Search for the Quark-Gluon Plasma in Heavy Ion Collision V. Greco.
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Transcript of Search for the Quark-Gluon Plasma in Heavy Ion Collision V. Greco.
Outline
Introduction: definitons & concepts - Quark-Gluon Plasma (QGP) - Heavy-Ion-Collisions (HIC)
Theory and Experiments - probes of QGP in HIC - what we have found till now!
Introduction I Goals of the Ultra-RHIC program: Production of high energy density matter better understanding of the origin of the masses of ordinary nuclei Produce matter where confinement -> deconf QGP and hadronization Structure of the nucleon how quantum numbers arise (charge spin, baryon number)
Big Bang
• Hadronization (T~ 0.2 GeV, t~ 10-2s)
• Quark and gluons
• Atomic nuclei (T~100 KeV, t ~200s) “chemical freeze-out”
• but matter opaqueopaque to e.m. radiation
• e. m. decouple (T~ 1eV , t ~ 3.105 ys) “thermal freeze-out “
We’ll never see what happened t < 3 .105 ys (hidden behind the curtain of the cosmic microwave background)
HIC can do it!BangBang
Little Bang
22)( CMSBANN Epps
From high regime
to high T regime
We do not observe hadronic systems with T> 170 MeV (Hagerdon prediction)
AGS
SPS
RHIC
Freeze-out
Hadron Gas
Phase Transition
Plasma-phase
Pre-Equilibrium
Different stages of the Little Bang
finite t
NN “Elastic”
44 R
CB
V
EP H
H
HRP 0
4
0
3
3 30)(
)2(Tgpfppd
g
V
Etot
Bag Model (cosm. cost.)
Euristic QGP phase transition
Pressure exceeds the Bag pressure -> quark liberation
Extension to finite
B1/4 ~ 210 MeV Tc~ 145 MeVBT 42
90
37 4/1
4/1
23790
BTc
Free massless gas)(8
7qqgtot gggg
fscqqg NNNggg ,16
Phase TransitionDef.Def. Phase transition of order n-th means the n-th derivative of the free energy F is discontinous
V
TF TF
I order
2
2
T
FCV
II order
Cross over Not a mixed phase, but a continous modification of the matter between the two phases
Mixed phaseMixed phase
Critical behaviorCritical behavior
Quantum ChromoDynamics
a
aaiiiia
a
n
ii FFmgAi
f
41
ψψψ2
γψ1
cbabcaaa AAfiAAF
Similar to QED, but much richer structureSimilar to QED, but much richer structure: SU(3) gauge symmetry in color space Approximate Chiral Symmetry in the light sector
broken in the vacuum.
UA(1) iral
Scale Invariance broken by quantum effects
Confinement Chiral Symmetry Restoration
Chiral Symmetry
Eight goldstone Bosons
() Absence of parity doublets
)1()1()3()3()3( AVVAC UUSUSUSU
RL
i
RL
jjRLe ,,
,
)1( 5, RL QCD is nearly invariant under rotation among u,d,s
associate Axial and Vector currents are conserved
Constituent quark masses explicit breaking of chiral simmetry
MeVqq 3)250(
a
f
P-S V-A splitting In the physical vacuum
Mas
s (M
eV)
Lattice QCDQCD can be solved in a discretized space !
)(exp)ˆ,( nAtignnU aa
)(ψ n
It is less trivial than it seems, Ex.: fermion action, determinant
,,3
0)()()(ALxddi
a exDxDxADZ
FFxdnFgiaTr
gnUTr
gS a
pp pclosed
4022
22 4
1)(exp
2
1)(
2
1Gluon field Continuum limit
Lattice QCD is the algorithm to evaluate Z in theSpace-time -> static at finite temperature
Ti /1 HiHt ee
Dynamics -> Statistics
time dim. regulate the temperature
,,4
)()()( ALxdia exDxDxADZ
Lattice QCD
CPU time is very large quark loops is very time consuming
(mq=∞ no quark loops = “quenched approximation”) lattice spacing a 0 baryon chemical potential
ProspectivesQuark –gluon plasma properties (vs density and temperature) Hadron properties (mass, spin, ) vacuum QCD structure (istantons ..) CKM matrix elements (f,fk,fc,fB)
Limitations No real time processes Scattering Non equilibrium Physical understanding
Effective models are always necessary !!!
0 0 ),( dtxAigeTrL
)0,0,0,1(2
)( xyigyJa
a
)(2
)()( 0
3
int xAigyAyJydH aa
aa
-static quark-only gluon dynamics
Polyakov Loop
tconfinemen
HL
int0
int0 0 ),( HdtxAig eTreTrL
If quark mass is not infinite and quark loops are present L is not really an order parameter !
Lattice QCD
Chiral CondensatePolyakov Loop
• Coincident transitions: deconfinement and chiral symmetry restoration it is seen to hold also vs quark mass
Phase Transition to Quark-Gluon PlasmaEnhancement of the degrees of freedom towards the QGP
42
1664
7
30Tn fgqq
Quantum-massless non interacting
MeVT
fmGeV
c 15173
/7.0 3
Gap in the energy density(I0 order or cross over ?)
Soft and Hard
• Small momentum transfer • Bulk particle production
– How ? How many ? How are distributed?
• Only phenomenological descriptions available (pQCD
doesn’t work)
SOFT (npQCD) string fragmentation in e+epp … or(pT<2 GeV) string melting in AA (AMPT, HIJING, NEXUS…)
QGP
HARD minijets from first NN collisions Indipendent Fragmentation : pQCD + phenomenologyphenomenology
99% of particles
Collision Geometry - “Centrality”
0 N_part 394
15 fm b 0 fm
Spectators
Participants
For a given b, Glauber model predicts Npart and Nbinary
S. Modiuswescki
Kinematical observables
z
zz pE
pEy
ln21 Additive like Galilean velocity
zTzT
TT
ympymE
pmm
sinh,cosh
2/122
z
z
pppp
||||
ln21
)2/tan(ln
Angle respect z beam axis
TTT pdyddN
ymm
pdddN
22
2
cosh1
CMLABLABjCMj yyy ///
Transverse mass
Rapidity -pseudorapidity
Energy Density
Energy density a la Bjorken:
dydE
τπR1
Aε T
2T
T dz
dE
fm/c 14.0τ
fm/c 1τ
7A 1.18R
RHIC
SPS
1/3
fm
dET/dy ~ 720 GeV
Estimate for RHIC:
38~6.0 GeV/fmfm/c
Time estimate from hydro:
Tinitial ~ 300-350 MeV
5.0|| y
dyydz
yt
zzz
cosh
tanhv
Particle streaming from origin
Collective Flow I: RadialObservable in the spectra, that have a slope due to temperature folded with Radial flow expansion <T> due to the pressure.
T
TfslT
2
TfslT
v1
v1TT,mpicRelativistUltra
vm2
1TT,p icRelativistNon
m
Slope for hadrons with different masses allow to separate thermal from collective flow
Absence
Tf ~ (120 ± 10) MeV
<T> ~ (0.5 ± 0.05)
Collective flow II: Elliptic Flow
Anisotropic Flowx
yz
px
py
v2 is the 2nd harmonic Fourier coeff.of the distribution of particles.
nn
TT
ndpdN
ddpdN
)cos(v21
Perform a Fourier decomposition of the momentum space particle distributions in the x-y plane
22
22
2 2cosyx
yx
pp
ppv
Measure of the Pressure gradient
Good probe of early pressure
Yield Mass Quantum Numbers
Temperature Chemical Potential
Statistical Model
Hydro add radial flow, freeze-out hypersurfacefor describing the differential spectrum
There is a dynamical evolution that Leads to such values of Temp. & abundances?
Yes, but what is Hydro?
Maximum entropy principle
Maximum Entropy Principle
k V
ffffxpdd
S )1ln()1(ln)2( 3
33
i
ii fEdE
i
ii fBdB
i
ii fsdS
All processes costrained by the conservation laws
Maximizing S with this constraintsthe solution is the statistical thermal equilibrium
The apparent “equilibrium” is not achieved kinetically but statistically !
HYDRODYNAMICS
0)(
0)(
xj
xT
B
Local conservation Laws
)()()(
)()()()()()(
xuxnxj
gxpxuxuxpxexT
BB
5 partial diff. eq. for 6 fields (p,e,n,u)+ Equation of State p(e,nB)
No details about collision dynamics (mean free path 0)
Follow distribution function time evolutionFollow distribution function time evolution: Initial non-equilibrium gluon phase
final chemical and thermal equlibrated system How hydrodynamical behavior is reached Relevance of npQCD cross section Description of the QCD field dynamics
Another level of Knoweledge
collprr IfUfm
p
t
f
Non-relativistically
)()( 4321
4
34121 2 3
2143
22 ppppWffffIcoll
Transport Theory
),,(, tprf gq
Follow distribution function time evolutionFrom the initial non-equilibrium gluon phase
drifting mean field collision
To be treated:- Multiparticle collision (elastic and inelastic)- Quantum transport theory (off-shell effect, … )- Mean field or condensate dynamics
...213222 collcollcoll IIIfp
Relativistically
at High density
ggggg ggg
• Chemical equilibrium with a limiting Tc ~170MeV
• Thermal equilibrium with collective behavior
- Tth ~120 MeV and <>~ 0.5
• Early thermalization (< 1fm/c, ~ 10 GeV)
- very large v2
We have not just crashed 400 balls to get fireworks, but we have created a transient state of plasma
A deeper and dynamical knowledge of the system is still pending!
Outline II
Probes of QGP in HICProbes of QGP in HIC
What we have find till now! strangeness enhancement jet quenching coalescence J/ suppression
What we have learned ?