7 Relativistic Nucleus-Nucleus Collisions and the QCD Matter Phase Diagram
337
RHIC, as far as small Q 2 bulk charged particle production is concerned. We have
illustrated this by the CGC model fits [64] to the PHOBOS charged particle rapidity
distributions, shown in Fig. 7.7.
Conversely, QCD processes falling in the transition region between such limiting
conditions, such that typical Q 2 ≈ Q 2
s (x), should present observables that are
functions of the ratio between the transferred momentum Q 2 and the appropriate
saturation scale, expressed by Q 2
s (x). As Q 2 defines the effective transverse
sampling area, and Q 2
s (x) the characteristic areal size at which saturation is expected
to set in, a characteristic behavior of cross sections, namely that they are universal
functions of Q 2 /Q 2
s , is called “geometric scaling”. The HERA ep scattering data
obey this scaling law closely [78], and the idea arises to apply the universality
principle that we mentioned above: at small enough x, all hadrons or nuclei are
similar, their specific properties only coming in via the appropriate saturation scales
Q 2
s (x, h) or Q 2
s (x, A). Knowing the latter for RHIC conditions we will understand
the systematics of charged particle production illustrated in the previous chapter, and
thus also be able to extrapolate toward LHC conditions in pp and AA collisions.
All data for the virtual photo-absorption cross section σ γp (x, Q 2 ) in deep
inelastic ep scattering with x ≤ 0.01 (which is also the RHIC mid-rapidity xdomain) have been found [78] to lie on a single curve when plotted against Q 2 /Q 2
s ,
with
Q
2
s (x) ∼
x 0
x
λ
1 GeV
2
(7.12)
with λ 0.3 and x 0 10 −4 . This scaling [79] with τ = Q 2 /Q 2
s is shown
in Fig. 7.15 (top panel) to interpolate all data. A chain of arguments, proposed
by Armesto et al. [63] connects a fit to these data with photo-absorption data for
(virtual) photon-A interactions [80] via the geometrical scaling ansatz
σ γ A (τ A )
πR 2
A
=
σ γp (τ p = τ A )
πR 2
p
(7.13)
assuming that the scale in the nucleus grows with the ratio of the transverse parton
densities, raised to the power 1/δ (a free parameter),
Q
2
s,A = Q
2
s,p
AπR 2
p
πR 2
A
1/δ
, τ A = τ h
πR 2
A
AπR 2
h
1/δ
.
(7.14)
Figure 7.15 (middle and bottom panels) shows their fit to the nuclear photoabsorption data which fixes δ = 0.79 and πR 2
p = 1.57 fm 2 (see ref. [63] for detail).
The essential step in transforming these findings to the case of A+A collisions is
then taken by the empirical ansatz
dN AA
dy
(at y 0) ∝ Q
2
s,A (x)πR
2
A
(7.15)
337
RHIC, as far as small Q 2 bulk charged particle production is concerned. We have
illustrated this by the CGC model fits [64] to the PHOBOS charged particle rapidity
distributions, shown in Fig. 7.7.
Conversely, QCD processes falling in the transition region between such limiting
conditions, such that typical Q 2 ≈ Q 2
s (x), should present observables that are
functions of the ratio between the transferred momentum Q 2 and the appropriate
saturation scale, expressed by Q 2
s (x). As Q 2 defines the effective transverse
sampling area, and Q 2
s (x) the characteristic areal size at which saturation is expected
to set in, a characteristic behavior of cross sections, namely that they are universal
functions of Q 2 /Q 2
s , is called “geometric scaling”. The HERA ep scattering data
obey this scaling law closely [78], and the idea arises to apply the universality
principle that we mentioned above: at small enough x, all hadrons or nuclei are
similar, their specific properties only coming in via the appropriate saturation scales
Q 2
s (x, h) or Q 2
s (x, A). Knowing the latter for RHIC conditions we will understand
the systematics of charged particle production illustrated in the previous chapter, and
thus also be able to extrapolate toward LHC conditions in pp and AA collisions.
All data for the virtual photo-absorption cross section σ γp (x, Q 2 ) in deep
inelastic ep scattering with x ≤ 0.01 (which is also the RHIC mid-rapidity xdomain) have been found [78] to lie on a single curve when plotted against Q 2 /Q 2
s ,
with
Q
2
s (x) ∼
x 0
x
λ
1 GeV
2
(7.12)
with λ 0.3 and x 0 10 −4 . This scaling [79] with τ = Q 2 /Q 2
s is shown
in Fig. 7.15 (top panel) to interpolate all data. A chain of arguments, proposed
by Armesto et al. [63] connects a fit to these data with photo-absorption data for
(virtual) photon-A interactions [80] via the geometrical scaling ansatz
σ γ A (τ A )
πR 2
A
=
σ γp (τ p = τ A )
πR 2
p
(7.13)
assuming that the scale in the nucleus grows with the ratio of the transverse parton
densities, raised to the power 1/δ (a free parameter),
Q
2
s,A = Q
2
s,p
AπR 2
p
πR 2
A
1/δ
, τ A = τ h
πR 2
A
AπR 2
h
1/δ
.
(7.14)
Figure 7.15 (middle and bottom panels) shows their fit to the nuclear photoabsorption data which fixes δ = 0.79 and πR 2
p = 1.57 fm 2 (see ref. [63] for detail).
The essential step in transforming these findings to the case of A+A collisions is
then taken by the empirical ansatz
dN AA
dy
(at y 0) ∝ Q
2
s,A (x)πR
2
A
(7.15)