Magnetic side of Strongly coupled QuarkGluon Plasma

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Magnetic side of Strongly coupled Quark-Gluon
Plasma

• (GGI program,
• June 2008)
• Edward Shuryak
• Stony Brook

Collaborators Jinfeng Liao, Marco Cristoforetti
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outline

• Map and main questions
• Electric-magnetic duality and couplings
  (fight,competition) on the QCD phase diagram
• Lattice monopoles behave like the usual
  particles lattice correlators vs MD
• Novel plasmas with both electric and magnetic
  particles MD gt transport
• Stable and metastable flux tubes
• BEC condensation criterium for interacting gases
• conclusions

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Prologue multiple views on sQGP
(which forced us to learn a lot in the last few
years)
Quantum mechanics
Stronly coupled cold trapped Atoms 2nd best
liquid
Manybody theory
Lattice simulations
Quasiparticles Potentials correlators
Bound states of EQP and MQP J/psi,mesons,baryons,
calorons
Bose-Einstein Condensation -gt confinement
EoS
Flux tubes-gt

• sQGP

RHIC data
Hydrodynamics
Molecular dynamics
Monopoles
Transport properties, Entropy generation
Plasma physics
E/M duality
Collective modes Energy loss, Mach cones
AdS/CFT duality
Gauge theories, SUSY models
Black hole physics, String theory
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The only hydro slide (P.Kolb)

• 3 stages take about the same time at RHIC
• QGP, mixed phase, hadronic phase
• News is that mixed phase magnetic plasma

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Deconfinement and Electric-magnetic
fight/competition in sQGP
.
Magnetic plasma monopoles and dyons Assumed
dominant at 0.9ltTlt 1.5Tc
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Magnetic objects and their dynamics classics

• t Hooft and Polyakov discovered monopoles in
  Non-Abelian gauge theories
• t Hooft and Mandelstamm suggested dual
  superconductor mechanism for confinement
• Seiberg and Witten shown that it does work in N2
  Super YangMills theory

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Recent developments

• LiaoES running coupling gt magnetic liquid near
  Tc
• ChernodubZakharovgt high monopole density near
  Tc, e-3p from monopoles
• DElliaDAlessandro gt monopole density and
  spatial correlators
• LiaoES gt correlators are the same as in the
  Coulomb liquid

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electric/magnetic couplings (e/g) run in the
opposite directions!
Liao,ES hep-ph/0611131
?s(electric) ?s(magnetic)1
Old good Dirac condition (in QED-type units e2
?s)
?s(el)
at the eg equilibrium line ?s(el) ?s(mag)
1 (the best liquid there?)
?s(mag)
monopoles must get sufficently weakly coupled
before BEC deconfinement, also they are much
lighter/denser than gluons/quarks gt?s(mag)
smaller than ?s(el) how small can ?s(mag) be?
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Electric and magnetic screening from the lattice
Nakamura et al, 2004 arrow shows the
self-dual EM point
MeltMm Magnetic Dominated At T0
magnetic Screening mass Is about 2 GeV (de
Forcrand et al) (a glueball mass) (Other lattice
data -Karsch et al- show how Me Vanishes at Tc
better)
MegtMm Electrric dominated
ME/TO(g) ES 78 MM/TO(g2) Polyakov 79
Why is QGP getting magnetic as TgtTc?
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Strong coupling regime in plasma physics Gamma
ltEpotgt/ltEkingt gtgt1gas gt liquid gt solid

• Strongly compressed matter inside Jupiter etc
  when electrons gets collective
• dusty plasmas at International Space Station
• This is of course for /- Abelian charges,
• But green and anti-green quarks do the
  same!

• local order would be preserved in a liquid also,
• as it is in molten solts (strongly coupled TCP
  with
• ltpotgt/ltkingtO(60), about 3-10 in sQGP)

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Gelman,ES,Zahed,nucl-th/0601029
With a non-Abelian color gt Wong eqn
Gas, liquid
solid
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Lattice SU(2) gauge theory, monopoles found and
followed by Min.Ab.gauge DeTar 1980s, Kanazawa
and ITEP group

• x-Correlations
• give Coulomb like MM potential
• First lattice sighting of a liquid!

Recent results
-
monopole density strongly grows as Tgt Tc

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Our MD for 50-50 MQP/EQP
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?s(electric) and ?s(magnetic)
do run in opposite directions!

• Squares fitted magnetic coupling, circles its
  inverse compared to asymptotic freedom (dashed)
• Effective plasma parameter (here for magnetic)
• So, the monopoles are never really weakly
  coupled!

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VFTS potential energy V(r,T) from
Bielefeld/BNL lattice group (Karsch)

• tension nearly 5 times that at T0 (black line)

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Two potentials - two tensions
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two types of flux tubes

• Stable with supercurrent (no dissipation),
• metastable with normal current

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• Fslowall level crossing, VFTS fastno level
  crossing (ESZahed,03)
• Landau-Zener formula (1932),for transition when
  2 levels are crossing with the velocity v12
• Creation of metastable flux tube is possible at
  and even above Tc

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We solve ellipsoidal bags with 2 charges at focal
points

• bag constant related to potential at any T
• This constant is made of two components,
  condenced and uncondeced monopoles

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Condences monopoles ltF
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Uncondenced monopoles lt V

• Direct observation of MAG monopoles wrapping
  around lattice (time)

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• dE/dx??V
• lt Energy loss
• v2ltcos2phigt
• Nobody was able to get so large v2 if absorbtion
  is proportional to density
• But we do !
• So main dE/dx seems to be near Tc?

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So why are collisions so often in sQGP making it
the best liquid? Because of magnetic bottle
effect static eDipoleMPS
Note that Lorentz force is O(v)!

E
M
V
E-
-
Monopole rotates around the electric field line,
bouncing off both charges (whatever the sign)
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two charges play ping-pong with a monopole
without even moving!
Indeed, collisions are much more frequent than
in cascades

• Dual to Budkers
• magnetic bottle

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MD simulation for novel plasma containing both
charges and monopoles (Liao,ES hep-ph/0611131)
monopole admixture up to M5050 , 1000
particles, numerically solveddiffusion decreases
indefinitely, viscosity does not
50-50 mixture makes the best liquid, as
it creates maximal trapping
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short transport summary log(inverse viscosity
s/eta)- vs. log(inverse heavy q diffusion const
D2piT) (avoids messy discussion of couplings)
-gtStronger coupled -gt
Most perfect liquid

• RHIC data very small viscosity and diffusion
• vs theory - AdS/CFT and our MD

4pi
MD results, with specified monopole fraction
Weak coupling end gt (Perturbative results shown
here) Both related to mean free path
50-50 E/M is the most ideal liquid
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Understanding monopole dynamics further

• Chernodub,V.Zakharov monopole percolation on
  the lattice, monopole contribution to e-3p, etc
• Claudia RattiES HiggsingltL(T)gt for g,q,
• tHooft-Polyakov monopoles lattice data (e.g
  n(mon,T)) gtmasses of q,g,m and
  ?s(el,T),?s(mag,T)
• Marco Cristoforetti ES Bose-condensation in
  strongly interacting liquids gt Monopole mass at
  Tc from Feynman condition

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Bose-Einstein condensation of strongly
interacting particles (with M.Cristoforetti,now
TU Munich)

• Feynman theory polygon jumps BEC if
  ?S(jump)ltSc (1.65 for ideal gas, 1.44 from
  combinatorics of polygons
• if used for He4 Tc3.5K not 2.17 as observed)

d

• We calculated instantons for particles jumping
  paths in a liquid and
• solid He4 incuding realistic atomic potentials
  and confirmed by quantum 1-body path int.
  with/without permutations numerically, to refine
  conditions when BEC transitions take place

Jumping paths Feynman, interacting
Liquid He4 is superfluid, But solid He4 is NOT
supersolid,why? lt interacting stronger because
of a bit higher density
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ltPotential in He4the whole row moves by
agtdelta S/atom
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BEC (confinement) condition for monopoles

• For charged Bose gas (monopoles) the action for
  the jump can be calculated similarly, but
  relativistically jumps in space d and in time
• Comparable)
• ?SM sqrt(d2(1/Tc)2) ?S(interaction) Sc
  1.44
• provides the monopole mass M at Tc
• M Tc approx 1.5 gt M(monopoles) as low as 200 MeV
• (to be compared to 600-800 MeV for q,g and 1 gev
  for dyons)

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Conclusions

• Two tensions gt two flux tubes gt two components
  of the monopole ensemble, condenced and
  uncondenced
• This is the region where electric/magnetic
  couplings cross 1
• Magnetic component is also a liquid!
• the most perfect liquid (because of the
  magnetic-bottle trapping) for 50-50
  electric/magnetic plasma
• RHIC data
• on transport (dE/dx, eta/s,D), ADS/CFT and
  electric/magnetic QGP qualitatively agree! But
  why?

• QGP strongly coupled liquid with record low
  eta/s, diffusion, large dE/dx
• Large density of normal (non-Bose-condensed)
• monopoles near Tc may be the reason
• (Is it also true in quasi-conformal regime Tgt2Tc?
  LHC will tell)

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reserve
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Do we have Higgsing (ltA0gt) in QCD at TgtTc in AA
collisions? lt its evolution is quite slow

• At RHIC the QGP lifetime is about 5 fm/c
• (Same for mixed phase, same for hadronic)