336
R. Stock
thus sampling smaller x domains in Fig. 7.14 according to Eq. (7.9). It will further
increase in proceeding from hadronic to nuclear reaction partners A+A. Will it be
in proportion to A 4/3 ? We know from the previous sections (Sects. 7.2.2 and 7.2.3)
that this is not the case, the data indicating an increase with A 1.08 . This observation
is, in fact caused by the parton saturation effect, to which we turn now.
For given transverse resolution Q 2 and increasing 1/x the parton density of
Fig. 7.14 becomes so large that one cannot neglect their mutual interactions any
longer. One expects such interactions to produce “shadowing”, a decrease of
the scattering cross section relative to incoherent independent scattering [70, 71].
As an effect of such shadowed interactions there occurs [75] a saturation [61–
65, 70, 71, 75] of the cross section at each given Q 2 , slowing the increase with 1/x
to become logarithmic once 1/x exceeds a certain critical value x s (Q 2 ). Conversely,
for fixed x, saturation occurs for transverse momenta below some critical Q 2 (x),
Q
2
s (x) = α s N c
1
πR 2
dN
dy
(7.11)
where dN/dy is the x-dependent gluon density (at y = y proj −ln(1/x)). Q 2
s is called
the saturation scale. In Eq. (7.11) πR 2 is the hadron area (in transverse projection),
and α s N c is the color charge squared of a single gluon. More intuitively, Q 2
s (x)
defines an inversely proportional resolution area F s (x) and at each x we have to
choose F s (x) such that the ratio of total area πR 2 to F s (x) (the number of resolved
areal pixels) equals the number of single gluon charge sources featured by the total
hadron area. As a consequence the saturation scale Q 2
s (x) defines a critical areal
resolution, with two different types of QCD scattering theory defined, at each x, for
Q 2 > Q 2
s and Q 2 < Q 2
s , respectively [62, 65, 75].
As one expects a soft transition between such theories, to occur along the
transition line implied by Q 2
s (x), the two types of QCD scattering are best studied
with processes featuring typical Q 2 well above, or below Q 2
s (x). Jet production at
√
s ≥ 200 GeV in pp or AA collisions with typical Q 2 above about 10 3 GeV 2 ,
clearly falls into the former class, to be described e.g. by QCD DGLAP evolution
of partonic showers [76]. The acronym DGLAP refers to the inventors of the
perturbative QCD evolution of parton scattering with the “running” strong coupling
constant α s (Q 2 ), Dokshitzer, Gribov, Levine, Altarelli and Parisi. On the other
hand, mid-rapidity bulk hadron production at the upcoming CERN LHC facility
(
√
s = 14 TeV for pp, and 5.5 TeV for A+A), with typical Q 2 ≤ 5 GeV 2 at
x ≤ 10 −3 , will present a clear case for QCD saturation physics, as formulated
e.g. in the “Color Glass Condensate (CGC)” formalism developed by McLerran,
Venugopalan and collaborators [64, 65, 75, 77]. This model develops a classical
gluon field theory for the limiting case of a high areal occupation number density,
i.e. for the conceivable limit of the situation depicted in Fig. 7.14 (right hand panel)
where the amalgamating small x gluons would overlap completely, within any
finite resolution area at modest Q 2 . Classical field theory captures, by construction,
the effects of color charge coherence, absent in DGLAP parton cascade evolution
theories [75]. This model appears to work well already at
√
s as “low” as at
R. Stock
thus sampling smaller x domains in Fig. 7.14 according to Eq. (7.9). It will further
increase in proceeding from hadronic to nuclear reaction partners A+A. Will it be
in proportion to A 4/3 ? We know from the previous sections (Sects. 7.2.2 and 7.2.3)
that this is not the case, the data indicating an increase with A 1.08 . This observation
is, in fact caused by the parton saturation effect, to which we turn now.
For given transverse resolution Q 2 and increasing 1/x the parton density of
Fig. 7.14 becomes so large that one cannot neglect their mutual interactions any
longer. One expects such interactions to produce “shadowing”, a decrease of
the scattering cross section relative to incoherent independent scattering [70, 71].
As an effect of such shadowed interactions there occurs [75] a saturation [61–
65, 70, 71, 75] of the cross section at each given Q 2 , slowing the increase with 1/x
to become logarithmic once 1/x exceeds a certain critical value x s (Q 2 ). Conversely,
for fixed x, saturation occurs for transverse momenta below some critical Q 2 (x),
Q
2
s (x) = α s N c
1
πR 2
dN
dy
(7.11)
where dN/dy is the x-dependent gluon density (at y = y proj −ln(1/x)). Q 2
s is called
the saturation scale. In Eq. (7.11) πR 2 is the hadron area (in transverse projection),
and α s N c is the color charge squared of a single gluon. More intuitively, Q 2
s (x)
defines an inversely proportional resolution area F s (x) and at each x we have to
choose F s (x) such that the ratio of total area πR 2 to F s (x) (the number of resolved
areal pixels) equals the number of single gluon charge sources featured by the total
hadron area. As a consequence the saturation scale Q 2
s (x) defines a critical areal
resolution, with two different types of QCD scattering theory defined, at each x, for
Q 2 > Q 2
s and Q 2 < Q 2
s , respectively [62, 65, 75].
As one expects a soft transition between such theories, to occur along the
transition line implied by Q 2
s (x), the two types of QCD scattering are best studied
with processes featuring typical Q 2 well above, or below Q 2
s (x). Jet production at
√
s ≥ 200 GeV in pp or AA collisions with typical Q 2 above about 10 3 GeV 2 ,
clearly falls into the former class, to be described e.g. by QCD DGLAP evolution
of partonic showers [76]. The acronym DGLAP refers to the inventors of the
perturbative QCD evolution of parton scattering with the “running” strong coupling
constant α s (Q 2 ), Dokshitzer, Gribov, Levine, Altarelli and Parisi. On the other
hand, mid-rapidity bulk hadron production at the upcoming CERN LHC facility
(
√
s = 14 TeV for pp, and 5.5 TeV for A+A), with typical Q 2 ≤ 5 GeV 2 at
x ≤ 10 −3 , will present a clear case for QCD saturation physics, as formulated
e.g. in the “Color Glass Condensate (CGC)” formalism developed by McLerran,
Venugopalan and collaborators [64, 65, 75, 77]. This model develops a classical
gluon field theory for the limiting case of a high areal occupation number density,
i.e. for the conceivable limit of the situation depicted in Fig. 7.14 (right hand panel)
where the amalgamating small x gluons would overlap completely, within any
finite resolution area at modest Q 2 . Classical field theory captures, by construction,
the effects of color charge coherence, absent in DGLAP parton cascade evolution
theories [75]. This model appears to work well already at
√
s as “low” as at