1. 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

3. 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.

6. 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

14. SATURATION OF PARTONS Number of gluons. Size gluons Total Area
New Scale QS

15. The whole gluon cascade, (ordered in longitudinal momenta)
gives

16. 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

17. Small x, interaction among gluon sources
BK equation

18. 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)

20. 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

23. ELLIPTIC FLOW

24. 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

25. Perfect fluid should have scaling properties
Limiting fragmentation
Centrality dependence

27. This scaling suggests that the collective
flow is at the partonic stage
OK with coalescence models

31. Transverse Momentum Suppression
Photons in agreement
with perturbative QCD
Energy loss by
medium induced gluon
radiation

32. 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

33. 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

39. J/Ψ SUPPRESSION hA

40. 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

41. 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

42. 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

44. 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

45. 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

46. STAR DATA

50. Color Glass Condensate
As the centrality increases, Qs increases, αs decreases and b increases

51. 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

52. 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

55. 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.

56. 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

58. If you can not get rid of the noise…. study the noise
Penzias and Wilson
RHIC FAIR
LHC

59. 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

60. 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

61. Reflection, Mixing and Transparency
Significant amount of mixing of particles projectile and target sources

62. 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

63. 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.

64. FLUCTUATIONS AT RHIC %

65. (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.