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An Introduction to Particle
Production in High Energy
Nuclear Collisions
Jamal Jalilian-Marian
Institute for Nuclear Theory
University of Washington
Outline
 Perturbative QCD (pQCD)
 Proton-proton collisions
 Collinear factorization
 Distribution functions
 QCD at high energy/large A
 Color Glass Condensate (CGC)
 Proton (deuteron)-nucleus collisions
 Particle production
 Signatures of CGC at RHIC
 Outlook
Quantum ChromoDynamics (QCD)
Theory of strong interactions between quarks and gluons (partons)
Quarks: fermions (spin 1/2)
Flavor: up, down, strange,
charm, bottom, top
Color: 3 (up up up)
Gluons: bosons (spin 1)
gs
the coupling constant:
Flavor: blind
Color: 8
gs
running of the coupling constant
perturbative QCD: expansion in the coupling constant
pQCD in pp Collisions
Collinear factorization: separation of long and short distances
fragmentation
function
distribution
functions
hard
scattering
Parton model
 Bjorken:
but xBj=Q2/S fixed
distribution functions
depend only on xBj
 Feynman:
Parton constituents of proton
are “quasi-free” on interaction
time scale 1/Q << 1/L (interaction
time scale between partons)
Fraction of hadron momentum carried by a parton = xF
evolution of
distribution functions
Bj scaling
Dokshitzer-Gribov-Lipatov-Altarelli-Pari
Resolving the hadron
-DGLAP evolution
increasing
But… the phase space density decreases
-the proton becomes more dilute
How about scattering of nuclei?
RHIC, LHC
I) modification of initial state: “nuclear shadowing”
II) modification of hard scattering: multiple scattering
III) modification of fragmentation functions
modification of the nuclear structure functions
QCD in the Regge-Gribov limit
Regge
Gribov
DIS in the Regge-Gribov limit: evolution with x
Balitsky-Fadin-Kuraev-Lipato
Resolving the nucleus/hadron:
Regge-Gribov limit
Radiated gluons have the
same size (1/Q2) - the number
of partons increase due to the
increased longitudinal phase space
Physics of strong fields in QCD, multi-particle productionpossibly discover novel universal properties of theory in this limit
Particle production in the Regge-Gribov limit
kt factorization:
QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.
Incoming partons have kt
Un-integrated distributions: are they universal?
Factorization theorems are proven to Leading Order+ in as
Energy
(rapidity)
L2QCD
Momentum Resolution Q2
Non-linear evolution:
Gluon recombination
QCD
Bremsstrahlung
Gribov,Levin,Ryskin
Nucleus
Mechanism for parton saturation
Competition between “attractive” bremsstrahlun
and “repulsive” recombination effects
Maximal phase space density =>
saturated for
Nucleus/Hadron at high energy is a Color Glass Condensate
 Gluons are colored
 Random sources evolving on time scales much larger
than natural time scales-very similar to spin glasses
 Bosons with large occupation # ~
 Typical momentum of gluons is
- form a condensate
The nuclear “oomph” factor
d ~ 0.3
The effective action
Generating functional:
Scale separating
sources and fields
Gauge invariant weight functional describing distribution of the
sources
wher
e
To lowest order,
McLerran,Venugopalan;
Jalilian-Marian,Kovner,Leonidov,Weigert;
Fukushima
The classical field of the nucleus at high energies
Saddle point of effective action-> Yang-Mills equations
Solutions are non-Abelian
Weizsäcker-Williams fields
Careful solution requires smearing in
Random Electric & Magnetic fields in the plane of
the fast moving nucleus
z
QCD at High Energy: Wilsonian RG
( as Log 1/x )
Fields
Sources
Integrate out small fluctuations => Increase color charge of sour
Color charge grows due to inclusion of fields into hard
source with decreasing x:
Because of strong fields
All insertions are O(1)
QuickTime™ and a
TIFF (LZW) decompressor
QuickTime™ and a are needed to see this picture.
TIFF (LZW) decompressor
are needed to see this picture.
obeys a non-linear Wilson renormalization group
equation
At each step in the evolution, compute 1-point and 2-point
functions in the background field
QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.
The JIMWLK (functional RG) equation
Jalilian-Marian,Iancu,McLerran,Weigert,Leonidov,Kovner
JIMWLK equations describe
evolution of all
N-point correlation functions with
the 2-point function energy
Tr [1 - U+ (xt) U (yt)]
(probability for scattering of a quark-anti-quark dipole on a target)
Rummukainen,Weigert
Can solve JIMWLK in two limits:
I) Strong field: exact scaling - f (Q2/Q2s) for Q < Qs
II) Weak field: perturbative QCD
How does Q_s behave as function of Y?
Fixed coupling LO BFKL:
LO BFKL+ running coupling:
Re-summed NLO BFKL + CGC:
Triantafyllopolous
Very close to
HERA result!
QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.
How can we probe all this?
Signatures of CGC at RHIC
 Multiplicities (dominated by pt < Qs):
energy, rapidity, centrality dependence
 Single particle production: hadrons, photons, dileptons
rapidity, pt, centrality dependence
i) Fixed pt: vary rapidity (evolution in x)
ii) Fixed rapidity: vary pt (transition from dense to dilute)
Two particle production:
back to back correlations
RHIC (S = 200 GeV):  y ~ 5.3
LHC (S = 5.5 TeV):  y ~ 8.6
LHC (S = 14 TeV):  y ~ 9.6
beam
remnants
y
mid rapidity
(y = 0,  = 900)
forward
rapidity
Kinematics
 --> 0
y = 0: x1 = x2 = 10-2
y ~ 4: x1~ 0.55, x2~10-4
(RHIC: for pt2 = 4 GeV2)
Qs2 (y=0) = 2 GeV2
Qs2 (y=4) = 2 e0.3 y = 6.65 GeV2
two orders of magnitude evolution in x
CGC: qualitative expectations
Classical (multiple elastic scattering):
pt >> Qs : enhancement
RpA = 1 + (Qs2/pt2) log pt2/L2 + …
RpA (pt ~ Qs) ~ log A
Gelis,Jalilian-Marian
position and height of enhancement are increasing with centrality
Quantum evolution in x: essential as we go to forward rapidity
can show analytically the peak disappears as energy/rapidity grows
and levels off at RpA ~ A-1/6
Kharzeev,Kovchegov,Tuchin
CGC vs. RHIC
enhancement
suppression
BRAHMS
Consider scattering of a quark from the classical field Am
if the field is strong, we need to include multiple scattering
Weak field:
single gluon
exchange
=
strong field
similar for gluon scattering
Single inclusive hadron production: as corrections
+
integration over final state momenta: collinear divergence
2
2
as Pg/q Log Q2
2
dsg A --> g X
Single Hadron Production in pA
NF, NA are dipoles in fundamental and adjoint
representation and satisfy the JIMWLK evolution equation
Dumitru, Hayashigaki, Jalilian-Marian NPA765 (2006) 464
2 ---> 1 Kinematics for dA at RHIC
Application to dA at RHIC
 Distribution/fragmentation functions
 fq/p, fg/p from HERA, Dh/q,g from e+ e Ignore deuteron shadowing
 Dipole cross sections: NF , NA
 Solution of JIMWLK evolution
equations
 Parameterizations
 IIM (fit to HERA data on protons)
 KKT (fit to RHIC data on dA)
 DHJ (fit to RHIC data on dA)
Application to dA at RHIC
Predictions for dA at RHIC
Dumitru, Hayashigaki, Jalilian-Marian NPA765 (2006) 464
J. Adams for STAR , nucl-ex/0602011 submitted to PRL
2 ---> 1 Kinematics for dA at RHIC
KKT
IIM vs. DHJ
Particle production in dA at RHIC
Dumitru, Hayashigaki, Jalilian-Marian hep-ph/0512129
Photon + Hadron production
Jalilian-Marian, NPA
Photon + Hadron: isolation cut
Jalilian-Marian, NPA
Current and future colliders
Parton
density
LHC
eRHIC
RHIC
HERA
SLAC
~1fm
R
CMS - Detector Coverage
H
CASTOR
A
L
HCAL
Large Range of Hermetic Coverage
kinematics:
~ mid
2forward
, x ~ up toRHIC
10 -7 and
Q 2 rapidity
> 1 GeV 2 LHC
Unique Forward Capability
11/14/04
UoA - Apostolos D. Panagiotou
4
From pA to DIS: crossing symmetry
+
pA:
DIS:
+
CGC degrees of freedom: dipoles
+
Gelis,Jalilian-Marian
PRD67 (2003) 074019
Deep Inelastic Scattering
structure function: F2
HERA
Dumitru,Hayashigaki,Jalilian-Marian, in progress
eRHIC
Deep Inelastic Scattering
two particle production
Jalilian-Marian,Kovchegov PRD70 (2004) 114017
Summary
Exploring QCD phase space by high energy nuclei
“Higher twists”
Leading
twist shadowing
A
BACK UP SLIDES
parameterization of the dipole cross section
Parameterizations of anomalous dimension
2 ---> 1 Kinematics for dA at RHIC
2 ---> 1 Kinematics for dA at RHIC
P
p
l
k
K
q
= gluon phase space
density =
JalilianMarian,Kovner,McLerran,Weigert
Particle production in dA at RHIC
Dumitru, Hayashigaki, Jalilian-Marian
pQCD in pp Collisions at RHIC
STAR
The hadron at high energies - III
Mean field solution of JIMWLK = B-K equation
Balitsky-Kovchegov
DIS:
Dipole amplitude N satisfies
BFKL kernel
DIS:
IN CGC:
BK:
Evolution eqn. for the dipole cross-section
Rapidit
y:
1
1/2
 From saturation condition,
partonic cross sections
calculable in pQCD
+
gs
gs
systematic expansion
in the coupling constant
process
dependent
collinear factorization
Incoherence: independent probabilities
QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.
Incoming partons have kt=0
Quark and gluon distributions are universal, evaluated at hard scale
Factorization theorems are proven to all order in as
parton distribution functions
non-perturbative but process independent
e p (A) ---> e X
QED
Kinematic Invariants:
Center of mass energy squared
Momentum resolution
squared
QCD:
Structure Functions F1 , F2
DIS inclusive cross-section:
Structure functions
Rutherford cross-section
CGC at HERA (ep: S = 310 GeV)
Structure Functions
sdiff/stot energy dependence
Geometric Scaling
, J/ production, ….
Bjorken/Feynman or Regge/Gribov?
depends on kinematics!