Transcript MKEP 1.2: Particle Physics WS 2012/13

Strong Interaction
Confinement
isolated quarks and
gluons cannot be
observed, only
color-neutral hadrons
Asymptotic freedom
Coupling constant αs gets weaker for high
momentum transfer Q2, i.e. for small distance
αs(Q2)→ 0, Q2→∞
(perturbative methods applied for r < 0.1 fm)
Limit of low particle density and weak interaction well tested
→ QCD perturbation theory
Content of todays lecture: Nucleus-Nucleus collisions
QCD at high temperature and high density: “QCD thermodynamics”
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Why do we expect some New Phenomena/State?
High density
remember: radius of proton 0.8 fm
If average distance between hadrons gets smaller
than ~1 fm, potential overlap
can not assume that our models of isolated hadrons
are still valid
High temperature
Hagedorn's problem (1965)
long befor any quark model was introduced,
Hagedorn stated an upper temperature for hadronic
medium
Canonical partition function Z:
if T > b
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Quark Gluon Plasma
If temperature and/or nuclear
density are high enough strongly
Interacting quarks become free.
Quark Gluon Plasma:
- No interactions between
quarks and gluons: ideal gas
Or
- significant interaction between
quarks and gluons: ideal liquid
(hydrodynamic system)
Data seems to favour ideal liquid
(see later)
Need thermodynamics to describe a collective phenomena of QGP
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Quark Gluon Plasma in the Early Universe
- transition from QGP to a gas of hadrons at T ~ 1012 °C
(100 000 times hotter than the interior of the sun)
- In the early universe: QGP exist several micro seconds after the big bang
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Reminder: Phase Diagram of Water
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Phase Transition
FAIR (future facility at GSI)
?
100 MeV → 1.16 x 1012 K
T= 300 K → kb T = 1/40 eV
Baryochemical potential/net baryon density μB
(measure of the pressure)
Gibbs criterion: phase with higher pressure at given
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temperature is realized
Compute the Phase Transition PQGP = PGas
Hadron gas consists essentially out of pions:
3 bosonic degree of freedom π+, π0, π-
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Compute the Phase Transition PQGP = PGas
Hadron gas consists essentially out of pions:
3 bosonic degree of freedom
Quark Gluon Plasma consists of quarks and gluons
fermionic degrees of freedom: 2 (u,d) x 2 (quark+antiquark) x 2 (spin) x 3 (color) = 24
bosonic degrees of freedom: 8 (gluons) x 2 (polarizations) = 16
Average occupation number:
𝑛𝑑𝑓
n(E) = 𝑒 (𝐸−μ
𝐵
)/𝑇 ±1
“+” bosons, “-” fermions
phase space
𝐸
energy density ε = 𝑛 𝐸 2π 3 𝑑3𝑝
Pressure:
Pπ,gas = 1/3 επ,gas =
𝑛𝑑𝑓π π2
90
𝑇4 ~0.33 𝑇4
PQGP = 1/3 (εg + εq) = (ndfg +
7
π2
ndfq) 90
8
+B
𝑇4 ~4.1 𝑇4
From stability criteria of hadrons, compute QCD vacuum pressure B (bag model)
Transition from pion gas to QGP at Tc = 100-170 MeV (at μB = 0) (conditions of early universe)
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Lattice QCD Computation
Typical parameters:
inside nucleus
nucleon density: ρ0 = 0.16 nucleons/fm3
nucleon mass: mn ~ 0.931 GeV
energy density: ε = ρ0 mn ~ 0.15 GeV/fm3
Pertubation theory, doesn‘t
work, thus computation
from first principle
(with some/many approximations)
Lattice QCD
inside nucleon
ρ0 = 0.16 nucleons/fm3
mN ~ 0.931 GeV
0.94 𝐺𝑒𝑉
ε= 4
~ 0.44 GeV/fm3
π 𝑟𝑁3
3
limit
ideal gas;
QGP is NOT
an ideal gas
clear phase transition
observed around Tc = 170 MeV
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Ultra relativistic Heavy-Ion Collison
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Time Development of Heavy Ion Collisions
Lorentz contraction: 100 (RHIC); 2700 (LHC)
Hard scatter happen before the formation of QGP!
(Q2 >> Λ2QCD)
formation time t0 = 1 fm/c = 3,3 10-24s
temperature T0 > Tc (160-190 MeV)
lifetime 5 fm/c = 1,6 10-23 s (@ RHIC)
135 fm/c = 44 10-23s (@LHC)
[profite from Lorentz contraction]
Critical temp. corresponds to energy
density of ~ 1 GeV/fm3
Transition QGP → hadron gas
Chemical freeze out/hadronisation,
particle ratios (inelastic scattering still possible)
Freeze-out phase
Hadrons (including all momenta distributions) are fixed
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Time Development of Heavy Ion Collisions
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Time Development of Heavy Ion Collisions
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Time Development of Heavy Ion Collisions
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Evidence for Quark Gluon Plasma
- particle multiplicities and ratios
- jet quenching
- elliptical flow (→ QGP is a ideal liquid)
- J/Ψ suppression/enhancement
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Temperature Determination
Ratios are determined at the chemical freeze out temperature, particle ratios are then fixed!
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particle multiplicity
Temperature Determination
measured particle multiplicity
consistent with particles beeing
produced at T ~ 170 MeV
(measurement from RICH)
M
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Grand Canonical Ensemble
Quantum Statistics
[Theromdynamics & Statistical Physics]
𝑉 𝑔𝑖
ln 𝑍𝑖 =
2π2
𝑝2
𝑑𝑝 ln(1 ± 𝑒
−𝑖
partition function for
fermions/bosons describe
system in equilibrium
𝐸𝑖 −μ𝑖
𝑇 )
with μi = μbBi + μSSi + μI3,i
Each conserved quantum number
has chemical potential μ:
after collision before collision
Bi : baryon number
Si : strangeness
I3,i : isospin (only 3 quarks)
ni = Ni/V = -
𝑇 𝜕𝑙𝑛𝑍𝑖
𝑉 𝜕μ
=
𝑔𝑖
2π2
(gi: ndf)
V
𝑖
𝑛𝑖 𝐵𝑖 = 𝑍 + 𝑁
V
𝑖
𝑛𝑖 𝑆 = 0
→ μs
V
𝑖
𝑛𝑖 𝐼3, 𝑖 = 𝑍 − 𝑁
→ μI3
→V
𝑝2𝑑𝑝
𝐸𝑖−μ𝑖
𝑒 𝑇 ±1
Particle multiplicities yield T and μB
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Conditions at Chemical Freeze-Out
Use thermal model
to describe ratios of
particles vs anti-particles
Fit to data:
T = 174 MeV
μB = 46 MeV
agrees with
Tc from theory
Conlcusion: Hadron yields are in chemical equilibrium.
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ALICE results
Use thermal model
to describe ratios of
particles vs anti-particles
good agreement but for p/π
ratio
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Geometry of AA collisions – Impact Parameter
Npart: number of nucleons which took part in at least one collision
Ncoll/Npart: number of binary collisions (Nbin)
b: impact parameter
Cannot directly measure the impact parameter
thus use total number of produced particles to
measure „centrality“ (↔„pripheral“) of event.
„Glauber Model“
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Zero Degree Calorimeter
In order to measure spectators (only elastic
scattering, thus mainly continue to fly in
forward direction), heavy ion experiments
Have a calorimeter in very forward direction
(Zero Degree Calorimeter ZDE)
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 Shape of ET and EZDC follows
from nuclear geometry
 Centrality selection: Cuts on ET,
EZDC (or charged particle multiplicity)
higher EZC, less central collision
How to determine “Centrality”
very little
interation,
particles stay
in beam pipe
thus undetected
Higher transverse energy, more central collision
Jet Quenching
expectation:
Simple scaling from
p+p to Au+Au
expectation:
pion supression in A+A
expectation:
Simple scaling from
P+p to A+A for direct
photons
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Nuclear Modification Factor RAA
Simple scaling from pp IA works for photons but not for jets!
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Suppression of away side Jet
φ distribution of tracks relative to trigger particle
Trigger particle: pT > 4 GeV
Associated particle: pT> 2 GeV
No jet correlation around 180⁰ in central Au-Au collisions
Consistent with jet quenching picture
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Types of Collective Flow
The only type of collective flow in A+A collisions with
impact parameter b=0
Caused by anisotropy of the overlap zone (b≠0)
Is produced in the pre-equilibrium phase of the collision
gets smaller with increasing 𝑠
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Elliptical Flow
Matter state in thermal equilibrium described by relativistic hydrodynamics?
↔ Can QGP be described as ideal gas or as ideal liquid?
𝑑3𝑁
E 𝑑3𝑝
=
1
𝑑2𝑁
2π 𝑝𝑡𝑑𝑝𝑡𝑑𝑦
Direct flow (v1)
(1 +2
∞
𝑛=1 𝑣𝑛
cos[𝑛(φ)] )
Fourier expansion
Ellpitical flow (v2)
Gradient of almond-shape surface will lead to preferential expansion in the reaction plane
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Elliptical Flow
Higher transverse momenta for particles emerging in the reaction plane
Lower momenta for particles perpendicular to the raction plane (elliptical flow)
Bulk evolution well described by model using hydrodynamics and equation of state
determined by weakly interating quarks and gluons.
Matter state seems to behave like ideal liquid!
One of the most important findings at RHIC!
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Elliptical Flow
Hydrodynamic model predictions are able to describe the LHC data as well.
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J/Ψ Suppression in QGP
Rate of heavy quark pair production (energy dependent)
At RHIC energy rather low.
Pure combinatorial effect causes suppression.
With more heavy quarks at LHC (higher energies),
combinatorial effect less pronounced.
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J/Ψ Supression at RHIC
peripheral
central
Clear suppression observed in central collisions relative to peripheral collisions!
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Discovery of the Quark Gluon Plasma?
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First ALICE Data on J/Ψ RAA
peripheral
central
Less supression at LHC than at RHIC! Could point to charm quark recombination!
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Summary
 QCD breaks down at high density/ high temeprature
→ possible existance of phase transition to new state of hadronic matter:
the Quark Gluon Plasma
 experimental signature for Quark Gluon Plasma are:
 Lattice QCD calculation (best we can do, but still with some
approximations) predict phase transition around Tc ~ 170 MeV
 measured particle multiplicities and ratios reflect the composition
at the temperature of freeze out (Tc ~ 170 MeV)
 Jets are suppressed in heavy ion collissions relative to pp collisions

elliptical flow (momentum distribution due to collective behaviour)
→ QGP is an (almost) ideal liquid
 J/Ψ suppression/enhancement
 There is some experimental evidence for Quark Gluon Plasma
 Quark gluon plasma is very active research focus of Physikalsisches institut
[input to slides shown today to large extend from lectures from K.Reygers
(http://www.physi.uni-heidelberg.de/~reygers/) ]
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