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) Flavor: blind Color: 8 gsgs gsgs 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 = x F but x Bj =Q 2 /S fixed distribution functions depend only on x Bj  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, LHC How 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

ReggeGribov 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/Q 2 ) - 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

k t factorization: Incoming partons have k t Un-integrated distributions: are they universal? Factorization theorems are proven to Leading Order + in  s Particle production in the Regge-Gribov limit

Momentum Resolution Q 2 Energy (rapidity)   QCD

Nucleus QCD Bremsstrahlung Non-linear evolution: Gluon recombination Gribov,Levin,Ryskin

Competition between “attractive” bremsstrahlung and “repulsive” recombination effects Maximal phase space density => saturated for Mechanism 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” factor  ~ 0.3

Generating functional: Gauge invariant weight functional describing distribution of the sources Scale separating sources and fields wher e To lowest order, The 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 FieldsSources Integrate out small fluctuations => Increase color charge of sources (  s Log 1/x )

Color charge grows due to inclusion of fields into hard source with decreasing x: 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 The JIMWLK (functional RG) equation Jalilian-Marian,Iancu,McLerran,Weigert,Leonidov,Kovner

the 2-point function Tr [1 - U + (x t ) U (y t )] (probability for scattering of a quark-anti-quark dipole on a target) Can solve JIMWLK in two limits: I) Strong field: exact scaling - f (Q 2 /Q 2 s ) for Q < Q s II) Weak field: perturbative QCD Rummukainen,Weigert JIMWLK JIMWLK 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: Triantafyllopolous Very close to HERA result!

How can we probe all this?

Multiplicities (dominated by p t < Q s ): energy, rapidity, centrality dependence  Single particle production: hadrons, photons, dileptons rapidity, p t, centrality dependence i)Fixed p t : vary rapidity (evolution in x) ii)Fixed rapidity: vary p t (transition from dense to dilute)  Two particle production: back to back correlations Signatures of CGC at RHIC

mid rapidity (y = 0,  = 90 0 )  --> 0 forward rapidity y = 0: x 1 = x 2 = y ~ 4: x 1 ~ 0.55, x 2 ~10 -4 (RHIC: for p t 2 = 4 GeV 2 ) Kinematics Q s 2 (y=0) = 2 GeV 2 Q s 2 (y=4) = 2 e 0.3 y = 6.65 GeV 2  S = 200 GeV): RHIC (  S = 200 GeV):  y ~ 5.3  S = 5.5 TeV): LHC (  S = 5.5 TeV):  y ~ 8.6  S = 14 TeV): LHC (  S = 14 TeV):  y ~ 9.6  y beam remnants two orders of magnitude evolution in x

Classical (multiple elastic scattering): p t >> Q s : enhancement R pA = 1 + (Q s 2 /p t 2 ) log p t 2 /  2 + … R pA (p t ~ Q s ) ~ log A position and height of enhancement are increasing with centrality CGC: qualitative expectations Gelis,Jalilian-Marian 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 R pA ~ A -1/6 Kharzeev,Kovchegov,Tuchin

suppression CGC 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 + collinear divergence integration over final state momenta: collinear divergence  s P g/q Log Q 2 d  g A --> g X

Single Hadron Production in pA N F, N A 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  f q/p, f g/p from HERA, D h/q,g from e + e -  Ignore deuteron shadowing  Dipole cross sections: N F, N A  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)  p t spectra at y=0, 3.2 and y=4

Application to dA at RHIC

Predictions for dA at RHIC Dumitru, Hayashigaki, Jalilian-Marian NPA765 (2006) 464 J. Adams for STAR, nucl-ex/ 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/

Photon + Hadron production Jalilian-Marian, NPA

Photon + Hadron: isolation cut

SLAC RHIC HERA eRHIC LHC R ~1fm Parton density Current and future colliders

kinematics: forward RHIC ~ mid rapidity LHC

From pA to DIS: crossing symmetry DIS: pA : CGC degrees of freedom: dipoles Gelis,Jalilian-Marian PRD67 (2003)

Deep Inelastic Scattering HERAeRHIC Dumitru,Hayashigaki,Jalilian-Marian, in progress structure function: F 2

Deep Inelastic Scattering two particle production Jalilian-Marian,Kovchegov PRD70 (2004)

Exploring QCD phase space by high energy nuclei “Higher twists” Leading twist shadowingSummary A

BACK UP SLIDES

parameterization of the dipole cross section

Parameterizations of anomalous dimension

2 ---> 1 Kinematics for dA at RHIC

P p q l 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 equation Balitsky-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 Rapidit y:

partonic cross sections calculable in pQCD gsgs + gsgs systematic expansion in the coupling constant process dependent

collinear factorization Incoherence: independent probabilities Incoming partons have k t =0 Quark and gluon distributions are universal, evaluated at hard scale Factorization 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 F 1, F 2 parton distribution functions non-perturbative but process independent

DIS inclusive cross-section: Structure functions Rutherford cross-section

CGC at HERA (ep:  S = 310 GeV) Structure Functions  diff /  tot energy dependence Geometric Scaling , J/  production, ….

depends on kinematics! Bjorken/Feynman or Regge/Gribov?