1. Forward correlations and the ridge - theory
Cyrille Marquet
Theory Division, CERN

2. Outline
Di-hadron correlations, p+p vs d+Au collisions - central/central rapidities : nuclear effects are small - forward/central rapidities: high-x nuclear effects: pT-broadening - forward/forward rapidities : low-x nuclear effects: saturation
Long-range rapidity correlations, A+A vs p+p collisions - A+A collisions: radial flow turns the early-time spacial correlations into a ridge - p+p collisions: in the absence of flow, the ridge reflects the actual momentum correlations of the early times

3. Di-hadron correlations, p+p vs d+Au collisions

4. The hadron wavefunction in QCD
x : parton longitudinal momentum fraction
kT : parton transverse momentum
the distribution of partons
as a function of x and kT :
QCD linear evolutions:
DGLAP evolution to larger kT (and a more dilute hadron)
BFKL evolution to smaller x (and denser hadron)
dilute/dense separation characterized by the saturation scale Qs(x)
QCD non-linear evolution: meaning
recombination cross-section
gluon density per unit area
it grows with decreasing x
recombinations important when
the saturation regime: for with
this regime is non-linear
yet weakly coupled

5. Di-hadron final-state kinematics
scanning the wave-functions
xp ~ xA < 1
central rapidities probe moderate x
forward/central doesn’t probe much smaller x
xp ~ 1, xA < 1
xp increases xA ~ unchanged
forward rapidities probe small x
xp ~ 1, xA << 1
xp ~ unchanged xA decreases

6. Dijets in standard pQCD
in pQCD calculations based on collinear factorization, dijets are back-to-back
this is supported by Tevatron
data with high pT’s
transverse view ~p
probing QCD/pT <<1
power corrections
are negligible
peak narrower with higher pT

7. pT broadening at large x
with lower transverse momenta, multiple scatterings become important
probing pT not much higher than QCD
higher twists are important, especially with nuclei
Qiu and Vitev (2006)
xA not small > 0.01
a Gaussian model with Away ~
also Kharzeev, Levin, McLerran (2005) q ^

8. Forward/central data
STAR (2006)
qualitative agreement with data, but quantitative ?
coincidence
probability
signal Df pp
Correlation Function
dAu 0-20%
1.0 < pTt < 2.0 GeV/c
for all plots
<pTa>=0.55 GeV/c
<pTa>=0.77 GeV/c
<pTa>=1.00 GeV/c

9. What changes at small x forward dijet production
at small x, multiple scatterings are characterized by QS (not QCD anymore) q ^
or intrinsic kT , or whatever is introduced to
account for higher twists in the OPE becomes ~ QS
in addition, when pT ~ QS and therefore multiple
scatterings are important, so is parton saturation
the OPE approach is not appropriate at small x, because all twists contribute equally
starting from the leading twist result and calculating the next term is not efficient
calculations with different
levels of approximations
Jalilian-Marian and Kovchegov (2005)
Baier, Kovner, Nardi and Wiedemann (2005)
Nikolaev, Schafer, Zakharov and Zoller (2005)
C.M. (2007)
forward dijet production
when x is large, we don’t know a better way,
but when x is small (such that QS >> QCD ), we do
the CGC can be used to resum the expansion QS/pT expansion

10. Evidence of monojets p+p d+Au central ~p Df=0 (near side) Df=p
(away side)
(rad) ~p
transverse view

11. Monojets in central d+Au
in central collisions where QS is the biggest
an offset is needed to account for the background
there is a very good agreement of the
saturation predictions with STAR data
Albacete and C.M. (2010) Tuchin (2010)
to calculate the near-side peak, one
needs di-pion fragmentation functions
the focus is on the away-side peak
where non-linearities have the biggest effect
suppressed away-side peak
standard (DGLAP-like) QCD calculations cannot reproduce this

12. About the CGC calculation
in the large-Nc limit, the cross section is obtained from
and
the 2-point function is fully constrained
by e+A DIS and d+Au single hadron data
in principle the 4-point function should be obtained from an evolution equation (equivalent to JIMWLK + large Nc)
Jalilian-Marian and Kovchegov (2006)
Dumitru and Jalilian-Marian (2010)
even though the knowledge of S(2) is enough to predict the
forward dihadron spectrum, there is no kT factorization:
the cross section is a non-linear function of the gluon distribution
in practice one uses an approximation that allows to express S(4) as a (non-linear) function of S(2)
C.M. (2007)
this approximation misses some leading-Nc terms
Dominguez, Xiao and Yuan (2010)
they may become dominant when pT >> Qs

13. Long-range rapidity correlations, A+A vs p+p collisions

14. Collision of two CGCs
the initial condition for the time evolution in heavy-ion collisions
before the collision:
the distributions of ρ contain the small-x
evolution of the nuclear wave functions r1 r2
the gluon field is a complicated function of the two classical color sources
after the collision
the field decays, once it is no longer strong (classical)
a particle description is again appropriate
hard modes decay faster than soft modes (τ ~ 1/pT)

15. General strategy solve Yang-Mills equations
this is done numerically (it could be
done analytically in the p+A case)
express observables in terms of the field
determine , in general a
non-linear function of the sources
examples later : single- and double-inclusive gluon production
perform the CGC averages
rapidity factorization proved recently at
leading-order for (multi-)gluon production
Gelis, Lappi and Venugopalan (2008)

16. Probing features of the Glasma
features of the Glasma fields
in general, the following phases (QGP, …) destroy the information coming from the glasma
HIC are not great probes of parton saturation
nevertheless, some observables are still sensitive to the physics of the early stages
long-range rapidity correlations

17. Particle production in the glasma
single gluon production
Krasnitz and Venugopalan (1998)
strength of the color charge of the projectile
p+A
A+A
the target is always dense
in A+A collisions, disconnected diagrams
dominate multi-gluon production
strength of the diagrams
the exact implementation of the
small-x evolution is still not achieved
as in the single-particle case
Gelis, Lappi and Venugopalan (2008)
two-gluon production
easily obtained from the single-gluon result

18. The ridge in A+A collisions
the ridge is qualitatively understood within the CGC framework
the Δϕ collimation is due to the radial flow
if it is very extended in rapidity,
the ridge is a manifestation of early-time phenomena:
Dusling, Gelis, Lappi and Venugopalan (2009)
STAR data (2009)
quantitative calculations are underway

19. The ridge in p+p collisions
in the absence of flow, the ridge reflect the actual momentum correlations of the early times
Dumitru, Dusling, Gélis, Jalilian-Marian, Lappi and Venugopalan (2010)
CMS data (2010)
no ridge at low pT, there can’t be much flow
ridge with pT ~ Qs
diagram which gives the Δϕ dependence
at the moment, the agreement is only qualitative
(some leading-Nc diagrams are notoriously difficult to include)

20. Conclusions CGC and forward particle production in d+Au collisions
the magnitude of the away-side peak,
compared to that of the near-side peak,
decreases from p+p to d+Au central
this happens at forward rapidities,
but at central rapidities, the p+p and
d+Au signal are almost identical
 the suppression of the away-side peak occurs when QS increases
this was predicted, in some cases quantitatively with no parameter adjustments
so far all di-hadron correlations measured in d+Au vs. p+p are consistent with saturation
CGC and the A+A or p+p ridges
the features of the data are qualitatively consistent with the CGC expectations
but at the moment, there is nothing quantitative