* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download ppt - Cyclotron Institute
Wave packet wikipedia , lookup
Path integral formulation wikipedia , lookup
Cross section (physics) wikipedia , lookup
Photon polarization wikipedia , lookup
Renormalization wikipedia , lookup
Mathematical formulation of the Standard Model wikipedia , lookup
Eigenstate thermalization hypothesis wikipedia , lookup
Technicolor (physics) wikipedia , lookup
Standard Model wikipedia , lookup
Scale invariance wikipedia , lookup
Atomic nucleus wikipedia , lookup
ATLAS experiment wikipedia , lookup
Scalar field theory wikipedia , lookup
Elementary particle wikipedia , lookup
Yang–Mills theory wikipedia , lookup
Nuclear structure wikipedia , lookup
Relativistic quantum mechanics wikipedia , lookup
Large Hadron Collider wikipedia , lookup
Compact Muon Solenoid wikipedia , lookup
Renormalization group wikipedia , lookup
ALICE experiment wikipedia , lookup
Theoretical and experimental justification for the Schrödinger equation wikipedia , lookup
Light-front quantization applications wikipedia , lookup
Strangeness production wikipedia , lookup
Future Circular Collider wikipedia , lookup
Monte Carlo methods for electron transport wikipedia , lookup
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!