Quark Gluon Plasma

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• Quark Gluon Plasma
• coupling and particle content
• (learning from cold atomic plasmas)

B. Jacak March 22, 2007
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stolen from Thomas Pohl
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What is going on at RHIC?

• The objects colliding inside the plasma are
  clearly not baryons and mesons
• They are also not quarks and gluons totally free
  of the influence of their neighbors
• Are there even objects colliding in there?
• Is it, in fact, strongly coupled?

hydrodynamic flow implies that there are but q,g
number is not conserved (baryon number is)
ltPEgt/ltKEgt of WHAT?
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What we DO know
PRL87, 052301 (2001)
Colliding system expands

• e ? 5.5 GeV/fm3 (200 GeV AuAu)

value is lower limit longitudinal expansion
rate, formation time overestimated
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energy loss by induced gluon radiation
I. Vitev
dAu
interaction of radiated gluons with gluons
in the plasma greatly enhances the amount of
radiation
AuAu
calculate using opacity expansion (answer L/mfp
3.5) ? r 1000 gluons/dy e 15
GeV/fm3 hydro initial condition constrained by
data also requires e 15 GeV/fm3
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Plasma Coulomb coupling parameter G

• ratio of mean potential energy to mean kinetic
  energy
• a interparticle distance
• e charge
• T temperature
• typically a small number in a normal, fully
  shielded plasma
• G 1/(number particles in Debye sphere)
• when G gt 1 have a strongly coupled, or non-Debye
  plasma
• many-body spatial correlations exist
• behave like liquids, or even crystals when G gt
  150
• lD lt a

Ge (e2/4pe0 a)/kBTe
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Debye screening in QCD a tricky concept

• in leading order QCD (O. Philipsen,
  hep-ph/0010327)
• vv

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give up on the concept?

• Of course not!!!
• Two options proposed by Philipsen
• 1) assume a pole in the propagator and attempt to
  measure its value from the exponential fall-off
  in some fixed gauge (done with lattice QCD)
• 2) seek a manifestly gauge invariant definition
• idea determine lD for strongly coupled plasma
  convert e inside to particle density to get G

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lets get a feel by oversimplifying

• estimate G ltPEgt/ltKEgt
• using QCD coupling strength g
• gluon density (? T3)
• ltPEgtg2/d d 1/(41/3T)
• ltKEgt 3T
• G g2 (41/3T) / 3T
• g2 4-6 (value runs with T)
• for T200 MeV plasma parameter G 3
• quark gluon plasma should be a strongly coupled
  plasma
• As in warm, dense plasma at lower (but still
  high) T
• dusty plasmas, cold atom systems
• such EM plasmas are known to behave as liquids!

G gt 1 strongly coupled, few particles inside
Debye radius
see M. Thoma, J.Phys. G31(2005)L7
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2nd try take screening length from lattice QCD
Karsch, et al.
running coupling
coupling drops off for r gt 0.3 fm
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use to estimate Coupling parameter, G

• G ltPEgt/ltKEgt but also G 1/ND
• for lD 0.3fm and e 15 GeV/fm3
• VD 4/3 p lD3 0.113 fm3
• ED 1.7 GeV
• energy of thermal, magnetic excitations gT, g2T
• to convert to number of particles, use gT or g2T
• for T 2Tc and g2 4
• get ND 1.2 2.5 ? G 1
• NB for G 1
• plasma is NOT fully screened its strongly
  coupled!
• affects interaction s!
• other strongly coupled plasmas behave as liquids,
  even crystals for G 150
• dusty plasmas, cold atomsions , warm dense
  matter

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generally a phenomenon in crystals but not liquids
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measuring viscosity in dusty plasma
melt crystal with laser light induce a shear flow
(laminar) image the dust to get velocity study
spatial profiles vx(y) moments, fluctuations ?
T(x,y) curvature of velocity profile ? drag
forces viscous transport of drag in ?
direction from laser compare to viscous hydro.
extract h/r shear viscosity/mass density PE
vs. KE competition governs coupling phase of
matter
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minimum h at phase boundary?
strongly coupled dusty plasma
B. Liu and J. Goree, cond-mat/0502009
quark gluon plasma
Csernai, Kapusta McLerran nucl-th/0604032
minimum arises because kinetic part of h
decreases with G potential part increases
(measure by density-density correlation)
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a minimum is characteristic
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screening length bound state spectroscopy
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summary

• its probably too soon to draw conclusions
• quark gluon plasma features
• fluid behavior
• opacity
• large drag on heavy quarks
• look like other strongly coupled plasmas
• color screening in QGP is not complete

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• backup slides

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from S. Ichimaru
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expect low viscosity in strongly coupled plasma
S. Ichimaru, Univ. of Tokyo
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why is correlation among particles interesting?
S(p) 1/N ltr(p)r(-p)gt r(p) is Fourier
transformed particle density r(r)
plasma physicists hope to measure by Thomson
scattering ? small angle scattering of soft g
from e charges coherent scattering off the
electrons is there an analogous measurement for
us?
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screening masses from gluon propagator

• Screening mass, mD, defines inverse length scale
• Inside this distance, an equilibrated plasma is
  sensitive to insertion of a static source
• Outside its not.

Nakamura, Saito Sakai, hep-lat/0311024
T dependence of electric magnetic screening
masses Quenched lattice study of gluon
propagator figure shows mD,m 3Tc, mD,e
6Tc at 2Tc lD 0.4 0.2 fm
magnetic screening mass is non-zero not very
gauge-dependent, but DOES grow w/ lattice size
(long range is important)