shower evolution [83] during which the initially
created qq pair, of “virtually” Q =
√
s/2 each, multiplies in the course of the
QCD DGLAP evolution in perturbative vacuum, giving rise to daughter partons of
far lower virtuality, of a few GeV. In A+A collisions this shower era should last
longer, due to the interpenetrational spread of primordial collision time. It should
be over by about 0.25 fm/c. The shower partons in e + e − annihilation are localized
within back to back cone geometry reflecting the directions of the primordial quark
pair. The eventually observed “jet” signal, created by an initial Q 2 of 10 4 GeV 2 , is
established by then. Upon a slow-down of the dynamical evolution time scale to τ ≈
1 fm/c the shower partons fragment further, acquiring transverse momentum and yet
lower virtuality, then to enter a non perturbative QCD phase of color neutralization
during which hadron-like singlet parton clusters are formed. Their net initial pQCD
virtuality, in pQCD vacuum, is recast in terms of non-perturbative vacuum hadron
mass. The evolution ends with on-shell, observed jet-hadrons after about 3 fm/c of
overall reaction time.
Remarkably, even in this, somehow most elementary process of QCD evolution,
an aspect of equilibrium formation is observed, not in the narrowly focused final
dijet momentum topology but in the relative production rates of the various created
hadronic species. This so-called “hadrochemical” equilibrium among the hadronic
species is documented in Fig. 7.17. The hadron multiplicities per e + e − annihilation
event at
√
s = 91.2 GeV [38] are confronted with a Hagedorn [38] canonical
statistical Gibbs ensemble prediction [84] which reveals that the apparent species
equilibrium was fixed at a temperature of T = 165 MeV, which turns out to be the
universal hadronization temperature of all elementary and nuclear collisions at high
√
s (Hagedorns limiting temperature of the hadronic phase of matter). We shall
return to this topic in Sect. 7.3 but note, for now, that reactions with as few as 20
charged particles exhibit such statistical equilibrium properties, a pre-requisite for
application of thermodynamic or hydrodynamic concepts.
What happens with parton (and hadron) dynamics in A+A collisions after τ 0 ?
There will not be a QCD evolution in vacuum (which would be over after 3 fm/c)
as the transverse radius of the interacting system is large. It may grow to about
twice the nuclear radius, i.e. to about 15 fm before interactions cease; i.e. the system
needs about 15 fm/c to decouple. This simple fact is the key to our expectation that
the expansive evolution of the initial high energy density deposited in a cylinder
of considerable diameter (about 10 fm), may create certain equilibrium properties
that allow us to treat the contained particles and energy in terms of thermodynamic
phases of matter, such as a partonic QGP liquid, or a hadronic liquid or gas, etc.
Such that the expansion dynamics makes contact to the phase diagram illustrated in
Fig. 7.1. This expectation turns out to be justified as we shall describe in Sects. 7.3
and 7.4. What results for the evolution after τ 0 in a central A+A collision is sketched
in Fig. 7.18 by means of a schematic 2-dimensional light cone diagram, which is
entered by the two reactant nuclei along z = t trajectories where z is the beam
direction and Lorentz contraction has been taken to an extreme, such that there