7 Relativistic Nucleus-Nucleus Collisions and the QCD Matter Phase Diagram
323
fourth power of the temperature,
= gT
4
(7.3)
where g is related to the number of degrees of freedom. For an ideal gluon gas,
g = 16 π 2 /30; in an interacting system the effective g is smaller. The results of
Fig. 7.5 show, in fact, that the Stefan-Boltzmann limit SB is not reached, due to non
perturbative effects, even at four times the critical temperature T c = 170 MeV. The
density /T 4 = g is seen to ascend steeply, within the interval T c ± 25 MeV. At T c
the critical QCD energy density = 0.6–1.0 GeV/fm 3 . Relating the thermal energy
density with the Bjorken estimates discussed above, one arrives at an estimate of the
initial temperatures reached in nucleus-nucleus collisions, thus implying thermal
partonic equilibrium to be accomplished at time scale τ 0 (see Sect. 7.2.5). For
the SPS, RHIC and LHC energy domains this gives an initial temperature in the
range 190 ≤ T SPS ≤ 220 MeV, 220 ≤ T RHIC ≤ 400 MeV (assuming [47]
that τ 0 decreases to about 0.3 fm/c here) and T LHC ≥ 600 MeV, respectively.
From such estimates one tends to conclude that the immediate vicinity of the phase
transformation is sampled at SPS energy, whereas the dynamical evolution at RHIC
and LHC energies dives deeply into the “quark-gluon-plasma” domain of QCD. We
shall return to a more critical discussion of such ascertations in Sect. 7.2.5.
One further aspect of the mid-rapidity charged particle densities per participant
pair requires attention: the comparison with data from elementary collisions.
Figure 7.4 shows a compilation of pp, pp and e + e − data covering the range from
ISR to LEP and Tevatron energies.
The data from e + e − represent dN ch /dy, the rapidity density along the event
thrust axis, calculated assuming the pion mass [49] (the difference between dN/dy
and dN/dη can be ignored here). Remarkably, they superimpose with the central
A+A collision data, whereas pp and pp show similar slope but amount to only about
60% of the AA and e + e − values. This difference between e + e − annihilation to
hadrons, and pp or pp hadro-production has been ascribed [50] to the characteristic
leading particle effect of minimum bias hadron-hadron collisions which is absent
in e + e − . It thus appears to be reduced in AA collisions due to subsequent
interaction of the leading parton with the oncoming thickness of the remaining
target/projectile density distribution. This naturally leads to the scaling of total
particle production with N part that is illustrated in Fig. 7.6, for three RHIC energies
and minimum bias Au+Au collisions; the close agreement with e + e − annihilation
data is obvious again. One might conclude that, analogously, the participating
nucleons get “annihilated” at high
√
s, their net quantum number content being
spread out over phase space (as we shall show in the next section).
323
fourth power of the temperature,
= gT
4
(7.3)
where g is related to the number of degrees of freedom. For an ideal gluon gas,
g = 16 π 2 /30; in an interacting system the effective g is smaller. The results of
Fig. 7.5 show, in fact, that the Stefan-Boltzmann limit SB is not reached, due to non
perturbative effects, even at four times the critical temperature T c = 170 MeV. The
density /T 4 = g is seen to ascend steeply, within the interval T c ± 25 MeV. At T c
the critical QCD energy density = 0.6–1.0 GeV/fm 3 . Relating the thermal energy
density with the Bjorken estimates discussed above, one arrives at an estimate of the
initial temperatures reached in nucleus-nucleus collisions, thus implying thermal
partonic equilibrium to be accomplished at time scale τ 0 (see Sect. 7.2.5). For
the SPS, RHIC and LHC energy domains this gives an initial temperature in the
range 190 ≤ T SPS ≤ 220 MeV, 220 ≤ T RHIC ≤ 400 MeV (assuming [47]
that τ 0 decreases to about 0.3 fm/c here) and T LHC ≥ 600 MeV, respectively.
From such estimates one tends to conclude that the immediate vicinity of the phase
transformation is sampled at SPS energy, whereas the dynamical evolution at RHIC
and LHC energies dives deeply into the “quark-gluon-plasma” domain of QCD. We
shall return to a more critical discussion of such ascertations in Sect. 7.2.5.
One further aspect of the mid-rapidity charged particle densities per participant
pair requires attention: the comparison with data from elementary collisions.
Figure 7.4 shows a compilation of pp, pp and e + e − data covering the range from
ISR to LEP and Tevatron energies.
The data from e + e − represent dN ch /dy, the rapidity density along the event
thrust axis, calculated assuming the pion mass [49] (the difference between dN/dy
and dN/dη can be ignored here). Remarkably, they superimpose with the central
A+A collision data, whereas pp and pp show similar slope but amount to only about
60% of the AA and e + e − values. This difference between e + e − annihilation to
hadrons, and pp or pp hadro-production has been ascribed [50] to the characteristic
leading particle effect of minimum bias hadron-hadron collisions which is absent
in e + e − . It thus appears to be reduced in AA collisions due to subsequent
interaction of the leading parton with the oncoming thickness of the remaining
target/projectile density distribution. This naturally leads to the scaling of total
particle production with N part that is illustrated in Fig. 7.6, for three RHIC energies
and minimum bias Au+Au collisions; the close agreement with e + e − annihilation
data is obvious again. One might conclude that, analogously, the participating
nucleons get “annihilated” at high
√
s, their net quantum number content being
spread out over phase space (as we shall show in the next section).