330
R. Stock
Venugopulan. The success of these models demonstrates that “successive binary
baryon scattering” is not an appropriate picture at high
√
s. One can free the partons
from the nucleonic parton density distributions only once, and their corresponding
transverse areal density sets the stage for the ensuing QCD parton shower evolution
[62]. Moreover, an additional saturation effect appears to modify this evolution at
high transverse areal parton density (see Sect. 7.2.4).
7.2.3 Dependence on System Size
We have discussed above a first attempt toward a variable (N part ) that scales the
system size dependence in A+A collisions. Note that one can vary the size either
by centrally colliding a sequence of nuclei, A 1 + A 1 , A 2 + A 2 etc., or by selecting
different windows in N part out of minimum bias collision ensembles obtained for
heavy nuclei for which BNL employs 197 Au and CERN 208 Pb. The third alternative,
scattering a relatively light projectile, such as 32 S, from increasing A nuclear targets,
has been employed initially both at the AGS and SPS but got disfavored in view
of numerous disadvantages, of both experimental (the need to measure the entire
rapidity distribution, i.e. lab momenta from about 0.3–100 GeV/c, with uniform
efficiency) and theoretical nature (different density distributions of projectile and
target; occurrence of an “effective” center of mass, different for hard and soft
collisions, and depending on impact parameter).
The determination of N part is of central interest, and thus we need to look at
technicalities, briefly. The approximate linear scaling with N part that we observed in
the total transverse energy and the total charged particle number (Figs. 7.3 and 7.6)
is a reflection of the primordial redistribution of partons and energy. Whereas all
observable properties that refer to the system evolution at later times, which are of
interest as potential signals from the equilibrium, QCD plasma “matter” phase, have
different specific dependences on N part , be it suppressions (high p T signals, jets,
quarkonia production) or enhancements (collective hydrodynamic flow, strangeness
production). N part thus emerges as a suitable common reference scale.
N part captures the number of potentially directly hit nucleons. It is estimated from
an eikonal straight trajectory Glauber model as applied to the overlap region arising,
in dependence of impact parameter b, from the superposition along beam direction
of the two initial Woods-Saxon density distributions of the interacting nuclei. To
account for the dilute surfaces of these distributions (within which the intersecting
nucleons might not find an interaction partner) each incident nucleon trajectory gets
equipped with a transverse radius that represents the total inelastic NN cross section
at the corresponding
√
s. The formalism is imbedded into a Monte Carlo simulation
(for detail see [66]) starting from random microscopic nucleon positions within
the transversely projected initial Woods-Saxon density profiles. Overlapping cross
sectional tubes of target and projectile nucleons are counted as a participant nucleon
pair. Owing to the statistics of nucleon initial position sampling each considered
impact parameter geometry thus results in a probability distribution of derived N part .
R. Stock
Venugopulan. The success of these models demonstrates that “successive binary
baryon scattering” is not an appropriate picture at high
√
s. One can free the partons
from the nucleonic parton density distributions only once, and their corresponding
transverse areal density sets the stage for the ensuing QCD parton shower evolution
[62]. Moreover, an additional saturation effect appears to modify this evolution at
high transverse areal parton density (see Sect. 7.2.4).
7.2.3 Dependence on System Size
We have discussed above a first attempt toward a variable (N part ) that scales the
system size dependence in A+A collisions. Note that one can vary the size either
by centrally colliding a sequence of nuclei, A 1 + A 1 , A 2 + A 2 etc., or by selecting
different windows in N part out of minimum bias collision ensembles obtained for
heavy nuclei for which BNL employs 197 Au and CERN 208 Pb. The third alternative,
scattering a relatively light projectile, such as 32 S, from increasing A nuclear targets,
has been employed initially both at the AGS and SPS but got disfavored in view
of numerous disadvantages, of both experimental (the need to measure the entire
rapidity distribution, i.e. lab momenta from about 0.3–100 GeV/c, with uniform
efficiency) and theoretical nature (different density distributions of projectile and
target; occurrence of an “effective” center of mass, different for hard and soft
collisions, and depending on impact parameter).
The determination of N part is of central interest, and thus we need to look at
technicalities, briefly. The approximate linear scaling with N part that we observed in
the total transverse energy and the total charged particle number (Figs. 7.3 and 7.6)
is a reflection of the primordial redistribution of partons and energy. Whereas all
observable properties that refer to the system evolution at later times, which are of
interest as potential signals from the equilibrium, QCD plasma “matter” phase, have
different specific dependences on N part , be it suppressions (high p T signals, jets,
quarkonia production) or enhancements (collective hydrodynamic flow, strangeness
production). N part thus emerges as a suitable common reference scale.
N part captures the number of potentially directly hit nucleons. It is estimated from
an eikonal straight trajectory Glauber model as applied to the overlap region arising,
in dependence of impact parameter b, from the superposition along beam direction
of the two initial Woods-Saxon density distributions of the interacting nuclei. To
account for the dilute surfaces of these distributions (within which the intersecting
nucleons might not find an interaction partner) each incident nucleon trajectory gets
equipped with a transverse radius that represents the total inelastic NN cross section
at the corresponding
√
s. The formalism is imbedded into a Monte Carlo simulation
(for detail see [66]) starting from random microscopic nucleon positions within
the transversely projected initial Woods-Saxon density profiles. Overlapping cross
sectional tubes of target and projectile nucleons are counted as a participant nucleon
pair. Owing to the statistics of nucleon initial position sampling each considered
impact parameter geometry thus results in a probability distribution of derived N part .