Download - Introduction to the physics of the Quark-Gluon Plasma and the relativistic heavy-ion collisions
Introduction to the physics of the Quark-Gluon Plasma
and the relativistic heavy-ion collisions
Villa Gualino-Torino, 7-3-2011
Fermi Notes on Thermodynamics
QGPQGP
Matter under extreme conditions…
Eleven Science Questions for the New CenturyEleven Science Questions for the New CenturyNATIONAL RESEARCH COUNCIL OF THE NATIONAL ACADEMIES…NATIONAL RESEARCH COUNCIL OF THE NATIONAL ACADEMIES…
No. 7 - What Are the New States of Matter at Exceedingly No. 7 - What Are the New States of Matter at Exceedingly High Density and Temperature? High Density and Temperature? QGP is at T QGP is at T>>10101212K and K and >>
10104040 cm cm-3-3
p
p
p,n,
1911 - Rutherford discovered the NucleusIn ’30 started the study of a new force:Nuclear Force between nucleons
Bashing nucleons with increasing energy …
It became clear that nucleons and more generally hadrons are made of
quarks exchanging gluons
Let’s start from 100 years ago …Let’s start from 100 years ago …
In 1974 the theory of the strong interactionwas written down and calledQuantum Chromodynamics
aaaiiii
aa
n
iiQCD FFmgAiL
f
4
1ψψψ
2γψ
1
cbabcaaa AAfiAAF
Quantum ChromodynamicsQuantum Chromodynamics
Similar to QED but 3 charges + gauge invarianceimply that the gauge field (gluons) self-interact:
- Asymptotic freedomAsymptotic freedom- ConfinementConfinement
electric charge
colour charge
Two regimes:Two regimes:
- Q>>QCD one can use perturbative QCD (pQCD)
- Q ~QCD , Q >QCD non perturbative methods :
lattice QCD (lQCD) and effective lagrangian approach
Several arguments already in the ’70-’80 leadto think that at some temperature and/ordensity quarks “can roam freely in a medium”-> QGP
Quark-Gluon PlasmaQuark-Gluon Plasma
Inside nuclei strong interaction manifest in an extremely non-perturbative regime (QCD~ 1 fm-1) and quarks are not the relevant degrees of freedom
1) ASYMPTOTIC FREEDOM At large T there are interaction q2 ~ (3T)2 and the coupling is weak
2) OVERLAP (percolation) Hadrons Overlap does not allow to identify the hadrons itself: T0 ~ 150 MeV
3) BAG PRESSURE MODELING Pressure of pion gas smaller than the quark gas one: T0 ~ 150 MeV
4) HAGERDON LIMITING TEMPERATURE Hadron gas partition function has a singularity at T0 ~ 160 MeV
Hagerdon’s limiting temperatureHagerdon’s limiting temperature
From the Hadronic side increasing temperature leads to the productionof higher mass hadronic states, but the density of states grows exponentially with the mass
Cabibbo-Parisi, PLB59(1975): Divergency of the partition function has to be associated with a phase transition of hadronic matter to quark-gluon matter
Hagerdon, Nuovo Cimento (1965): T0 is a limiting temperature for hadronic systems
Partition functon for a gas o particle with density of states (m)
m>>T
Quark-antiQuark free energy in lQCD
Kaczmarek et al., PPS 129,560(2004)
lQCD
String breaking
Charm Quarks
We cannot observe quarks, but at large Twe can envisage a weakly interacting gas of quarks and gluons
Asymptotic value
vacuum
Order Parameters of the Phase TransitionOrder Parameters of the Phase Transition
int0 0 ),( HdtxAig eTreTrL
0)250( 3 MeVqq
Polyakov Loop Chiral Condensate
What is the order of the phase transition? [Ratti]
T~170 MeV T~170 MeVlQCD
The basic relations of reference
Ideally our reference is a gas of non-interacting massless quarks and gluons
Multiplied by degrees of freedomdq+q=2*2*3*Nf =24-30 , dg=8*2
x d.o.f
x d.o.f
From lattice QCDFrom lattice QCD
Enhancement of the degrees Enhancement of the degrees of freedom towards the QGPof freedom towards the QGP
MeVT
fmGeV
c
c
15175
/7.0 3
RHIC
Stefan-Boltzmann limit Stefan-Boltzmann limit not reached by 20 % for not reached by 20 % for : :
QGP as a weak interacting gas?!QGP as a weak interacting gas?!
In Ads/CFT this can be a very strongIn Ads/CFT this can be a very strong
interacting systeminteracting system
B=0
gqq
SB ddT 8
7
30
2
4
RHIC
LHC
Interaction measure
No interaction means also =3p(for a massless gas)
[Cotrone]
QGP in the Early Universe Evolution
• Hadronization (Hadronization (T~ 0.2 GeV, t~ 10T~ 0.2 GeV, t~ 10-5-5ss) )
• Quark and gluonsQuark 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 “
BangBang
g(T
)g
(T)
...215.3116...33442)( cbudsgeTg
Quark-Gluon Plasma
HICHIC
10-5s4
)(T
Tg
Degrees of freedom in the Universe
D.J.Schwartz, Ann. Phys. 2004
How to produce a matter How to produce a matter
with with >>1 GeV/fm >>1 GeV/fm33
lasting for lasting for > 1 fm/c > 1 fm/c
in a volume much larger than an hadron?in a volume much larger than an hadron?
Let’s bash again at higher energy…
High Energy Heavy Ion Collision FacilitiesHigh Energy Heavy Ion Collision FacilitiesAccelerator Lab. Ebeam
[AGeV]
Contraction
AGS
(’80s)
BNL 10 (*) 4.5 2
SPS
(94-…)
CERN 160(*) 17.3 9
RHIC
(00-…)
BNL 100 +100 200 100
LHC
(09-…)
CERN 2750+2750 5500 2750
beamNN Es 2
beamNN Ems 2Fixed target
Collider
AGeVs
m
s
m
ECMγ
22)( CMSBANN Epps
Max energy density complete stopping
33max 4
3
4
3
mR
sN
R
Ns
V
E partpart
A
CM
RHIC -> max~ 102 GeV/fm3
LHC -> emax~ 3 103 GeV/fm3
Exploring the phase diagram
Time – 5-15 fm/c = 15-45ys~10-22s
RHIC
LHCLHC
new medium created from the energy deposited B=0 (quark=antiquarks)
Hotter-denser-longer increasing EHotter-denser-longer increasing Ebeambeam
nuclei
RHIC
SPS
Increasing beam energy -> transparencyEnergy distributed in a larger volume
How to make simple estimates?
AGS (BNL)
SPS(CERN)
RHIC (BNL)
Hagerdon limitingtemperature
Yield Mass Quantum Numbers
Temperature Chemical Potential
F. Becattini
Statistical Model analysis
T
Energy Density and Temperature Estimate I
dyydz
yt
zzz
cosh
tanhv
Energy density a la Bjorken:
dy
dE
Rz
NE
V
E T
02
02T
T0
1
y
N
τπR
m
Aε
dET/dy ~ 720 GeV
385~ GeV/fmRHIC
5.0|| y
Particle streaming from origin
experimentstheory estimate
RHIC~0.6-1 fm/c
We can estimate the initial Is this correct?
Energy Density and Temperature Estimate II
TTsssVS 03
000cost
But this means that the previous estimate cannot be correct because it supposes that but to conserve entropy
3
3/1
002
151021
ε
fmGeV
dy
dE
R BjorkenfT
Estimate of QGP lifetimeEstimate of QGP lifetime (~0.6 fm/c at RHIC)
RHIC - T=2TcQGP=0.6*23 =5 fm/c
LHC - T=3.5 TcQGP=0.4*3.53 =15 fm/c
So with uRHIC 0>>c
QGP>fm/c
V> 103 fm3
1D expansion
3
00
cQGP T
T
3
00
T
T3/4
00
Entropy Conservation
MeVfmfmg
T 3357.110
12830 114/14/1
020
Different stages of the Little Bang
2 Freeze-out
Hadron Gas
Phase Transition
Plasma-phase
Pre-Equilibrium <0.2 fm/c
~0.6 fm/c
~20 fm/c
System expands and cools down
cost2/122 zt
~5 fm/c
Soft and Hard probes
SOFT (pT ~QCD,T) driven by non perturbative QCD
HARD (pT >> QCD)Early production, pQCD applicable, comparable with pp, pA
95% of particles
jet quenching, heavy quarks, quarkonia, hard photons
Hadron yields, collective modes of the bulk, strangeness enhancement, fluctuations, thermal radiation, dilepton enhancement
BULK (pT~T)
MINIJETS MINIJETS (p(pTT>>T,>>T,QCDQCD))
CGC (x<<1)Gluon saturation
Heavy Quarks Heavy Quarks (m(mqq>>T,>>T,QCDQCD))
Microscopic Microscopic MechanismMechanism
Matters!Matters!
Initial Conditions Quark-Gluon Plasma Hadronization
Initial ConditionInitial Condition – “exotic” non equilibrium CGC Bulk Bulk –– Hydrodynamics BUTBUT finite viscosities () MinijetsMinijets – perturbative QCD BUTBUT strong Jet-Bulk “talk” Heavy QuarksHeavy Quarks – Brownian motion (?) BUT strongly dragged by the Bulk Quarkonia – Are suppressed (only resonances?) or regenerated HadronizationHadronization – Microscopic mechanism can modify QGP observables
The Several ProbesThe Several Probes
[Albacete] [Bruna] [Arnaldi]
[Romatschke], [Snellings],[Beraudo]
[Becattini][Blume]
LHCRHIC
Dominance of QGP phase (Dominance of QGP phase (QGPQGP> > 10 10
fm/cfm/c)) Vanishing hadronic contamination?
Very large yield of heavy quark (Very large yield of heavy quark (mmqq>>T>>T) and jets ) and jets ((ppTT>>T>>T))
Increasing relevance of non-equilibrated “objects”!
A new QGP phase: perturbative plasma? A new QGP phase: perturbative plasma? Larger /s we get close to the pQCD estimates?
Existence of a primordial non-equilibrium phaseExistence of a primordial non-equilibrium phase Color Glass Condensate (CGC) as high-energy limit of QCD?
Hopefully with several other surprises…Enjoy the School!
Collective Expansion of the BulkCollective Expansion of the Bulk
x
yz
px
py
22
22
2yx
yx
pp
ppv
22
22
xy
xyx
cc22ss=dP/=dP/
ddEoSEoS
ssviscosityviscosity
v2/ measures efficiencyin converting the eccentricity
from CoordinateCoordinate to Momentum Momentum spacespace
SPSRHIC
Vis
cosi
ty s
Transverse Density [fm-2]
For the first time closeFor the first time close to ideal Hydrodynamicsto ideal Hydrodynamics
The fluid with lowest The fluid with lowest ever observed ever observed /s/s
QGP
Color Glass Condensate initial conditions?Color Glass Condensate initial conditions?
pT
dN
/d2p
T
Qsat(s)
3/12
222 ),()()( A
R
QxxgQsQ ssat
At RHIC Q2 ~ 2 GeV2
At LHC Q2 ~ ?
Ideal Sketch
yT es
px
At small x (pT) dense gluon matter
Gluons of small x (pT) -> larger size >1/Qs
overlapand the gluon dostribution stops growing
Parton distr. funct
What is the impactWhat is the impactof a different intial condition?of a different intial condition?
Jet QuenchingJet Quenching
Suppression of minijetsSuppression of minijets
Suppression should increase with density and temperature.Allows a further measure of energy density.
It is due to gluon radiation?Jet energy loss produce mach cones?
Jet triggered angular Jet triggered angular correl.correl.
y
x
away
near
Medium
Heavy Quarks dragged by the medium?Heavy Quarks dragged by the medium?
Strong suppression Large elliptic Flow
Indirect measurement from semileptonic decay (D->Ke) came as a surprise:
- m- mc,bc,b >> >> QCDQCD produced by pQCD processes (out of
equil.)- 00 << << QGPQGP they go through all the QGP lifetime
-mmc,bc,b >> T >> T00 no thermal production no thermal production
A better test of pQCD scattering and energy loss:- mQ>>mq small drag from the bulk
r
eV
rm
eff
D
Quarkonia Suppression?Quarkonia Suppression?
QQ Quarkonium dissoved by charge screening: Thermometer
gTmr
DQQ
11
More binding smaller radiushigher temperature
cJbY, …
Suppression at SPS! More suppression at RHIC
because of high the higher temperature?!and even more at LHC?
Hadronization ModifiedHadronization ModifiedBaryon/MesonsBaryon/Mesons
Au+Au
p+p
PHENIX, PRL89(2003)
Use medium and not vacuumUse medium and not vacuum-> Quark coalescence-> Quark coalescenceMore easy to produce baryons!More easy to produce baryons!
Quark number scalingQuark number scaling
Hadronization is modifiedHadronization is modifiedDynamical quarks are visibleDynamical quarks are visible
Fries-Greco-Sorensen - Ann. Rev. Part. Sci. 58, 177 (2008)
ababMbbbaaba
aM qrprfprfPd
dN,),(),(
,3
/3)(p3v)(pv
/2)(p2v)(pv
Tq2,TB2,
Tq2,TM2,
n
p
nT
2V1
Baryon
Meson
Hadronization ModifiedHadronization Modified
Baryon/MesonsBaryon/Mesons
Au+Au
p+p
PHENIX, PRL89(2003)
Quark number scalingQuark number scaling
n
TT
qT
T
H nppd
dNp
pd
dN
)()(
22
n
p
nT
2V1
Dynamical quarks are visibleDynamical quarks are visibleCollective flowsCollective flows
)2cos(v21φ 2
TT
q
TT
q
dpp
dN
ddpp
dN
/3)(p3v)(pv
/2)(p2v)(pv
Tq2,TB2,
Tq2,TM2,
Enhancement of vEnhancement of v22
v2q fitted from v2
GKL
Coalescence scalingCoalescence scaling