An Introduction to Particle Production in High Energy

Nuclear Collisions

Jamal Jalilian-MarianInstitute for Nuclear TheoryUniversity 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)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) Flavor: blind Color: 8

gs gs

the coupling constant:

perturbative QCD: expansion in the coupling constant

running of the coupling constant

pQCD in pp Collisions Collinear factorization: separation of long and short

distances

distribution functions

fragmentation function

hard scattering

Bjorken:

Parton model

Parton constituents of proton are “quasi-free” on interaction time scale 1/Q << 1/ (interaction time scale between partons)

Fraction of hadron momentum carried by a parton = xF

but xBj=Q2/S fixed

distribution functions depend only on xBj

Feynman:

Bj scaling Dokshitzer-Gribov-Lipatov-Altarelli-Parisi

evolution of distribution functions

increasing

But… the phase space density decreases-the proton becomes more dilute

Resolving the hadron -DGLAP evolution

RHIC, LHCHow about scattering of nuclei?

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

Regge Gribov

QCD in the Regge-Gribov limit

DIS in the Regge-Gribov limit: evolution with x

Balitsky-Fadin-Kuraev-Lipatov

Radiated gluons have the same size (1/Q2) - the number of partons increase due to the increased longitudinal phase space

Resolving the nucleus/hadron:

Regge-Gribov limit

Physics of strong fields in QCD, multi-particle production- possibly discover novel universal properties of theory in this limit

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.kt factorization:

Incoming partons have kt

Un-integrated distributions: are they universal?Factorization theorems are proven to Leading Order+ in s

Particle production in the Regge-Gribov limit

Momentum Resolution Q2

Energy (rapidity)

QCD

Nucleus

QCD Bremsstrahlung

Non-linear evolution:Gluon recombinationGribov,Levin,Ryskin

Competition between “attractive” bremsstrahlungand “repulsive” recombination effects

Maximal phase space density =>

saturated for

Mechanism for parton saturationMechanism for parton saturation

Random sources evolving on time scales much larger than natural time scales-very

similar to spin glasses

Typical momentum of gluons is

Bosons with large occupation # ~ - form a condensate

Gluons are colored

Nucleus/Hadron at high energy is a Color Glass Condensate

The nuclear “oomph” factorThe nuclear “oomph” factor

~ 0.3

Generating functional:

Gauge invariant weight functional describing distribution of the sources

Scale separating sources and fields

where

To lowest order,

The effective actionThe effective action

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

z

Random Electric & Magnetic fields in the plane of the fast moving nucleus

QCD at High Energy: Wilsonian RG

Fields Sources

Integrate out small fluctuations => Increase color charge of sources

(s Log 1/x )

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.

Color charge grows due to inclusion of fields into hard source with decreasing x:

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.

Because of strong fields All insertions are O(1)

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 aTIFF (LZW) decompressor

are needed to see this picture.

The The JIMWLKJIMWLK (functional RG) equation (functional RG) equationJalilian-Marian,Iancu,McLerran,Weigert,Leonidov,Kovner

the 2-point function Tr [1 - U+ (xt) U (yt)] (probability for scattering of a quark-anti-quark dipole on a target)

Can solve JIMWLK in two limits: I) Strong field: exact scaling - f (Q2/Q2

s) for Q < Qs II) Weak field: perturbative QCD

Rummukainen,Weigert

JIMWLKJIMWLK equations describe evolution of all

N-point correlation functions with energy

How does Q_s behave as function of Y?

Fixed coupling LO BFKL: LO BFKL+ running coupling:Re-summed NLO BFKL + CGC:

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.Triantafyllopolous

Very close toHERA result!

How can we probe all this?How can we probe all this?

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

Signatures of CGC at RHICSignatures of CGC at RHIC

mid rapidity(y = 0, = 900) --> 0

forwardrapidity

y = 0: x1 = x2 = 10-2

y ~ 4: x1~ 0.55, x2~10-4 (RHIC: for pt

2 = 4 GeV2)

Kinematics

Qs2 (y=0) = 2 GeV2

Qs2 (y=4) = 2 e0.3 y = 6.65 GeV2

RHIC (S = 200 GeV): S = 200 GeV): y ~ 5.3LHC (S = 5.5 TeV): S = 5.5 TeV): y ~ 8.6LHC (S = 14 TeV): S = 14 TeV): y ~ 9.6

y

beam remnants

two orders of magnitude evolution in x

Classical (multiple elastic scattering):pt >> Qs : enhancement

RpA = 1 + (Qs2/pt

2) log pt2/2 + …

RpA (pt ~ Qs) ~ log A

position and height of enhancement are increasing with centrality

CGC: qualitative expectationsCGC: qualitative expectations

Gelis,Jalilian-Marian

Quantum evolution in x: essential as we go to forward rapiditycan show analytically the peak disappears as energy/rapidity growsand levels off at RpA ~ A-1/6 Kharzeev,Kovchegov,Tuchin

suppression

CGC vs. RHICCGC vs. RHIC

enhancement

BRAHMS

=

Consider scattering of a quark from the classical field A if the field is strong, we need to include multiple scattering

strong field

Weak field:single gluon exchange

similar for gluon scattering

Single inclusive hadron production: s corrections

+

integration over final state momenta: collinear divergence collinear divergence

22 22 22

s Pg/q Log Q2 dg A --> g X

Single Hadron Production in Single Hadron Production in pApA

NNFF, N, NAA are dipoles in fundamental and adjoint are dipoles in fundamental and adjoint representation and satisfy the representation and satisfy the JIMWLKJIMWLK evolution equation evolution equation

Dumitru, Hayashigaki, Jalilian-Marian NPA765 (2006) 464

2 ---> 1 Kinematics for dA at RHIC2 ---> 1 Kinematics for dA at RHIC

Application to dA at RHICApplication 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)

pptt spectra at y=0, 3.2 and y=4 spectra at y=0, 3.2 and y=4

Application to dA at RHICApplication to dA at RHIC

PredictionsPredictions for dA at RHIC for dA at RHICDumitru, Hayashigaki, Jalilian-Marian NPA765 (2006) 464

J. Adams for J. Adams for STARSTAR , nucl-ex/0602011 submitted to PRL, nucl-ex/0602011 submitted to PRL

2 ---> 1 Kinematics for dA at RHIC2 ---> 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

Jalilian-Marian, NPA

Photon + Hadron: isolation cut

SLAC

RHICHERA

eRHIC

LHC

R~1fm

Partondensity

Current and future colliders

11/14/0411/14/04 UoA - Apostolos D. PanagiotouUoA - Apostolos D. Panagiotou 44

Large Range of Hermetic Coverageη∼1.8,x~upto10-7nQ>1GeV

UniueForwrCpbility

CMS - Detector CoverageCMS - Detector Coverage

HCAL

HCASTORAL

kinematics: kinematics: forward RHIC forward RHIC ~~ mid rapidity mid rapidity LHCLHC

From pA to DIS: crossing symmetry

+

+

+DIS:

pA:

CGC degrees of freedom: dipolesGelis,Jalilian-MarianPRD67 (2003) 074019

Deep Inelastic ScatteringDeep Inelastic Scattering

HERA eRHIC

Dumitru,Hayashigaki,Jalilian-Marian, in progress

structure function: F2

Deep Inelastic ScatteringDeep Inelastic Scattering two particle production

Jalilian-Marian,Kovchegov PRD70 (2004) 114017

Exploring QCD phase space by high energy nuclei

“Higher twists”Leading twist shadowing

SummarySummary

A

BACK UP SLIDES

parameterization of the dipole cross section

Parameterizations of anomalous dimension

2 ---> 1 Kinematics for dA at RHIC2 ---> 1 Kinematics for dA at RHIC

2 ---> 1 Kinematics for dA at 2 ---> 1 Kinematics for dA at RHICRHIC

P p ql

k

K

= gluon phase space density =

Jalilian-Marian,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 equationBalitsky-Kovchegov

DIS:

Dipole amplitude N satisfies BFKL kernel

DIS:

IN CGC:

BK: Evolution eqn. for the dipole cross-section

From saturation condition,

1

1/2

Rapidity:

partonic cross sections

calculable in pQCD

gs+

gs

systematic expansion in the coupling constant

process dependent

collinear factorization

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.

Incoherence: independent probabilities

Incoming partons have kt=0Quark and gluon distributions are universal, evaluated at hard scaleFactorization theorems are proven to all order in s

Kinematic Invariants:Center of mass energy squared

Momentum resolution squared

QED e p (A) ---> e X

QCD:Structure Functions F1 , F2

parton distribution functions non-perturbative but process independent

DIS inclusive cross-section:

Structure functionsRutherford cross-section

CGC at HERA (ep: S = 310 GeV)

Structure Functionsdiff/tot energy dependence Geometric Scaling r, J/y production, ….

depends on kinematics!

Bjorken/Feynman or Regge/Gribov?