7 Relativistic Nucleus-Nucleus Collisions and the QCD Matter Phase Diagram
329
The data described above suggest that the stopping mechanism universally
resides in the primordial, first generation of collisions at the microscopic level. The
rapidity distributions of charged particle multiplicity, transverse energy and valence
quark exhibit qualitatively similar shapes (which also evolve similarly with
√
s)
in pp, pp, e + e − reactions, on the one hand, and in central or semi-peripheral
collisions of A ≈ 200 nuclei, on the other. Comparing in detail we formulate a
nuclear modification factor for the bulk hadron rapidity distributions,
R
AA
y
≡
dN ch /dy (y) in A+A
0.5 N part dN ch /dy in pp
(7.6)
where N part < 2A is the mean number of “participating nucleons” (which undergo
at least one inelastic collision with another nucleon) which increases with collision
centrality. For identical nuclei colliding
N
proj
part
N
targ
part
and thus 0.5 N part gives
the number of opposing nucleon pairs. R AA = 1 if each such “opposing” pair
contributes the same fraction to the total A+A yield as is produced in minimum bias
pp at similar
√
s. From Figs. 7.4 and 7.6 we infer that for | η |< 1, R AA = 1.5 at top
RHIC energy, and for the pseudo-rapidity integrated total N ch we find R AA = 1.36,
in central Au+Au collisions. AA collisions thus provide for a higher stopping power
than pp (which is also reflected in the higher rapidity shift δy of Fig. 7.10). The
observation that their stopping power resembles the e + e − inelasticity suggests a
substantially reduced leading particle effect in central collisions of heavy nuclei.
This might not be surprising. In a Glauber-view of successive minimum bias nucleon
collisions occurring during interpenetration, each participating nucleon is struck
ν > 3 times on average, which might saturate the possible inelasticity, removing
the leading fragment.
This view naturally leads to the scaling of the total particle production in nuclear
collisions with N part , as seen clearly in Fig. 7.6, reminiscent of the “wounded
nucleon model” [59] but with the scaling factor determined by e + e − rather than pp
[60]. Overall we conclude from the still rather close similarity between nuclear and
elementary collisions that the mechanisms of longitudinal phase space population
occur primordially, during interpenetration which is over after 0.15 fm/c at RHIC,
and after 1.5 fm/c at SPS energy. I.e. it is the primordial non-equilibrium pQCD
shower evolution that accounts for stopping, and its time extent should be a lower
limit to the formation time τ 0 employed in the Bjorken model [45], Eq. (7.1).
Equilibration at the partonic level might begin at t > τ 0 only (the development
toward a quark-gluon-plasma phase), but the primordial parton redistribution
processes set the stage for this phase, and control the relaxation time scales involved
in equilibration [61]. More about this in Sect. 7.2.5. We infer the existence of a
saturation scale [62] controlling the total inelasticity: with ever higher reactant
thickness, proportional to A 1/3 , one does not get a total rapidity or energy density
proportional to A 4/3 (the number of “successive binary collisions”) but to A 1.08 only
[63]. Note that the lines shown in Fig. 7.7 (right panel) refer to such a saturation
theory: the color glass condensate (CGC) model [64] developed by McLerran and
329
The data described above suggest that the stopping mechanism universally
resides in the primordial, first generation of collisions at the microscopic level. The
rapidity distributions of charged particle multiplicity, transverse energy and valence
quark exhibit qualitatively similar shapes (which also evolve similarly with
√
s)
in pp, pp, e + e − reactions, on the one hand, and in central or semi-peripheral
collisions of A ≈ 200 nuclei, on the other. Comparing in detail we formulate a
nuclear modification factor for the bulk hadron rapidity distributions,
R
AA
y
≡
dN ch /dy (y) in A+A
0.5 N part dN ch /dy in pp
(7.6)
where N part < 2A is the mean number of “participating nucleons” (which undergo
at least one inelastic collision with another nucleon) which increases with collision
centrality. For identical nuclei colliding
N
proj
part
N
targ
part
and thus 0.5 N part gives
the number of opposing nucleon pairs. R AA = 1 if each such “opposing” pair
contributes the same fraction to the total A+A yield as is produced in minimum bias
pp at similar
√
s. From Figs. 7.4 and 7.6 we infer that for | η |< 1, R AA = 1.5 at top
RHIC energy, and for the pseudo-rapidity integrated total N ch we find R AA = 1.36,
in central Au+Au collisions. AA collisions thus provide for a higher stopping power
than pp (which is also reflected in the higher rapidity shift δy of Fig. 7.10). The
observation that their stopping power resembles the e + e − inelasticity suggests a
substantially reduced leading particle effect in central collisions of heavy nuclei.
This might not be surprising. In a Glauber-view of successive minimum bias nucleon
collisions occurring during interpenetration, each participating nucleon is struck
ν > 3 times on average, which might saturate the possible inelasticity, removing
the leading fragment.
This view naturally leads to the scaling of the total particle production in nuclear
collisions with N part , as seen clearly in Fig. 7.6, reminiscent of the “wounded
nucleon model” [59] but with the scaling factor determined by e + e − rather than pp
[60]. Overall we conclude from the still rather close similarity between nuclear and
elementary collisions that the mechanisms of longitudinal phase space population
occur primordially, during interpenetration which is over after 0.15 fm/c at RHIC,
and after 1.5 fm/c at SPS energy. I.e. it is the primordial non-equilibrium pQCD
shower evolution that accounts for stopping, and its time extent should be a lower
limit to the formation time τ 0 employed in the Bjorken model [45], Eq. (7.1).
Equilibration at the partonic level might begin at t > τ 0 only (the development
toward a quark-gluon-plasma phase), but the primordial parton redistribution
processes set the stage for this phase, and control the relaxation time scales involved
in equilibration [61]. More about this in Sect. 7.2.5. We infer the existence of a
saturation scale [62] controlling the total inelasticity: with ever higher reactant
thickness, proportional to A 1/3 , one does not get a total rapidity or energy density
proportional to A 4/3 (the number of “successive binary collisions”) but to A 1.08 only
[63]. Note that the lines shown in Fig. 7.7 (right panel) refer to such a saturation
theory: the color glass condensate (CGC) model [64] developed by McLerran and