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INTRODUCTION TO HIGH DENSITY QCD
Carlos Pajares Dept Fisica de Particulas and IGFAE Universidad de Santiago de Compostela Temas Actuales en Fisica Nuclear Universidad Internacional del Mar,Julio 2011
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Energy density versus T/TC
Energy density versus T/TC. Curve 1-2 quark flavours, curve 2-2 light plus one Heavy flavour and curve 3-3 quark flavours.
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Outline Multiplicity Parton Saturation Elliptic Flow.
Transverse Momentum Suppression Charm, J/Ψ suppression Long Range correlations,Ridge structure Color Glass Condensate Percolation of color sources Quiral Magnetic effect
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SATURATION OF PARTONS Number of gluons. Size gluons Total Area
New Scale QS
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The whole gluon cascade, (ordered in longitudinal momenta)
gives
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A more detailed treatment, is the BFKL eq
Grows as a power of the energy (Violation unitarity) Diffusive behaviour, gluons can go inside non-perturbative region
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Small x, interaction among gluon sources
BK equation
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Solution At lower x (higher energy) N is large but lower than 1 (solving the unitarity problem) At small rT, N is small (color transparency) BFKL is OK. The transition between small rT takes place at a characteristic value rT~1/QS(τ). (solving the infrared diffusion problem) NEW SCALE QS (depends on y an A)
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MULTIPLICITY Extrapolation From lepton-Nucleon and p-A scaling on
At LHC energy gives 9.5, i.e. 1800 charged particles per unit rapidity Linear energy data extrapolation gives 6.5, 1200 charged particles String percolation in between Most of the models over 2000before RHIC.Now they are below
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ELLIPTIC FLOW
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We expect Hydrodynamics perfect fluid result is for full thermalized system and a soft EoS (e energy density cs speed sound) Reynolds number Re=eLv/viscosity;Mach number Ma=v/cs, compresibility; Knudsen number Kn=lambda/L Viscosity=ecslambda Ma=Re x Kn Ma=1;Re=1/Kn
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Perfect fluid should have scaling properties
Limiting fragmentation Centrality dependence
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This scaling suggests that the collective
flow is at the partonic stage OK with coalescence models
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Transverse Momentum Suppression
Photons in agreement with perturbative QCD Energy loss by medium induced gluon radiation
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Energy loss dependence on Npart
O.K. with Energy loss dependence on Npart Non photonic electrons Problems: Equally supressed as charged hadrons contrary to predictions (less supressed) Q=14 GeV2/fm
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Azimuthal distribution of away-side charged hadrons
For central collisions, suppression of the back jet The widths of the back-to-back peaks are independent of centrality (for pT (asso c)>6 and 4<pT<6) Possibilities to look for supersonic jets
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J/Ψ SUPPRESSION hA
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Data requires smaller σabs at most 3mb (usually σabs= 4.2 mb)
Low x2 ~ 0.003 (shadowing region) Data requires smaller σabs at most 3mb (usually σabs= 4.2 mb) No additional suppression seen at RHIC σab=1mb 3 4
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Grandchamp, Rapp, Brown PRL 92, (2004) Thews Eur.Phys.J C43, 97 (2005) Regeneration models fit the data. They predict, an increase of J/Ψ at LHC. Lattice studies indicate no suppression of J/Ψ at T=TC, only at T≥2TC. Ψ’ and are supressed at Defining SJ/Ψ,Ψ’ the survival probabilities once is substracted the absorption, as 60% J/Ψ are directly produced and 40% J/Ψ come from decays of Ψ’ and
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The prediction for LHC is
a large suppression of J/Ψ corresponding to the directly produced J/ Ψ. Clear difference at LHC between regeneration and sequential models
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LONG RANGE CORRELATIONS
A measurement of such correlations is the backward–forward dispersion D2FB=<nB nF> - <nB> <nF> where nB(nF ) is the number of particles in a backward (forward) rapidity <N> number of collisions: <n1B>,<n1F> F and B multiplicities in one collision In a superposition of independent sources model, is proportional to the fluctuations on the number of independent sources (It is assumed that Forward and backward are defined in such a way that there is a rapidity window to eliminate short range correlations). B F
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Sometimes, it is measured
with b in pp increases with energy. In hA increases with A also in AA,increases with centrality The dependence of b with rapidity gap is quite interesting, remaining flat for large values of the rapidity window. Existence of long rapidity correlations at high density
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STAR DATA
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Color Glass Condensate
As the centrality increases, Qs increases, αs decreases and b increases
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Qualitatively is rigth with exp data.Above
a density b does not depends on rapidity gap .b increases with energy and centrality (through α) Ridge:(Dumitru,Gelis,McLerran,Venugopalan) Radial flow+correlations
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CLUSTERING OF COLOR SOURCES
Color strings are stretched between the projectile and target Strings = Particle sources: particles are created via sea qq production in the field of the string Color strings = Small areas in the transverse space filled with color field created by the colliding partons With growing energy and/or atomic number of colliding particles, the number of sources grows So the elementary color sources start to overlap, forming clusters, very much like disk in the 2-dimensional percolation theory In particular, at a certain critical density, a macroscopic cluster appears, which marks the percolation phase transition
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How?: Strings fuse forming clusters. At a certain critical density ηc
(N. Armesto et al., PRL77 (96); J.Dias de Deus et al., PLB491 (00); M. Nardi and H. Satz). How?: Strings fuse forming clusters. At a certain critical density ηc (central PbPb at SPS, central AgAg at RHIC, central SS at LHC ) a macroscopic cluster appears which marks the percolation phase transition (second order, non thermal).The energy momentum of the cluster is the sum of the corresponding for each string.Therefore there is a longitudinal expansion Hypothesis: clusters of overlapping strings are the sources of particle production, and central multiplicities and transverse momentum distributions are little affected by rescattering.
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In the two steps scenario,it is obtained : b=1/(1+k/<nf>) 1/K is the normalized strings fluctuations As <nf> increases with centrality(saturates) and energy,b increases ( the K behaviour with centrality depends on the kinematical cuts,this can make that b can decrease) Qualitative agreement with data N.Armesto,M.A.Braun,P.Brogueira,J.Dias de Deus,E.G.Ferreiro,Kolevatov,C.Pajares V.V.Vechernin
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If you can not get rid of the noise…. study the noise
Penzias and Wilson RHIC FAIR LHC
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Narrowing of the Balance function with Centrality
number of identified charged pion pairs in The width sensitive to hadronization time. Delayed hadronization narrow balance function (stronger correlation in rapidity for the charged particles) Caveat: In PyTHIA and other models with short hadronization time are able to describe data. The narrowing is only observed at midrapidity
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Different Extreme Reaction Scenarios
MULTIPLICITY FLUCTUATIONS Different Extreme Reaction Scenarios NPTarg fluctuations contribute in target hemisphere (most string hadronic models) NPTarg fluctuations contribute in both hemispheres (most statistical models) NPTarg fluctuations contribute in Projectile hemisphere M. Bleicher M. Gazkzicki, M. Gorenstein arXiv:hep-ph/ Multiplicity fluctuations sensitive to reaction scenario
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Reflection, Mixing and Transparency
Significant amount of mixing of particles projectile and target sources
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String Hadronic Models
Projectile hemisphere HSD, UrQMD: V. Konchakovskyi et al. Phys. Rev. C 73 (2006) 034902 HIJING: M. Gyulassy, X. N. Wang Comput. Phys. Commun. 83 (1994) 307 Simulation performed by: M. Rybczynski String hadronic models shown (UrQMD, HSD, HIJING) belong to transparency class They do not reproduce data on multiplicity fluctuations
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PERCOLATION COLOR SOURCES
L.Cunqueiro,E.G.Ferreiro,F del Moral,C.P. Results for the scaled variance of negatively charged particles in Pb+Pb collisions at Plab=158 AGeV/c compared to NA49 experimental data. The dashed line corresponds to our results when clustering formation is not included, the continuous line takes into account clustering.
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FLUCTUATIONS AT RHIC %
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(N. Armesto et al. , PRL77 (96); J. Dias de Deus et al
(N. Armesto et al., PRL77 (96); J.Dias de Deus et al., PLB491 (00); M. Nardi and H. Satz). How?: Strings fuse forming clusters. At a certain critical density ηc (central PbPb at SPS, central AgAg at RHIC, central SS at LHC ) a macroscopic cluster appears which marks the percolation phase transition (second order, non thermal). Hypothesis: clusters of overlapping strings are the sources of particle production, and central multiplicities and transverse momentum distributions are little affected by rescattering.
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