quarkgluon plasma and relativistic heavy ion collisions
TRANSCRIPT
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QuarkGluon Plasma and Relativistic Heavy Ion Collisions
OUTLINE
Introduction QCD thermodynamics Heavy ion collisions and hadroproduction Heavy ion collisions and hydrodynamics Jet production Conclusions
F. Becattini (University of Florence and INFN)
ICTP 2012 Workshop on Recente Developments in Astronuclear and Astroparticle Physics
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Fermi Notes on Thermodynamics
HotQGP
Matter under extreme conditions…
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Tem
pera
ture
net baryon density
Earl
y u
niv
ers
e
nucleinucleon gas
hadron gas
quark-gluon plasma (QGP)Tc
ρ0
χ−symmetric
χ− Symmetry Broken
Colour superconductorneutron stars
Sketch of the phase diagram today
critical point ?
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Phase Transition: from the hadronic side
Hagedorn: density of hadronic states ρ(m) grows exponentially
T0=160 MeV
T0 is called Hagedorn limiting temperature (1965)
for an hadronic system (no quarks at that time)
Cabibbo-Parisi, PLB59(1975) – one year after Gross –Wilczek paper:
Divergency of the partition function has to be associated with a phase transition of hadronic matter to quark-gluon matter+ asymptotic freedom at large T -> weakly quark gluon gas
Partition function for a gas of hadrons, with m>~T
Number of Hadronic states
π,Κρ,ω,Ν,∆,Λ,Ω,Ν∗,…
0/)( TmeCmm αρ =
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Theory of Strong Interaction: QCD
- Asymptotic freedom- Confinement
Two regimes:- Q>>>ΛQCD one can use perturbative QCD (pQCD)
- Q ~ΛQCD , Q >ΛQCD non perturbative methods : lattice QCD (lQCD) and effective lagrangian approach
Similar to QED, but gluons self-interact!
∑∑ −−
−∂=
= aaaiiii
aa
n
iiQCD FFmgAiL
f
µυµυµµµ
λ4
1ψψψ
2γψ
1
µµµννµµνcbabcaaa AAfiAAF +∂−∂=
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Lattice QCD : a huge computational effort
Solving QCD on a grid of points in space and time with size (Ns)3xNt
Partition function
Only thermodynamical observables (EoS, susceptibility, …) or correlators No formulation for dynamical processes!
Cannot be directly used at finite baryon density (no neutron star aargh!!)
Only very recently, calculations for physical quark masses became feasible!
It is a fundamental guidance, but it is not sufficient !
Physical size : L = NS a, Time ->Temperature: T = 1/(Nt a)
Dynamics -> Statistics
( ))(exp)ˆ,( nAtignnU aa
µµ =+
[ ]∫∫
∫=ψψτ
µ
β
ψψ,,3
0)()()(ALxddi
a exDxDxADZβτ =→ Ti /1
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g(T
)
Quark-Gluon Plasma
10-5s
Degrees of freedom in the Universe
D.J.Schwartz, Ann. Phys. 2004
...215.3116...33442)( +++++++++= cbudsgeTg πµνγ
g(T) = ε3T 4
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Order Parameters of the Phase TransitionPolyakov Loop - Confinement
T~170 MeVlQCD
Crossover nature of the transition no real order parameter smooth behavior with temperature still exhibit a rapid change in the vicinity of the phase
transition
Order parameter for infinite quark mass
WB collaboration, JHEP (2010) Yaoki et al., Nature 443, 675-678 (2006)
Confinement
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RHIC
Stefan-Boltzmann limit not reached by 20 % : QGP as a weak interacting gas?
µB=0
Reference a gas of non-interacting masslessparticle … Stefan-Boltzmann
Interaction measure
EoS from lattice QCD
No interaction means also
I = ε-3p= 0(for a massless gas)
Wuppertal-Budapest collaboration, QM2012 talk
T > Tc not a hadron gas but not
a massless quark-gluon gas
+= + gqq
SB ddT 8
7
30
2
4
πε
MeVT
fmGeV
c
c
160
/7.0 3
≅≈ε
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How to produce a matter with ε >>1 GeV/fm3lasting for τ > 1 fm/c
in a volume much larger than a hadron?
Accelerator Lab √sNN
Nuclei
SPS (90's) CERN 6-18 Pb-Pb
RHIC (00-.. RHIC 7.7-200 Au-Au
LHC (09-..) CERN 2750 Pb-Pb
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τeqPre-equil. phase
Sketch of the nuclear collision process
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Probing the Quark Gluon Plasma formation
Several possible probes at our disposal, that can be clustered in three groups
Hadron radiation
Electromagnetic radiation
Hard probes: heavy quarks and quarkonia,jets, hard photons etc.Common feature: early production, “calculable” in perturbative QCD, easily comparable to pp and pA
The plasma is a transient and rapidly decays. This situation is dramatically different fromthe idealized situation of lattice QCD calculations.
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Some typical definitions
Transverse view
Longitudinal view
z
ϕ
y
x
In terms of pT and y
y =0
15 fm b 0 fm
0 Npart 394
Centrality of the collisions
zz
zz v
pE
pEy ≈
−+== − ln
2
1tanh 1 β
( )zyx pppEp ,,,=µ
( )ympymp TTT sinh,,cosh=µ
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Hadron radiation
Provides direct information about the hadronization stageof the plasma.Allows to determine the thermodynamical state at thestage when hadrons cease interactions and decouple
Enhanced production of strange particles was predictedto be a signature of QGP formation
F. B., J. Manninen, Phys. Rev. C 78 (2008) 054901
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The temperature at the chemical freezeout at RHIC is that of a hadronicblackbody and it is the largest ever measured on Earth (~ 2 1012 K)
F. B., J. Manninen, Phys. Rev. C 78 (2008) 054901F. B., J. Manninen, Phys. Rev. C 78 (2008) 054901
J. Cleymans et al. P hys.Rev. C73 (2006) 034905
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Freeze-out vs lattice QCD
Interesting the relative location between the freeze-out in HIC and critical Iine of the phase diagram
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Increasing the energy...
Time – 5-15 fm/c = 15-45ys~10-22s
Baryon stopping decreases, but a larger energy density is achieved(hotter, denser, longer)
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Have we overcome the critical T?Same observation as in elementary collisions. Statistical equilibrium as anIntrinsic feature of QCD at the soft scale, i.e. hadronization (F.B., U. Heinz, R. Stock, H. Satz et al)
In order to show that Tc has been overcome, i.e. that a QGP has been produced,we need to go to other observables
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Strangeness enhancement: Wroblewski ratio
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Relativistic hydrodynamical model
Early assumptions
Local thermodynamical equilibrium at chemical decoupling (CooperFrye distribution)
Lattice QCD Equation of State
Ideal fluid (now viscous)
Bjorken longitudinal solution v
z=z/t (2+1)
(now only at initial local time)
τeqPre-equil. phase
=∂
=∂
0)(
0)(
xj
xT
B
µµ
µνµ
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“Measuring” the initial temperature of the plasma with hydrodynamical model
(Huovinen, Kolb, Heinz, Hirano, Romatschke, Teaney,..)
The idea is to determine the initial conditions from the observed final spectra (in the transverse plane)
Fitted parameters. The initial T is correlatedto the initial equilibration time.
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Reaction plane
x
z
y
Elliptic flow in peripheral collisions
Anisotropic pressure gradient: if there iscollective flow, particles get a larger momentumon the reaction plane!
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Anisotropia di impulso
Spacial anisotropy gets converted into momentum anisotropy provided that:Thermalization occurs while the system is still almondshapedThis requires short times (~ 1 fm/c) when the system is still in the QGP phase
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b ≈ 4 fmb ≈ 6.5 fmb ≈ 10 fm
STAR, PRL90 032301 (2003)
Elliptic flow coefficient v2
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curves = hydrodynamic flowzero viscosity, Tc = 165 MeV
v2 in good agreement with quasiideal fluid
Local equilibrium distribution
Lattice QCD EoS
Initial energy density ~ 25 GeV/fm3
Mass ordering at low pT also in agreementwith hydro predictions
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Viscous hydrodynamics
but it violates causality, 2nd order expansion needed -> Israel-Stewart
Relativistic Navier-Stokes
two more parameters appears + δf ~ feq reduce the pT validity range
Fx
Ayz
=−η∂ux
∂y
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Similar phenomenon observed in atomic physics:Cold atom clouds (strongly coupled)expanding after switching off an optical trap(Lithium)
QGP: an almost ideal fluid
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Altri esempi di dualita' sono stati costruiti, ma in tutte le teorie di campo nel limite di accoppiamento grande:
Conjecture: it is a universal quantum bound which is reached for the maximal coupling
Shear viscosity in strongly interacting conformal quantum field theory (from AdS/CFT correspondance)
Kovtun, Son, Starinets PRL 94Kovtun, Son, Starinets PRL 94, , 111601 (2005)111601 (2005)
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η/s (limit) = 1/4π
η/s (water) >10
4π ⋅ η/s
Universal bound ?
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Recent development: from averages to Event-by-event hydrodynamics
εn for n>2 of similar size
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Ideal Viscous
Viscosity smoothens fluctuations and affect more higher harmonics
η/s=0 η/s=0.16
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High harmonics fluctuations reminds the CMB fluctuations...
Of course n=200 is not possible to be seen for a hadron system with R ~ 10 fm
Freeze-out τ ~ 380.000 y’s (QGP ~ 10-22 s)Sound horizon R ~ Mps (QGP ~ 6 fm)
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Staig & Shuryak, PRC (2011)
None of the models reproduce the correct shapes:- No peak at n=3- Too large for n> 6
A promising new challenge -> new findings and knoweledge
A recent ALICE measurement
η/s=0
η/s=0.08
η/s=0.16
Hydrodynamics, e=3pRenormalized to m=3
A first schematic calculation
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Jets as a probe of the plasma
Initial partonparton scattering with large momentum transfer Unlike in vacuum, quarks and gluons lose energy (brehmsstrahlung and collisions) before hadronizing
Theoretical task: to calculate energy distribution of hard partons traversing a lengthL within the medium
Nucleus-nucleus collisions hard initial scattering
scattered partons probe traversed hot
and dense medium
‘jet tomography’
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Suppression of high-pT hadrons
(not so for γ)
)(Yield
)(Yield)(
ppAA
AAAA
T
TT pNbin
ppR =
- Due to energy loss of partons, there is a strong suppression of high pt hadrons
- Even larger at LHC than @ RHIC
- Nuclear modification factor RAA(pT) for charged particles produced in 0-5% centrality range
– minimum (~ 0.14) for pT ~ 6-7 GeV/c
– then slow increase at high pT
RAA = 1 for hard QCD processesin absence of nuclear modifications
Including CDF data
0.9 TeV * NLO (2.76 TeV)/NLO(0.9 TeV)
PLB 696 (2011) 30-39
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Di-jet imbalance• Pb-Pb events with large di-jet imbalance observed at the LHC
•
recoiling jet strongly quenched!CMS: arXiv:1102.1957
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The largest temperature ever achieved on Earth(> 2 x 1012 K)
~ 103 K ~ 107 K ~ 108 K
~ 5 1012 K !
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Conclusions and outlook
There is little doubt that QGP has been produced in relativistic heavyion collisions
Many observations point to a system which is hotter than Tc andstrongly interacting (low viscosity), in accordance with QCD. The studyof its properties is ongoing at LHC
Search of the QCD critical point and the onset of deconfinement atlower energies
Relativistic heavy ion collisions have been a very effective laboratory for advanced theoretical subjects: not only QCD, but also relativistic statistical mechanics, relativistic hydrodynamics and even (maybe)string theory
Hopefully, there will be useful results for relativistic astrophysics and cosmology
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Soft and Hard probes
SOFT (pT ~ΛQCD,T) driven by non perturbative QCD
HARD (pT >>> ΛQCD)Early production, pQCD applicable, Baseline pp, pA
99%
jet quenching, heavy quarks, quarkonia, hard photons (W,Z)
Hadron yields, collective modes of the bulk, strangeness enhancement, fluctuations, thermal radiation, dilepton enhancement
RAA = 1 nothing new going on AA
Nuclear modification factor
RAA(pT ) = d2NAA / dpT
Ncolld2NNN / dpT
= mediumvacuum