1. Forward particle production in the presence of saturation
Cyrille Marquet
Columbia University

2. Outline
Saturation and the Color Glass Condensate the BK equation and the unintegrated gluon distribution
Forward particle production in pA collisions single particle production and the success of the CGC
Some predictions for the LHC in pp, pA and AA Mueller-Navelet jets in pp azimuthal correlations in pA particle multiplicity in AA

3. Saturation and the Color Glass Condensate

4. The saturation phenomenon
gluon recombination in the hadronic wave function
gluon density per unit area
it grows with decreasing x
recombination cross-section
recombinations important when
gluon kinematics
this regime is non-linear
yet weakly coupled
the saturation regime: for with
the idea of the CGC is to take into account this effect via strong classical fields
McLerran and Venugopalan (1994)
the CGC: an effective theory to describe the saturation regime
lifetime of the fluctuations
in the wave function ~
high-x partons ≡ static sources
low-x partons ≡ dynamical fields 

5. Scattering off the CGC this is described by Wilson lines
scattering of a quark:
dependence kept implicit in the following
in the CGC framework, any cross-section is determined by colorless combinations of
Wilson lines , averaged over the CGC wave function
x : quark space transverse coordinate
y : antiquark space transverse coordinate
the dipole scattering amplitude:
this is the most common average
for instance it determines deep inelastic scattering
the 2-point function or dipole amplitude
for 2-particle correlations
more complicated correlators
for instance

6. Evolution of the wave function
the JIMWLK equation
Jalilian-Marian, Iancu, McLerran, Weigert, Leonidov, Kovner
the energy evolution of cross-sections is encoded in the evolution of
this wave function is mainly non-perturbative, but its evolution is known
 Balitsky hierarchy for Wilson lines correlators
sums both and
the BK equation is a closed equation for obtained by assuming
robust only for impact-parameter independent solutions
the BK equation
r = dipole size
the unintegrated gluon distribution 

7. When is saturation relevant ?
in processes that are sensitive to the small-x part of the hadron wavefunction
deep inelastic scattering at small xBj :
particle production at forward rapidities y :
at HERA, xBj ~10-4 for Q² = 10 GeV²
in DIS small x corresponds to high energy
saturation relevant for inclusive,
diffractive, exclusive events
at RHIC, x2 ~10-4 for pT ² = 10 GeV²
pT , y
in particle production, small x corresponds
to high energy and forward rapidities
saturation relevant for the production of
jets, pions, heavy flavors, photons

8. Forward particle production in pA collisions

9. Forward particle production
forward rapidities probe small values of x
kT , y
transverse momentum kT, rapidity y > 0
values of x probed in the process:
the large-x hadron should be described by
standard leading-twist parton distributions
the small-x hadron/nucleus should be
described by CGC-averaged correlators
the cross-section:
single gluon production
probes only the unintegrated
gluon distribution (2-point function)

10. RHIC vs LHC
typical values of x being probed at forward rapidities (y~3) xA xp xd
RHIC
deuteron dominated by valence quarks
nucleus dominated by early CGC evolution
LHC
the proton description should include both quarks and gluons
on the nucleus side, the CGC
picture would be better tested
RHIC
LHC
if the emitted particle is a quark, involves
if the emitted particle is a gluon, involves
how the CGC is being probed

11. Running coupling corrections
running coupling corrections to the BK equation
taken into account by the substitution
Kovchegov
Weigert
Balitsky
consequences
similar to those first obtained by the simpler substitution
running coupling corrections slow down the increase of Qs with energy
also confirmed by numerical simulations, however
this asymptotic regime is reached for larger rapidities

12. The KKT parametrization
build to be used as an unintegrated gluon distribution
Kovchegov, Kharzeev and Tuchin (2004)
the idea is to play with the saturation exponent
the DHJ version
the BUW version
KKT modified to feature exact geometric scaling
Dumitru, Hayashigaki and Jalilian-Marian (2006)
Boer, Utermann and Wessels (2008)
in practice is always replaced by before the Fourier transformation
KKT modified to better account for geometric scaling violations

13. RdA and forward pion spectrum
the suppression of RdA was predicted
xA decreases
(y increases)
in the absence of nuclear
effects, meaning if the gluons in the
nucleus interact incoherently like in A protons
first comparison to data
RdA
Kharzeev, Kovchegov and Tuchin (2004)
qualitative agreement
with KKT parametrization

14. What about the large-x hadron?
getting a quantitative agreement requires correct treatment
Dumitru, Hayashigaki and Jalilian-Marian (2006)
for the pT – spectrum
with the DHJ model
shows the importance of both
evolutions: xA (CGC) and xd (DGLAP)
shows the dominance
of the valence quarks
it has been proposed as an alternative explanation
pA collisions at the LHC would answer that
suppression of RdA due to large-x effects?
both initial particles should not be described by a CGC, only the small-x hadron

15. Some predictions for the LHC

16. Mueller-Navelet jets in pp
Mueller and Navelet (1994)
moderate values of x1, x2, typically 0.05
k1, k2 >> QCD  collinear factorization of
large rapidity interval Δη ~ 8
pQCD: need ressumation of
powers of αS Δη ~ 1 in the
partonic cross-section gg → JXJ
azimuthal correlation predictions for
future measurements at CDF and LHC
C.M. and Royon, Sabio-Vera and Schwenssen (2007)
NLL-BFKL studies
Iancu, Kugeratski and Triantafyllopoulos (2008)
geometric scaling predictions
for ordered transverse momenta

17. 2-particle correlations in pA
inclusive two-particle production
at forward rapidities in order to probe small x
final state :
probes 2-, 4- and 6- point functions
one can test more information about the CGC compared to single particle production
as k2 decreases, it gets closer to QS and the
correlation in azimuthal angle is suppressed
some results for azimuthal correlations
obtained by solving BK, not from model
k2 is varied from 1.5 to 3 GeV
C.M. (2007)

18. Total multiplicity in AA
Albacete (2007)
predictions including running coupling
the extrapolation from RHIC to LHC
is driven by the small-x evolution
yellow band: uncertainties due to the
starting point of the small-x evolution
and the initial saturation scale
caveat: kT factorization is assumed
day-1 measurement
~ 1400 charged particles is a
robust prediction, if one gets
<1000 or >2500, this rules out the CGC

19. Conclusions
Forward particle production in d+Au collisions - the suppressed production at forward rapidities was predicted - there is a quantitative agreement with CGC predictions  this is often claimed as evidence for the CGC picture
Something we learned from RHIC - in d+Au, both p and A should not be described by a CGC - the proton pdf is important, uncertainties should be minimal
What observables should be looked at next ? - we only tested limited information about the CGC: 2-point function ~ gluon density - correlations should be investigated, this will be done at RHIC
What theorists are looking at now ? - predictions for LHC, A+A collisions, NLO corrections…