phenomenological description of the quark-gluon-plasma

B. Kampfer I Institute of Radiation Physics I www.hzdr.deMember of the Helmholtz Associationpage 1

B. Kampfer I Institute of Radiation Physics I www.hzdr.de

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


hadrons

quar

ks &

glu

ons

LHC RHIC SPSAGS

SIS

universe

An

dro

nic

, P

BM

, S

tach

el:

*


Scales

Confinement in Early Universe

no specific relics (unless p + n)(contrary to BBN: 25% He)

HICs

puzzle = entropy production (thermal.)

Neutron Stars proto-star in core collapse: t ~ 1 sec, T < 50 MeVquark cores?

Milne coordinates

Steiner et al., 1205.6871 - bursting NSs + photosperic expansion- transiently accreting NSs in quiescence


Landau & Fermi liquids: adiabaticity & Pauli‘s exclusion principle

Fermi gas Fermi liquid

no interaction interaction keeps spin, charge, momenta ...but modifies masses ...

in this spirit: QGP = Bose + Fermi gases masses = self-energies

m(T) ~ T G(T), large T: G g(pQCD)

Quasi-Particle Model

does not apply always: Luttinger fluid, ...


2-Loop Approximation to CJT/Phi Funct.

1-loop self-energies

+ HTL self-energies gauge invariance

finite widths: Peshier-Cassing, Bratkovskaya


Going to High Temperatures

Boyd et al.

Fodor et al.

Aoki et al.

region of fit

M.Bluhm


Peshier‘s Flow Equation given form

Cauchy problem: initial values


Susceptibilities: Test of mu Dependence

data: Allton et al., Nf = 2

10% problem



also good agreement with Gavai-Gupta data for

sensible test of flow eq. & baryon charge carriers (no di-quarks etc. needed)

F. Karsch: cumulants & fluctuations HRG & QPM


Purely Imaginary mu

M.P. Lombardo et al.

polyn. cont.

Roberge-Weiss Z3 symmetry

T=3.5,2.5,1.5,1.1 Tc

Nf = 4

cont. to real mu:

I = II, I‘ = inflected I‘‘

QPM


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


water:

Gluon Plasma

Viscous Fluids

data: Meyer Nakamura, Sakai

AMY 2003

QPM

Intro: V. Greco


QPM Viscosities

Decomposition:

Kinetic eq.:

e.m. tensor:

Relaxation time approx.:

EoS

transp.


further details: Bluhm, BK, Redlich, PLB 2012, PRC 2011

EoS

strong coupling:Gubser, Buchel

pQCD:

ad hoc

2 Vosresensky et al. (2011): ambiguity of rel. time ansatz


KSS

data: Boyd et al. Okoamoto et al.


AdS/YMinstead of QCD

Maldacena 1998Witten 1998Gubser et al. 1998

AdS5/CFT4

super YM

gravity5

holographyQCD4

Einstein + scalar field 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

common symmetry group SO(2,d)


EoS SU(3) YM4 Panero: mild/no dependence

I/T4 = T (p/T4)‘

e = I + 3ps = (I + 4p)/Tcs

2 = p‘ / (T p‘‘)

non-pert.


Einstein4

Riemann space-time: glk;n = 0

Rij + gij R/2 = k Tij

gravity/geometrygravity/geometry

mattermatter

Gubser, Kajantie, Kiritsis

Li et al.

AdS: , constant curvature negative L in

Lorentz inv. vacuum: Tij = (e + p) uiuj + p gij -> - L gij

= 0Einstein‘s GRG is well tested (PPN coefficients fit observations)

maximally symmetric

(e < 0, p > 0)


Black Holes, e.g. Schwarzschild ds2 = f(r)-1 dr2 + r2 dO2

2 – f(r) dt2

f(r) = 1 – 2M/r: r H = 2M horizon (simple zero)

Hawking temperature Hawking-Bekenstein entropyHawking‘s hairless theorem: M, Q, J

s(T) EoS

Schwarzschild vacuole in Friedmann-Walker-Lemaitre universe

BH

Schwarzschild


z = 1/r

t, xAdS, UV

horizon, IR

z = 0

zH

1st ansatz:

2nd ansatz:

3rd ansatz:

boundary conds.: AdS

BH


Transport Coefficients: Gubser 2008

fluctuations:

linearize Einstein eqs.

shear mode:

with phi as holographic coordinate (instead of r or z) Kubo formulae

bulk mode:


mimicks EoS


next steps: fine tuning of V or As robustness of zeta? spectral functions (no transport peaks) quarks, mu > 0

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

Kajantie et al.... et al.


Quark Matter in Neutron Stars?

1054 AD: supernova radio pulsar

X ray source


Neutron Stars & White Dwarfs

R [km]

M / M_sun

1.4

2.0

10 20 10,000

unstable

stable

e, n

p

Chandrasekhar

e-, nuclei

n, (p, e-)


Neutron Stars with Quark Cores (1)

R [km]

M / M_sun

1.4

2.0

10 20 10,000

unstable

stable

e, n

p

Chandrasekhar

e-, nuclei

n, (p, e-)

q

q


Neutron Stars with Quark Cores (2)

R [km]

M / M_sun

1.4

2.0

10 20 10,000

unstable

1)2)

3)

density jump e2/e1 is- very small: 1)- < 1.5: 2)- > 1.5: 3)

T

n

CEP

mixNf = 3

e, n

p qmix

e1 e2


The Third Island

R [km]

M / M_sun

1.4

2.0

10 20 10,000

T

n

CEP

mixNf = 3

e, n

p qmix

e1 e2

1)

2)

density jump is- small and EoS(q) stiff: 1)- larger and/or EoS(q) soft: 2)

BK, PLB 1982Stocker, Schaffner-B. 2000


Pure Quark Starsfit to Bielefeld & WuppertalBp data

hybrid stars:sensitive tomatching of EoS


Examples of Side Conditions

T = 1.1 Tc

solid: pure Nf=2 quark matter, electr.neutr.dashed: Nf=2 quark matter + electrons in beta equilibrium

d

u

e


Gubser: VLi: As(z)


mild increase (Gubser, Kiritsis)strong increase (Kharzeev, Tuchin Karsch et al.)

phenomenological description of the quark-gluon-plasma

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