344
R. Stock
justified to employ Eq. (7.1) or (7.17) for the initial conditions at RHIC, obtaining
[61, 84]
6 GeV/fm
3
≤ ≤ 20 GeV/fm
3
(7.18)
for the interval 0.3 fm/c ≤ t 0 ≤ 1 fm/c, in central Au+Au collisions at y ≈ 0
and
√
s = 200 GeV. The energy density at top SPS energy,
√
s = 17.3 GeV, can
similarly be estimated [43, 44] to amount to about 3 GeV/fm 3 at a t 0 of 1 fm/c but
we cannot identify conditions at τ 0 < t 0 in this case as the mere interpenetration of
two Pb nuclei takes 1.4 fm/c. Thus the commonly accepted t 0 = 1 fm/c may lead
to a high estimate. An application of the parton-hadron transport model of Ellis and
Geiger [85, 86] to this collision finds = 3.3 GeV/fm 3 at t = 1 fm/c. A primordial
energy density of about 3 GeV/fm 3 is 20 times ρ 0 ≈ 0.15 GeV/fm 3 , the average
energy density of ground state nuclear matter, and it also exceeds, by far, the critical
QCD energy density, of 0.6 ≤ c ≤ 1 GeV/fm 3 according to lattice QCD [48]. The
initial dynamics thus clearly proceeds in a deconfined QCD system also at top SPS
energy, and similarly so with strikingly higher energy density, at RHIC, where time
scales below 1 fm/c can be resolved.
However, in order now to clarify the key question as to whether, and when conditions of partonic dynamical equilibrium may arise under such initial conditions,
we need estimates both of the proper relaxation time scale (which will, obviously,
depend on energy density and related collision frequency), and of the expansion
time scale as governed by the overall evolution of the collision volume. Only if
τ (relax.) < τ (expans.) one may conclude that the “deconfined partonic system”
can be identified with a “deconfined QGP state of QCD matter” as described e.g. by
lattice QCD, and implied in the phase diagram of QCD matter suggested in Fig. 7.1.
For guidance concerning the overall time-order of the system evolution we
consider information [87] obtained from Bose-Einstein correlation analysis of pion
pair emission in momentum space (for detail see Sect. 7.7). Note that pions should
be emitted at any stage of the evolution, after formation time, from the surface
regions of the evolving “fire-tube”. Bulk emission of pions occurs, of course, after
hadronization (the latest stages illustrated in the evolution sketch given in Fig. 7.18).
The dynamical pion source expansion models by Heinz [88] and Sinyukov [89]
elaborate a Gaussian emission time profile, with mean τ f (the decoupling time) and
width τ (the duration of emission).
Figure 7.19 shows an application of this analysis to central Pb+Pb collision
negative pion pair correlation data obtained by NA49 at top SPS energy,
√
s =
17.3 GeV [90], where τ f ≈ 8 fm/c and ≈ 4 fm/c (note that τ = 0 in Fig. 7.19
corresponds, not to interaction time t = 0 but to t ≈ 1.4 fm/c, the end of the
interpenetration phase). We see, first of all, that the overall dynamical evolution
of a central Pb+Pb collision at
√
s = 17.3 GeV is ending at about 15 fm/c;
the proper time defines the position of the last, decoupling profile illustrated in
Fig. 7.18, for the SPS collisions considered here. While the details of Fig. 7.19
will turn out to be relevant to our later discussion of hadronization (Sect. 7.3) and
hadronic expansion (Sect. 7.4), we are concerned here with the average proper time
R. Stock
justified to employ Eq. (7.1) or (7.17) for the initial conditions at RHIC, obtaining
[61, 84]
6 GeV/fm
3
≤ ≤ 20 GeV/fm
3
(7.18)
for the interval 0.3 fm/c ≤ t 0 ≤ 1 fm/c, in central Au+Au collisions at y ≈ 0
and
√
s = 200 GeV. The energy density at top SPS energy,
√
s = 17.3 GeV, can
similarly be estimated [43, 44] to amount to about 3 GeV/fm 3 at a t 0 of 1 fm/c but
we cannot identify conditions at τ 0 < t 0 in this case as the mere interpenetration of
two Pb nuclei takes 1.4 fm/c. Thus the commonly accepted t 0 = 1 fm/c may lead
to a high estimate. An application of the parton-hadron transport model of Ellis and
Geiger [85, 86] to this collision finds = 3.3 GeV/fm 3 at t = 1 fm/c. A primordial
energy density of about 3 GeV/fm 3 is 20 times ρ 0 ≈ 0.15 GeV/fm 3 , the average
energy density of ground state nuclear matter, and it also exceeds, by far, the critical
QCD energy density, of 0.6 ≤ c ≤ 1 GeV/fm 3 according to lattice QCD [48]. The
initial dynamics thus clearly proceeds in a deconfined QCD system also at top SPS
energy, and similarly so with strikingly higher energy density, at RHIC, where time
scales below 1 fm/c can be resolved.
However, in order now to clarify the key question as to whether, and when conditions of partonic dynamical equilibrium may arise under such initial conditions,
we need estimates both of the proper relaxation time scale (which will, obviously,
depend on energy density and related collision frequency), and of the expansion
time scale as governed by the overall evolution of the collision volume. Only if
τ (relax.) < τ (expans.) one may conclude that the “deconfined partonic system”
can be identified with a “deconfined QGP state of QCD matter” as described e.g. by
lattice QCD, and implied in the phase diagram of QCD matter suggested in Fig. 7.1.
For guidance concerning the overall time-order of the system evolution we
consider information [87] obtained from Bose-Einstein correlation analysis of pion
pair emission in momentum space (for detail see Sect. 7.7). Note that pions should
be emitted at any stage of the evolution, after formation time, from the surface
regions of the evolving “fire-tube”. Bulk emission of pions occurs, of course, after
hadronization (the latest stages illustrated in the evolution sketch given in Fig. 7.18).
The dynamical pion source expansion models by Heinz [88] and Sinyukov [89]
elaborate a Gaussian emission time profile, with mean τ f (the decoupling time) and
width τ (the duration of emission).
Figure 7.19 shows an application of this analysis to central Pb+Pb collision
negative pion pair correlation data obtained by NA49 at top SPS energy,
√
s =
17.3 GeV [90], where τ f ≈ 8 fm/c and ≈ 4 fm/c (note that τ = 0 in Fig. 7.19
corresponds, not to interaction time t = 0 but to t ≈ 1.4 fm/c, the end of the
interpenetration phase). We see, first of all, that the overall dynamical evolution
of a central Pb+Pb collision at
√
s = 17.3 GeV is ending at about 15 fm/c;
the proper time defines the position of the last, decoupling profile illustrated in
Fig. 7.18, for the SPS collisions considered here. While the details of Fig. 7.19
will turn out to be relevant to our later discussion of hadronization (Sect. 7.3) and
hadronic expansion (Sect. 7.4), we are concerned here with the average proper time