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Modern Nuclear Physics with STAR @ RHIC: Recreating the Creation of the Universe. Rene Bellwied Wayne State University ( email@example.com ) Lecture 1: Why and How ? Lecture 2: Bulk plasma matter ? (soft particle production) Lecture 3: Probing the plasma (via hard probes).
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Wayne State University
(soft particle production)
(via hard probes)
The quarks and gluons deconfine because energy or parton density gets too high
(best visualized in the bag model).
Chiral symmetry restoration
Massive hadrons in the hadron gas are massless partons in the plasma. Mass breaks chiral symmetry, therefore it has to be restored in the plasma
What is the mechanism of hadronization ?
How do hadrons obtain their mass ?
(link to LHC and HERA physics)
For more detail see for example: J. Harris and B. Müller, Annu, Rev. Nucl. Part. Sci. 1996 46:71-107
Phase transitions are signaled thermodynamically by a ‘step function’ when plotting temperature vs. entropy (i.e. # of degrees of freedom).
The temperature (or energy) is used to increase the number of degrees of freedom rather than heat the existing form of matter.
In the simplest approximation the number of degrees of freedom should scale with the particle multiplicity.
At the step some signatures drop
and some signatures rise
Central Au + Au
?Evidence: Some particles are suppressed
If things are produced in pairs then one might make it out and the other one not.
If things require the fusion of very heavy rare quarks they might be suppressed in a dense medium
Solves the problem of divergences in pQCD calculations (which arise due to loop diagrams)
(F. Karsch, hep-lat/9909006)
T = 150-200 MeV
e ~ 0.6-1.8 GeV/fm3
Bjorken-Formula for Energy Density:
PRD 27, 140 (1983) – watch out for typo (factor 2)
Time it takes to thermalize system (t0 ~ 1 fm/c)
Central Au+Au (Pb+Pb) Collisions:
17 GeV: eBJ 3.2 GeV/fm3
130 GeV: eBJ 4.6 GeV/fm3
200 GeV: eBJ 5.0 GeV/fm3
Note: t0 (RHIC) < t0 (SPS)
commonly use 1 fm/c in both cases
Bjorken-Formula for Energy Density:
Gives interestingly always slightly smaller values than with calorimetry (~15% in NA49 and STAR).
eBj~ 4.6 GeV/fm3
Lattice ecThe Problem with eBJ
roughly factor 2
(yields & ratios)
(shapes of pT,mT spectra):
We get a chemical freeze-out temperature and
a baryochemical potential out of the fit
Seems to work rather well ?!
Beccatini, Heinz, Z.Phys. C76 (1997) 269
This type of “thermal” behavior requires no rescattering and no interactions. The collisions simply serve as a mechanism to populate phase space without ever reaching thermal or chemical equilibrium
In RHI we are looking for large collective effects.
Ensemble of events constitutes a statistical ensemble
T and µ are simply Lagrange multipliers
“Phase Space Dominance”
Good success with thermal models in e+e-, pp, and AA collisions.
Thermal models generally make
tell us nothing about QGP, but
(e.g. PBM et al., nucl-th/0112051):
Elementary particle collisions: canonical description, i.e. local quantum number conservation (e.g.strangeness) over small volume.
Just Lagrange multipliers, not indicators of thermalization.
Heavy ion collisions:
grand-canonical description, i.e. percolation of strangeness over large volumes, most likely in deconfined phase if chemical freeze-out is close to phase boundary.
[Satz: Nucl.Phys. A715 (2003) 3c]
Data – Fit (s) Ratio
Short life time [fm/c]
K* < *< (1520) <
4 < 6 < 13 < 40
Medium effects on resonance and their decay products before (inelastic) and after chemical freeze out (elastic).
Red: before chemical freeze out
Blue: after chemical freeze out
Life time [fm/c] :
(1020) = 40
L(1520) = 13
K(892) = 4
++ = 1.7
Thermal model :
T = 177 MeV
mB = 29 MeV
 P. Braun-Munzinger et.al., PLB 518(2001) 41
D.Magestro, private communication
 Marcus Bleicher and Jörg Aichelin
Phys. Lett. B530 (2002) 81-87.
M. Bleicher, private communication
Rescattering and regeneration is needed !
[Rafelski: Phys. Rep. 88 (1982) 331]
[Rafelski-Müller: P. R. Lett. 48 (1982) 1066]
[Koch, Müller & Rafelski: Phys. Rep. 142 (1986) 167]
Strangeness production depends strongly on baryon density
(i.e. stopping vs. transparency, finite baryo-chemical potential)
I. Increase instrange/non-strangeparticle ratios
PBM et al., hep-ph/0106066
II. Maximum isreached
III. Ratios decrease
(Strange baryonsaffected more stronglythan strange mesons)
See P.Senger’s talk
hidden strangeness mesons
<E>/<N> = 1 GeV
Peaks at 30 A GeV in AA collisions due to strong mB dependenceStrangeness enhancement:Wroblewski factor evolution
dependent on T and mB
dominated by Kaons
The strangeness enhancement factors at the SPS (WA97) can
be explained not as an enhancement in AA but a suppression in pp.
The pp phase space for particle production is small. The volume is small and the volume term will dominate the ensemble (canonical (local)). The grand-canonical approach works for central AA collisions, but because the enhancements are quoted relative to pp they are due to a canonical suppression of strangeness in pp.
STAR: 5%Identified Particle Spectra for Au-Au @ 200 GeV
Explains: spectra, flow & HBT
Invariant spectrum of particles radiated by a thermal source:
where: mT= (m2+pT2)½transverse mass (Note: requires knowledge of mass)
m = b mb + s ms grand canonical chem. potential
T temperature of source
Neglect quantum statistics (small effect) and integrating over rapidity gives:
R. Hagedorn, Supplemento al Nuovo Cimento Vol. III, No.2 (1965)
At mid-rapidityE = mT cosh y = mTand hence:
N.B. Constituent quark and parton recombination models yield exponential spectra with partons following a pQCD power-law distribution. (Biro, Müller, hep-ph/0309052)
T is not related to actual “temperature” but reflects pQCD parameter p0 and n.
Assume commonflow pattern and common
1. Fit Data T
2. Plot T(m) Tth, bT
This yields a common thermal freezeout temperature and a common b.
Spectrum of longitudinal and transverse boosted thermal source:
Ref. : Schnedermann, Sollfrank & Heinz,
PRC48 (1993) 2462
Static Freeze-out picture,
No dynamical evolution to freezeout
Au+Au sNN=200 GeV
From fits to p, K, p spectra:
Slightly model dependent
Dashed lines: hard
sphere radii of nuclei
Re-interactions among what? Hadrons, partons or both?
In other words, what equation of state?
Multistrange v2 establishes partonic collectivity ?
Based on entropy: Dt ~ (Tch/Tkin – 1) R/bs
More resonance measurements are needed
to verify the model and lifetimesLifetime and centrality dependence from (1520) / and K(892)/K
G. Torrieri and J. Rafelski, Phys. Lett. B509 (2001) 239
K(892) = 4 fm/c
L(1520) = 13 fm/c
(1520)/ = 0.034 0.011 0.013
K*/K- = 0.20 0.03 at 0-10% most central Au+Au
dN/dy ~ 800-1200
Statistical thermal models appear to work well at SPS and RHIC
into equilibrium at RHIC (SPS)
consistent with thermalization
for all particles if radial flow
is taken into account.
T and bT are correlated
no direct proof but it is consistent with thermalization
indeed to QGP formation
- collective flow
- thermal behavior
- high energy density
- strange particle production enhancement