selected topics in heavy ion physics primorsko 2014 peter hristov
DESCRIPTION
Phase diagram of quark-gluon plasma (QGP) 3 Temperature Baryon Density Neutron stars Early Universe Nuclei Nuclon gas Hadron gas “color superconductor” Quark-gluon plasma TcTc 00 Critical point? vacuum “Color-Flavor Locking” High temperature High baryon density Free quarks Restoration of chiral symmetry Increased collision energyTRANSCRIPT
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Selected topics in Heavy Ion PhysicsPrimorsko 2014
Peter Hristov
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Lecture 2 QCD phase diagram Yields, spectra, thermodynamics
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Phase diagram of quark-gluon plasma (QGP)Te
mpe
ratu
re
Baryon DensityNeutron stars
Early Universe
NucleiNuclon gas
Hadron gas“color superconductor”
Quark-gluon plasmaTc
r0
Critical point?
vacuum
“Color-FlavorLocking”
High temperature
High baryon density
Free quarksRestoration of chiral symmetry
Increased collision energy
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Yields, spectra, thermodynamics
Based on the lectures ofR.Bellwied, A.Kalweit, J.Stachel and QM2014 overviewof J.F. Grosse-Oetringhaus
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Statistical hadronization models Assume systems in
thermal and chemical equilibrium
Chemical freeze-out: defines yields & ratios inelastic interactions cease particle abundances fixed
(except maybe resonances)
Thermal freeze-out: defines the shapes of pT, mT spectra: elastic interactions cease particle dynamics fixed
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Reminder: Boltzmann thermodynamics The maximum entropy principle
leads to the thermal most likely distribution for different particle species.
Macro-state is defined by given set of macroscopic variables (E, V, N)
Entropy S = kB lnΩ, where Ω is the number of micro-states compatible with the macro-state
Compatibility to a given macroscopic state can be realized exactly or only in the statistical mean.
L. Boltzmann
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Ensembles in statistical mechanics Micro-canonical ensemble: isolated system with fixed number of particles ("N"),
volume ("V"), and energy ("E"). Micro-states have the same energy and probability. Statistical model for e+e- collisions.
Canonical ensemble: system with constant number of particles ("N") and the volume ("V”), and with well defined temperature ("T"), which specifies fluctuation of energy (system coupled with heat bath). in small system, with small particle multiplicity, conservation laws must be implemented
locally on event-by-event basis (Hagedorn 1971, Shuryak 1972, Rafelski/Danos 1980, Hagedorn/Redlich 1985) => severe phase space reduction for particle production “canonical suppression”
Examples: Strangeness conservation in peripheral HI collisions; low energy HI collisions (Cleymans/Redlich/Oeschler 1998/1999); high energy hh or e+e- collisions (Becattini/Heinz 1996/1997)
Grand canonical ensemble: system with fixed volume ("V") which is in thermal and chemical equilibrium with a reservoir. Both, energy ("T") and particles ("N") are allowed to fluctuate. To specify the ("N") fluctuation it introduces a chemical potential (“μ”) in large system, with large number of produced particles, conservation of additive
quantum numbers (B, S, I3) can be implemented on average by use of chemical potential; asymptotic realization of exact canonical approach
Example: Central relativistic heavy-ion collisions
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Example: barometric formula Describes the density of the atmosphere at a
fixed temperature Probability to find a particle on a given energy
level j:
Energy on a given level is simply the potential energy: Epot= mgh
€
Pj =e
−E j
kBT
Z
Boltzmann factor
Partition function Z (Zustandssumme = “sum over states”)
€
n(h1)n(h2)
=N P(h1)N P(h2)
= e−
ΔE pot
kBT = e−
mgkBT
Δh
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Thermal model for heavy ion collisions Grand-canonical partition function for an relativistic ideal
quantum gas of hadrons of particle type i (i = π, K, p,…): quantum gas: (+) for bosons, (-) for fermions
gi – spin degeneracy – relativistic dispersion relation – chemical potential representing each
conserved quantity Only two free parameters are needed (T,μB), since the
conservation laws permit to calculate Baryon number: VΣniBi = Z+N =>V Strangeness and charm: VΣniSi = 0 => μS; VΣniCi = 0 => μC Charge: VΣniI3i = (Z-N)/2 =>μI3
€
lnZ i = ±giV
2π 2h3 dpp2 ln 1± exp −E i( p) − μ i( )
kBT
⎛
⎝ ⎜ ⎜
⎞
⎠ ⎟ ⎟
⎛
⎝ ⎜ ⎜
⎞
⎠ ⎟ ⎟
0
∞
∫
€
E i( p) = p2 + mi2
€
μi = μB Bi + μSSi + μ I 3I3i + μCCi
See thederivationi.e. in thetextbook ofR. Vogt
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Thermal model for heavy ion collisions From the partition function we can calculate all
other thermodynamic quantities:
The model uses iterative minimization procedure: For a given set of (T, μB) the other quantities are
recalculated to ensure conservation laws; Compare calculated particle yields/ratios with
experimental results in a 𝝌2- minimization in (T, μB) plane (thermal fit).
€
ni = N i /V =1V
∂ T lnZi( )∂μ i
=gi
2π 2h3
p2dpe E i ( p )−μ i( ) /(kBT ) ±10
∞
∫ ;
Pi =∂ T lnZ i( )
∂V; si =
1V
∂ T lnZi( )∂T
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Implementations of statistical models Original ideas go back to Pomeranchuk (1950s) and Hagedorn
(1970s). Precise implementations and also interpretations differ from
group to group: K. Redlich P. Braun-Munzinger, J. Stachel, A. Andronic (GSI)
Eigen-volume correction: ideal gas → Van-der-Waals gas emphasis on complete hadron list
F. Becattini non-equilibrium parameter 𝜸SN
J. Rafelski (SHARE) non-equilibrium parameter 𝜸SN and 𝜸qN
J. Cleymans (THERMUS) Allows also canonical suppression in sub-volumes of the fireball
W. Broniowski, W. Florkowski (THERMINATOR) space time evolution, pT-spectra, HBT, fluctuations
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Comparison to experimental data
A. Andronic et al., Phys.Lett.B673 (2009) 142Thermal model from:A.Andronic et al, Nucl. Phys.A 772 (2006) 167
Resonance ratios deviate Rescattering & regenerationShort life times [fm/c] medium effects K* < *< (1520) < 4 < 6 < 13 < 40
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SHM model comparison based on yields including multi-strange baryons
Data: L.Milano for ALICE (QM 2012)Fit: R. Bellwied
Either a bad fitwith a commonfreeze-out…..
148
164
160
154
152
..or a good fit witha flavor specificfreeze-out
=> Potential evidence of flavor dependence in equilibrium freeze-out
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Thermal Fits p-Pb Statistical model
fits Freeze-out
temperature Volume µb
Equilibrium? (gS, gq)
High-multiplicity p-Pb THERMUS 2.3 gS = 0.96 ± 0.04
approximate thermal equilibrium
c2/ndf rather large though (about 30)
(model – data) / sdata
p K K0 K* f p L X W dTHERMUS: CPC 180 (2009) 84
JFGO@QM2014
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Physics origin?• Non equilibrium thermal model• Baryon annihilation• Freeze-out temperature hierarchy• Incomplete hadron spectrum
Thermal Fits Pb-Pb Equilibrium models yields T = 156-157 MeV
But with c2/ndf of about 2
Plenary: M. Floris
• Fits without the proton (and K*)– similar T, V but c2/ndf drops
from about 2 to about 1 proton anomaly?
Thermus 2.3 GSI SHARE 3
(model – data) / sdata
THERMUS: CPC 180 (2009) 84 | GSI: PLB 673 (2009) 142 | SHARE: arXiv:1310.5108
JFGO@QM2014
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Statistical Hadronic Models: Misconceptions Model says nothing about how system reaches
chemical equilibrium Model says nothing about when system
reaches chemical equilibrium Model makes no predictions of dynamical
quantities Some models use a strangeness suppression
factor, others not Model does not make assumptions about a
partonic phase; However the model findings can complement other studies of the phase diagram (e.g. Lattice-QCD)
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Experimental QCD phase diagram Build accelerator capable to
work at different energies and to use different nuclei
Build experiments with PID capabilities
Take and calibrate data For all the particles: π, K, p, Λ,
Ξ, Ω, Φ, K*0, d, 3He we have to: Use PID detectors and topological
selection to measure raw spectrum Correct for efficiency, acceptance,
feed-down, contamination Fit the spectrum and extrapolate
unmeasured region Determine the integrated yield
dN/dy Do the thermal fit and extract
(T,μB)
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Strangeness: Two historic QGP predictions restoration of c symmetry increased production of s
mass of strange quark in QGP expected to go back to current value (mS ~ 150 MeV ~ Tc)
Pauli suppression for (u,d) copious production of ss pairs,
mostly by gg fusion [Rafelski: Phys. Rep. 88 (1982) 331][Rafelski-Müller: P. R. Lett. 48 (1982) 1066]
deconfinement stronger effect for multi-strange baryons
by using uncorrelated s quarks produced in independent partonic reactions, faster and more copious than in hadronic phase
strangeness enhancement increasing with strangeness content [Koch, Müller & Rafelski: Phys. Rep. 142 (1986) 167]
q q s s g g s s
p N L K
K p L N
Ethres 2ms 300 MeV
Ethres 530 MeVEthres 1420 MeV
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The SPS ‘discovery plot’ (WA97/NA57)
Unusual strangeness enhancement
Npart Npart
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Strangeness enhancement: SPS, RHIC, LHC
enhancement still there at RHIC and LHC effect decreases with increasing √s strange/non-strange increases with √s in pp
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Strangeness enhancement (in AA) or suppression (in pp)? For smaller collision systems (pp, pPb, peripheral HI), the total
number of produced strange quarks is small and strangeness conservation has to be explicitly taken into account => canonical ensemble => suppression in small systems
Since the enhancements are quoted relative to pp they are due to a canonical suppression of strangeness in pp.
s
canonical
grand-canonicals
ssss
s
s
s
TB
TB
μs
s
P. Braun-Munzinger, K. Redlich, J. StachelarXiv:nucl-th/0304013
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“Thermal” Spectra
pdNdE
3
3
TE
TT
Eeddmmdy
dNdp
NdE /)(3
3
μ
f
Invariant spectrum of particles radiated by a thermal source:
where: mT= (m2+pT2)½ transverse mass (requires
knowledge of mass)μ = b μb + s μsgrand canonical chem. potential
(central AA)T temperature of
source
Neglect quantum statistics (small effect) and integrating over rapidity gives:
TmT
TmTT
TT
TT emTmKmdmm
dN /1 )/(
R. Hagedorn, Supplemento al Nuovo Cimento Vol. III, No.2 (1965)
TmT
TT
Temdmm
dN /
At mid-rapidity E = mT cosh y = mT and hence:“Boltzmann”
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“Thermal” spectra and radial expansion (flow)• The “thermal” fit fails at low pT
• Different spectral shapes for particles of differing mass strong collective radial flow
• Spectral shape is determined by more than a simple T at a minimum T, bT
mT
1/m
T dN/
dmT light
heavyT
purely thermalsource
explosivesource
T,b
mT1/
mT d
N/dm
T light
heavy
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Thermal + Flow: “Traditional” Approach
shift) (blue for
11
for 2
mpT
mpmT
TT
T
Tth
TTth
measured
bb
b
1. Fit Data T 2. Plot T(m) Tth, bT
b is the transverse expansion velocity. 2nd term = KE term (½ m b2) common Tth, b.
Assume common flow pattern and commontemperature Tth
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Blast wave: a hydro inspired description of spectra
R
bs
Ref. : Schnedermann, Sollfrank & Heinz,PRC48 (1993) 2462
Spectrum of longitudinal and transverse boosted thermal source:
r
n
sr
TTT
TT
Rrr
TmK
TpImdrr
dmmdN
br
bb
rr
tanh rapidity)(boost angleboost and
)(on distributi velocity transverse
with
cosh sinh
1
R
0 10
Static Freeze-out picture,No dynamical evolution to freeze-out
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Momentum spectra for identified particles
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Ratios: p K K* K0 p f L X W d 3He 3H
pp: no significant energy dependence
Strangeness enhancementDeuteron enhancement
K* Suppressionp ?
pp0.9 TeV2.76 TeV7 TeV pp
p-PbPb-Pb
JFGO@QM2014