Transcript Folie 1

Phenomenological Description of the
Quark-Gluon-Plasma
B. Kämpfer
Helmholtz-Zentrum Dresden-Rossendorf
Technische Universität Dresden
M. Bluhm, R. Schulze, R. Yaresko, F. Wunderlich, M. Viebach
K. Rajagopal, T. Schafer, U. Wiedemann
...: sQGP has no quasi-particle description
1. QGP parametrization: EoS, viscosities
(obituary or revival of QPM?)
2. bottom-up approach within AdS/QCD
page 1
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B.B.Kampfer
universe
LHC
RHIC SPS
AGS
Andronic, PBM, Stachel: *
SIS
page 2
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Scales
Confinement in
Early Universe
no specific relics (unless p + n)
(contrary to BBN: 25% He)
Milne coordinates
HICs
puzzle = entropy production (thermal.)
Neutron Stars
proto-star in core collapse: t ~ 1 sec,
T < 50 MeV
quark cores?
Steiner et al., 1205.6871
page 3
- bursting NSs + photosperic expansion
- transiently accreting NSs in Member
quiescence
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Quasi-Particle Model
Landau & Fermi liquids: adiabaticity & Pauli‘s exclusion principle
Fermi gas  Fermi liquid
no interaction
interaction keeps spin, charge, momenta ...
but modifies masses ...
does not apply always: Luttinger fluid, ...
in this spirit: QGP = Bose + Fermi gases
masses = self-energies
m(T) ~ T G(T),
page 4
large T: G  g(pQCD)
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2-Loop Approximation to CJT/Phi Funct.
 1-loop self-energies
+ HTL self-energies  gauge invariance
page 5
finite widths: Peshier-Cassing,
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Going to High Temperatures
Fodor et al.
Boyd et al.
region of fit
M.Bluhm
page 6
Aoki et al.
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Peshier‘s Flow Equation
given form
Cauchy problem:
initial values
page 7
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Susceptibilities: Test of mu Dependence

10% problem
page 8
data: Allton et al., Nf = 2
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data: Allton et al., Nf = 2
page 9
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also good agreement with Gavai-Gupta data for
data: Allton et al., Nf = 2
sensible test of flow eq. & baryon charge carriers
(no di-quarks etc. needed)
F. Karsch: cumulants & fluctuations  HRG & QPM
page 10
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Purely Imaginary mu
Nf = 4
M.P. Lombardo et al.
T=3.5,2.5,1.5,1.1 Tc
cont. to real mu:
polyn. cont.
Roberge-Weiss Z3 symmetry
page 11
I = II, I‘ = inflected I‘‘
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adjust QPM parameterization at
to get 1. phase border line (= characteristic trought Tc)
2. p(T)
data: Engels et al.
PLB 1997
tests Peshier‘s flow eq. (chem. pot. degree of freedom),
at least for Nf = 4 deg. quarks
page 12
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Viscous Fluids
Intro: V. Greco
water:
Gluon Plasma
AMY 2003
data: Meyer
Nakamura, Sakai
QPM
page 13
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QPM Viscosities
Decomposition:
EoS
transp.
Kinetic eq.:
e.m. tensor:
Relaxation time approx.:
page 14
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EoS
pQCD:
ad hoc
strong coupling:
Gubser, Buchel
further details: Bluhm, BK, Redlich, PLB 2012, PRC 2011
2
page 15
Vosresensky et al. (2011): ambiguity of rel. time ansatz
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data: Boyd et al.
Okoamoto et al.
KSS
page 16
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AdS/YM
instead of QCD
Maldacena 1998
Witten 1998
Gubser et al. 1998
AdS5/CFT4
common symmetry group
SO(2,d)
super YM
gravity5
holography
Einstein + scalar field
QCD4
large-Nc YM
bottom-up approach: adjust V(phi) to EoS
for free: drag & jet quentching, chir. symm.
spectra of glueballs, hadrons ...
quantitytive matching to QCD is difficult
page 17
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non-pert.
Panero: mild/no dependence
EoS SU(3) YM4
I/T4 = T (p/T4)‘
e = I + 3p
s = (I + 4p)/T
cs2 = p‘ / (T p‘‘)
page 18
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Einstein4
Riemann space-time: glk;n = 0
Rij + gij R/2 = k Tij
gravity/geometry
gravity/geometry
matter
matter
Gubser, Kajantie, Kiritsis
Li et al.
maximally symmetric
AdS:
, constant curvature
negative L in
Lorentz inv. vacuum: Tij = (e + p) uiuj + p gij -> - L gij
=0
(e < 0, p > 0)
Einstein‘s GRG is well tested
(PPN coefficients fit observations)
page 19
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Black Holes, e.g. Schwarzschild
ds2 = f(r)-1 dr2 + r2 dO22 – f(r) dt2
f(r) = 1 – 2M/r: r H = 2M  horizon (simple zero)
Hawking temperature
Hawking-Bekenstein entropy
Hawking‘s hairless theorem: M, Q, J
s(T)  EoS
Schwarzschild vacuole in Friedmann-Walker-Lemaitre universe
BH
Schwarzschild
page 20
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z = 1/r
zH
horizon, IR
z=0
AdS, UV
t, x
1st ansatz:
2nd ansatz:
3rd ansatz:
boundary conds.:
AdS
BH
page 21
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page 22
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page 23
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page 24
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Transport Coefficients: Gubser 2008
fluctuations:
linearize Einstein eqs.
Kubo formulae 
shear mode:
with phi as holographic coordinate
(instead of r or z)
bulk mode:
page 25
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mimicks EoS
page 26
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Summary
QPM parametrization of EoS: YM + QGP: mu = 0  T dep.
susceptibilities: mu > 0, mu_u,d
imaginary mu
T  0, mu > 0: quark stars?
AdS/YM: holographic improvement needed
(EoS vs. V(phi) or As(z); pert. regime?
eta = s / 4 pi vs. pert. Regime
zeta(T), zeta/eta vs. (1/3 – vs^2) )
No specific relicts of cosmic confinement (memory loss)
contrary to BBN
next steps: fine tuning of V or As  robustness of zeta?
et al.
spectral functions (no transport peaks) Kajantie
... et al.
quarks, mu > 0
page 27
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Quark Matter in Neutron Stars?
1054 AD: supernova
 radio pulsar
page 28
X ray source
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Neutron Stars & White Dwarfs
2.0
M / M_sun
stable
Chandrasekhar
1.4
unstable
n, (p, e-)
e-, nuclei
p
e, n
10
page 29
20
R [km]
10,000
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Neutron Stars with Quark Cores (1)
2.0
M / M_sun
q
stable
Chandrasekhar
1.4
unstable
n, (p, e-)
e-, nuclei
q
p
e, n
10
page 30
20
R [km]
10,000
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Neutron Stars with Quark Cores (2)
2.0
M / M_sun
density jump e2/e1 is
- very small: 1)
- < 1.5: 2)
- > 1.5: 3)
1)
2)
1.4
unstable
T
3)
CEP
p mix q
Nf = 3
mix
e, n
e1 e2
10
page 31
n
20
R [km]
10,000
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The Third Island
2.0
M / M_sun
density jump is
- small and EoS(q) stiff: 1)
- larger and/or EoS(q) soft: 2)
1)
1.4
BK, PLB 1982
Stocker, Schaffner-B. 2000
2)
T
CEP
p mix q
Nf = 3
mix
e, n
e1 e2
10
page 32
n
20
R [km]
10,000
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Pure Quark Stars
fit to Bielefeld & WuppertalBp data
hybrid stars:
sensitive to
matching of EoS
page 33
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Examples of Side Conditions
T = 1.1 Tc
d
u
e
solid: pure Nf=2 quark matter, electr.neutr.
dashed: Nf=2 quark matter + electrons
in beta equilibrium
page 34
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page 35
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Gubser: V
Li: As(z)
page 36
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page 37
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mild increase (Gubser, Kiritsis)
strong increase (Kharzeev, Tuchin
Karsch et al.)
page 38
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page 39
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page 40
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