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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
2forward
, 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!