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![Page 1: Ultra-relativistic heavy ion collisions Theoretical overview ICPAQGP5, KOLKATA February 8, 2005 Jean-Paul Blaizot, CNRS and ECT*](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649f3d5503460f94c5c69d/html5/thumbnails/1.jpg)
Ultra-relativistic heavy ion collisions Theoretical overview
ICPAQGP5, KOLKATA February 8, 2005
Jean-Paul Blaizot, CNRS and ECT*
![Page 2: Ultra-relativistic heavy ion collisions Theoretical overview ICPAQGP5, KOLKATA February 8, 2005 Jean-Paul Blaizot, CNRS and ECT*](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649f3d5503460f94c5c69d/html5/thumbnails/2.jpg)
Ultra-relativistic heavy ion collisions
Explore properties of matter under extreme conditons (density, temperature)
Study how QCD works in unusual conditions
Much focus on formation of « quark-gluon plasma »
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Fundamental questions
• What is the form of matter at « extreme » temperature or density?
• What is the wave function of a hadron, a nucleus, at asymptotically high energy?
SIMPLICITY emerges in extreme (asymptotic) situations
![Page 4: Ultra-relativistic heavy ion collisions Theoretical overview ICPAQGP5, KOLKATA February 8, 2005 Jean-Paul Blaizot, CNRS and ECT*](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649f3d5503460f94c5c69d/html5/thumbnails/4.jpg)
At high temperature and/or high density matter is « simple »
![Page 5: Ultra-relativistic heavy ion collisions Theoretical overview ICPAQGP5, KOLKATA February 8, 2005 Jean-Paul Blaizot, CNRS and ECT*](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649f3d5503460f94c5c69d/html5/thumbnails/5.jpg)
(S. Bethke, hep-ex/0211012)
QCD Interactions Weaken at High Energy
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The quark-gluon plasma
(from F. Karsch, hep-lat/0106019)
Energy density
Temperature
Free gas limit
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(from F. Kajantie et al, PRL86, PRD67)(from F. Karsch, hep-lat/0106019)
Weakly interacting quasiparticles
Weak coupling calculations provide adequate descriptionOf the thermodynamics at high temperature
SU(3) Pressure
Dimensional reduction€
(T ≥ 3Tc )
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T
B
Hadronic matter
Quark-Gluon Plasma
Nuclei
Colour superconductor
The QCD phase diagram
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Theory near Tc is difficult
Degrees of freedom?
Strong coupling?
Bound states?
… and present experiments may be Probing this region…
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Speed of sounds decreases as one approaches Tc from above
(from R. Gavai and S. Gupta)(from F. Csikor et al, hep-lat/0401022)
Simple quasiparticle picture breaks down close to Tc
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How does the wavefunction of a nucleus look like at
asymptotically high energy ?
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High density partonic systems
Parton density grows as x decreases
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The very early stages of nucleus-nucleus collisions
Physics of dense systems of quarks and gluons
Weak coupling but many active degrees of freedom
Non linear QCD effects become important when
€
∂A( )2
≈ g2 A4 ≈ g2 A2 2
![Page 14: Ultra-relativistic heavy ion collisions Theoretical overview ICPAQGP5, KOLKATA February 8, 2005 Jean-Paul Blaizot, CNRS and ECT*](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649f3d5503460f94c5c69d/html5/thumbnails/14.jpg)
Gluon saturation
Saturation scale
Non linear effects important when
(Gribov, Levin, Ryskin 83)
Large gluon densites at small x
i.e. at a characterisitic scale
€
∂A( )2
≈ g2 A2 2
€
A2 ≈xG(x,Q2)
πR2
€
Q2 ≈ g2 A2
€
Qs2 ≈ α s
xG(x,Q2)
πR2
€
kT ≤ Qs
€
kT ≥ Qs(saturated regime) (dilute regime)
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The saturation scale
In a nucleus
The densities in the central rapidity of a nucleus-nucleus collision at RHIC are similar to those at HERA.
From fit to DIS (HERA)
At the LHC
At RHIC, smaller x can be reached in the forward rapidity region
€
Qs2(x) = Q0
2 x0
x
⎛
⎝ ⎜
⎞
⎠ ⎟λ
€
Q02 → Q0
2A1/ 3
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Early stages of a nucleus-nucleus collision
Partons set free have typical tranverse momenta
They are set free at (proper) time
At that time €
kT ≈ Qs
€
τ ≈Qs−1
€
dN
dy≈ 2AxG(x,Qs)
€
dET
dy≈ 2QsAxG(x,Qs)
Phenomenology based on such arguments (refined) is reasonably successful at RHIC
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High density partonic systems
Large occupation numbers
Classical fields
McLerran-Venugopalan, etc.
€
Qs2 ≈ α s
xG(x,Q2)
πR2
€
n ≈xG(x,Q2)
πR2
€
πQs
2n ≈
π
α s
€
2 /Qs
Non linear evolution equations
Balitsky-Kovchegov equationCOLOR GLASS CONDENSATE and JIMWLK(*) equation
(*) Jalilian-Marian, Iancu, McLerran, Weigert, Leonidov, Kovner
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Experimental discoveries at RHIC
Large energy density achieved
Collective behaviour observed
Jet quenching and strong « final state » interactions
Hints of gluon saturation
And much more…(Focus on observables sensitive to initial state)
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Large energy density
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Moderate increase of multiplicity with beam energy
From Phenix
White paper
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Bjorken energy density
€
εBj (1 fm /c) ≈ 5.5GeV / fm3
εBj (0.35 fm /c) ≈16GeV / fm3
εBj (0.14 fm /c) ≈ 40GeV / fm3
€
εBj (τ 0) =1
πR2τ 0
dET
dy
€
(τ 0 ≈1/mT )
(τ 0 ≈1/Qs)
![Page 22: Ultra-relativistic heavy ion collisions Theoretical overview ICPAQGP5, KOLKATA February 8, 2005 Jean-Paul Blaizot, CNRS and ECT*](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649f3d5503460f94c5c69d/html5/thumbnails/22.jpg)
Elliptic flow
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Produced particles flow preferentiallyin the reaction plane
(J.-Y. Ollitrault, 1992)
€
εx =y 2 − x 2
y 2 + x 2
(P.F. Kolb, J. Sollfrank and U. Heinz, PRC 62 (2000) 054909)
€
V2 = cos(2ϕ )
(S. Voloshin and Y. Zhang, 1994)
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Elliptic flow
(Phenix white paper)
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Comparison with hydrodynamics
(From U. Heinz, nucl-th/0412094)
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Strong conclusions drawn from comparison with hydrodynamical calculations:
- early thermalisation time - sensitivity to equation of state- low viscosity
![Page 27: Ultra-relativistic heavy ion collisions Theoretical overview ICPAQGP5, KOLKATA February 8, 2005 Jean-Paul Blaizot, CNRS and ECT*](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649f3d5503460f94c5c69d/html5/thumbnails/27.jpg)
€
dr v
dt= −
r ∇P
ε + P
€
dr v
dt≈ −
cs2
1+ cs2
r ∇ε
ε
€
dP
dε= cs
2
Euler equation Speed of sound
Some simple remarks (*)
(* R. Bhalerao, J-P B, N. Borghini, J.-Y. Ollitrault)
The overall energy density scale is irrelevant for collective flow
For constant speed of sound
![Page 28: Ultra-relativistic heavy ion collisions Theoretical overview ICPAQGP5, KOLKATA February 8, 2005 Jean-Paul Blaizot, CNRS and ECT*](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649f3d5503460f94c5c69d/html5/thumbnails/28.jpg)
€
v(τ )
cs
≈ cs(τ − τ 0) ×1
R
For constant speed of sound
€
V2 ≈ cs
€
V2 ≈ ε
The time scale for establishing elliptic flow is
€
R /cs
Argument for early thermalisation= based on delayed hydro expansion. Natural time scale is large:
€
R/c
Small thermalisation time unatural (?)
(ellipticity)
![Page 29: Ultra-relativistic heavy ion collisions Theoretical overview ICPAQGP5, KOLKATA February 8, 2005 Jean-Paul Blaizot, CNRS and ECT*](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649f3d5503460f94c5c69d/html5/thumbnails/29.jpg)
Good control parameter ? -initial energy density (no) -average number of collisions during the build up of elliptic flow (?)
€
R
λ≈
σ
S
dN
dy
⎛
⎝ ⎜
⎞
⎠ ⎟
(From NA49, nucl-ex/0303001)
![Page 30: Ultra-relativistic heavy ion collisions Theoretical overview ICPAQGP5, KOLKATA February 8, 2005 Jean-Paul Blaizot, CNRS and ECT*](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649f3d5503460f94c5c69d/html5/thumbnails/30.jpg)
Jet quenching and strong « final state » interactions
![Page 31: Ultra-relativistic heavy ion collisions Theoretical overview ICPAQGP5, KOLKATA February 8, 2005 Jean-Paul Blaizot, CNRS and ECT*](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649f3d5503460f94c5c69d/html5/thumbnails/31.jpg)
q
q
pp
AuAubinaryAuAuAA Yield
NYieldR
/ ⟩⟨=
Au-Au nucl-ex/0304022
Jet production in matter
![Page 32: Ultra-relativistic heavy ion collisions Theoretical overview ICPAQGP5, KOLKATA February 8, 2005 Jean-Paul Blaizot, CNRS and ECT*](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649f3d5503460f94c5c69d/html5/thumbnails/32.jpg)
(PHENIX, nucl-ex/0401001)
Control experiment: d-AU
![Page 33: Ultra-relativistic heavy ion collisions Theoretical overview ICPAQGP5, KOLKATA February 8, 2005 Jean-Paul Blaizot, CNRS and ECT*](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649f3d5503460f94c5c69d/html5/thumbnails/33.jpg)
STAR: Phys.Rev.Lett.91:072304,2003
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Hints of gluon saturation
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Solution of the BK equation, Albacete et al, hep-ph/0307179
y0
0.05
0.1
0.2
0.4
0.6
1
1.4
2
(Related analytical work by Iancu, Itakura, Triantafyllopoulos hep-ph/0403103)
Suppression can also be due to initial state effects (nuclear wave function probed at small x; color glass condensate)
![Page 36: Ultra-relativistic heavy ion collisions Theoretical overview ICPAQGP5, KOLKATA February 8, 2005 Jean-Paul Blaizot, CNRS and ECT*](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649f3d5503460f94c5c69d/html5/thumbnails/36.jpg)
QuickTime™ et undécompresseur TIFF (LZW)
sont requis pour visionner cette image.
![Page 37: Ultra-relativistic heavy ion collisions Theoretical overview ICPAQGP5, KOLKATA February 8, 2005 Jean-Paul Blaizot, CNRS and ECT*](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649f3d5503460f94c5c69d/html5/thumbnails/37.jpg)
(Kharzeev, Kovchegov, Tuchin, hep-ph/0405045)
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SUMMARY-Strongly interacting matter is produced in high energy nucleus-nucleus collisions. Large « initial » energy density. Collective behaviour.
- Many (indirect) evidences that partonic degrees of freedom play an important role in the collision dynamics at RHIC
- Early stages of the collisions, and hence « initial state effects » are important at RHIC (and will be more so at LHC).
- Hints of saturation (color glass condensate) may be already present at RHIC. Phenomenology based on saturation ideas is reasonably successful at RHIC
- QCD has become a central reference in the analysis of the data