QCD Phenomenology and Heavy Ion Physics. Yuri Kovchegov The Ohio State University. Outline. We’ll describe application of Saturation/Color Glass Condensate physics to Heavy Ion Collisions, concentrating on: Multiplicity vs. Centrality and vs. Energy, dN/d η vs. rapidity η
The Ohio State University
We’ll describe application of Saturation/Color Glass
Condensate physics to Heavy Ion Collisions,
dN/dη vs. rapidity η
In Saturation/Color Glass Physics one has
The resulting gluon multiplicity is given by
since d2b ~ S ~ p R2 , with R the nuclear radius.
we get :
which is not a constant due to running of the coupling:
This simple reasoning
allowed D. Kharzeev
and E. Levin to fit
multiplicity as a function
Let’s try to use the same simple formula to check the
energy dependence of multiplicity. Start with
From saturation models of HERA DIS data we know that
Therefore we write
Using the known multiplicity at 130 GeV Kharzeev and Levin
predicted multiplicity at 200 GeV using the above model:
The result agreed nicely with the data:
To understand the rapidity dependence one has to make
a few more steps. Starting with factorization assumption
inspired by the production diagram,
and assuming a saturation/CGC form of
the unintegrated gluon distribution f:
Kharzeev and Levin obtained a successfull fit of the pseudo-rapidity distribution of charged particles in AA:
The value of the saturation
scale turned out to be
(see also Kharzeev & Nardi ’00, Kharzeev, Levin, Nardi ’01)
The same approach
works for pseudo-rapidity distribution of total charged multiplicity in dAu collisions:
(from Kharzeev, Levin, Nardi, hep-ph/0212316)
Baier, Mueller, Schiff, Son ‘00
Schiff, Son ‘02
instabilities. (Mrowczynski, Arnold, Lenaghan, Moore,
Romatschke, Strickland, Yaffe) However, it is not clear whether
instabilities would speed up the thermalization process and how
to interpret them diagrammatically .
Stronger than classical
field? Stronger than any
QCD gluon field?
It appears that
Let’s consider gluon production, it will have all the essential
features, and quark production could be done by analogy.
To find the gluon production
cross section in pA one
has to solve the same
for two sources – proton and
This classical field has been found by
Yu. K., A.H. Mueller in ‘98
The diagrams one has to resum are shown here: they resum
Yu. K., A.H. Mueller,
Classical gluon production: we
need to resum only the
multiple rescatterings of the
gluon on nucleons. Here’s one
of the graphs considered.
Yu. K., A.H. Mueller,
Resulting inclusive gluon production cross section is given by
With the gluon-gluon dipole-nucleus
forward scattering amplitude
To understand how the gluon production in pA is different from independent superposition of A proton-proton (pp) collisions one constructs the quantity
We can plot it for the quasi-classical
cross section calculated before (Y.K., A. M. ‘98):
Classical gluon production leads to Cronin effect!
Nucleus pushes gluons to higher transverse momentum!
(see also Kopeliovich et al, ’02; Baier et al, ’03; Accardi and Gyulassy, ‘03)
Cronin effect: one has to trust the
does take place one has to study the
behavior of RpA at large kT
(cf. Dumitru, Gelis, Jalilian-Marian,
quark production, ’02-’03):
Note the sign!
RpA approaches 1 from above at high pT there is an enhancement!
The position of the Cronin
maximum is given by
kT ~ QS~ A1/6
as QS2 ~ A1/3.
Using the formula above we see
that the height of the Cronin
RpA (kT=QS) ~ ln QS ~ ln A.
To understand the energy
dependence of particle
production in pA one needs to
include quantum evolution
resumming graphs like this one.
This resums powers of
a ln 1/x = a Y.
This has been done in Yu. K.,
K. Tuchin, hep-ph/0111362.
The rules accomplishing the inclusion of quantum corrections are
LO wave function
where the dipole-nucleus amplitude N is to be found from (Balitsky, Yu. K.)
Amazingly enough, gluon production cross section
reduces to kT –factorization expression (Yu. K., Tuchin, ‘01):
with the proton and nucleus “unintegrated
distributions” defined by
with NGp,A the amplitude of a GG dipole on a p or A.
Our analysis shows that as
energy/rapidity increases the
height of the Cronin peak
decreases. Cronin maximum
gets progressively lower and
off at roughly at
energy / rapidity
(Kharzeev, Levin, McLerran, ’02)
k / QS
D. Kharzeev, Yu. K., K. Tuchin, hep-ph/0307037; (see also numerical
simulations by Albacete, Armesto, Kovner, Salgado, Wiedemann,
hep-ph/0307179 and Baier, Kovner, Wiedemann hep-ph/0305265 v2.)
function of both energy and centrality.
Color Glass Condensate /
Saturation physics predictions
are in sharp contrast with other
The prediction presented here
uses a Glauber-like model for
dipole amplitude with energy
dependence in the exponent.
figure from I. Vitev, nucl-th/0302002,
see also a review by
M. Gyulassy, I. Vitev, X.-N. Wang, B.-W. Zhang, nucl-th/0302077
RCP – central
Most recent data from BRAHMS Collaboration nucl-ex/0403005
Our prediction of suppression was confirmed!
from D. Kharzeev, Yu. K., K. Tuchin, hep-ph/0405045, where we construct a
model based on above physics + add valence quark contribution
We can even make a prediction for LHC:
Dashed line is for mid-rapidity
pA run at LHC,
the solid line is for h=3.2
dAu at RHIC.
from D. Kharzeev, Yu. K., K. Tuchin, hep-ph/0405045
Saturation and small-x evolution effects may also deplete
back-to-back correlations of jets. Kharzeev, Levin and
McLerran came up with the model shown below (see also
Yu.K., Tuchin ’02) :
which leads to suppression of B2B
jets at mid-rapidity dAu (vs pp):
and at forward rapidity:
from Kharzeev, Levin,
Warning: only a model, for
exact analytical calculations
see J. Jalilian-Marian and
An interesting process to look at is when one jet is at forward
rapidity, while the other one is at mid-rapidity:
The evolution between the jets
makes the correlations disappear:
from Kharzeev, Levin, McLerran, hep-ph/0403271
(One has to solve 6 integral equations to get the answer.)
A general solution to BFKL equation can be written as
It turns out that the full solution of nonlinear evolution equation
N(z,y) is a function of a single variable, N=N(z QS(y)), with
(ii) In the extended geometric scaling region, where g≈1/2:
(Iancu, Itakura, McLerran ‘02)
Geometric scaling has been observed in DIS data by
Stasto, Golec-Biernat, Kwiecinski in ’00.
Here they plot the total
DIS cross section, which
is a function of 2 variables
- Q2 and x, as a function of just one variable:
High Energy or
kgeom = QS2 / QS0
Cronin effect and low-pT suppression
At very high momenta, pT >> kgeom, the gluon production is given by the
double logarithmic approximation, resumming powers of
Resulting produced particle multiplicity scales as
where y=ln(1/x) is rapidity and QS0 ~ A1/6 is the saturation scale of
McLerran-Venugopalan model. For pp collisions QS0 is replaced by L
as QS0 >> L.
RpA < 1 in Region I There is suppression in DLA region!
At somewhat lower but still large momenta, QS < kT < kgeom, the BFKL
evolution introduces anomalous dimension for gluon distributions:
Kharzeev, Levin, McLerran,
with BFKL g=1/2 (DLA g=1)
The resulting gluon production cross section scales as (we loose one power of QS)
For large enough nucleus RpA << 1 – high pT suppression!
How does energy dependence come into the game?
A more detailed analysis
gives the following ratio in
the extended geometric
scaling region – our region II:
RpA is also a decreasing function of energy,
leveling off to a constant RpA ~ A-1/6 at very high energy.
at high energy / rapidity.
(D. Kharzeev, Yu. K., K. Tuchin, hep-ph/0307037)
know the gluon distribution function of the nucleus at the saturation scale –
fA (kT = QS, y). For that we would have to solve nonlinear BK evolution
equation – a very difficult task.
which leads to
Levin, Tuchin ’99
Iancu, Itakura, McLerran, ‘02