Transcript Emerging theory of (strongly coupled) quark

Understanding strongly coupled
quark-gluon plasma (sQGP)
(SIS program,
Cambridge, Aug.2007)
Edward Shuryak
Stony Brook
The emerging theory of sQGP
Manybody
theory
Flux
tubes->
Plasma
physics
Stronly coupled
cold trapped
atoms
Quantum
mechanics
Quasiparticles
Potentials
correlators
Bound states
Bose-Einstein of EQP and MQP
Condensation J/psi,mesons,baryons,calorons
->
confinement
Hydrodynamics
sQGP
Molecular
dynamics
Energy
loss,
Collective
modes
Mach cones
Transport properties
Lattice
simulations
EoS
Monopoles
E/M duality
AdS/CFT
String theory
Gauge
theories,
SUSY models
RHIC
data
Outline
Qs: Why do we have strongly coupled quark-gluon plasma (sQGP) at
RHIC? Is it related to deconfinement (T=(1-1.5)Tc) or quasiconformal behaviour at $T>1.5Tc? What is the role of magnetic
objects? Can one explain RHIC results using AdS/CFT? A picture is
emerging…
 RHIC findings: collective flows and jet quenching
 Viscosity and diffusion constant from AdS/CFT,
complete gravity dual?
 Phase diagram and lattice. Electric and magnetic quasiparticles (EQPs
and MQPs) are fighting for dominance (J.F.Liao,ES, hep-ph/0611131,PRC 07)
Flux tube existence/dissolution
magnetic bottle effect
(J.F.Liao,ES, 0706.4465[hep-ph]) the
 molecular dynamics (MD) of Non-Abelian plasma with
monopoles(B.Gelman, I.Zahed,ES, PRC74,044908,044909 (2006), J.F.Liao,ES, hepph/0611131,PRC 07):
 transport summary; From RHIC to LHC
 Summary: are two explanations related???
RHIC findings
Strong radial and elliptic flows are very
well described by ideal hydro =>
``perfect liquid”
 Strong jet quenching, well beyond
pQCD gluon radiation rate, same for
heavy charm quarks (b coming)
 Jets destroyed and their energy goes
into hydrodynamical ``conical flow”

From Magdeburg hemispheres (1656)
to dreams of 1970’s…
QCD vacuum is
so compicated…
•“We cannot pump out complicated objects
populating the QCD vacuum, but we can
pump in something else, namely the QuarkGluon Plasma, and measure explosion”
(QGP in 1970’s was expected to be just a simple nearideal quark-gluon gas, to ``fill the bag”)
One may have an absolutely correct
theory and still
make accidental discoveries…
Columbus believed if he goes west he should
eventually come to India
But something else was on the way…
We believed if we increase the energy density, we should
eventually get weakly interacting QGP. But something
else was found on the way, sQGP
How Hydrodynamics Works at
RHIC
Elliptic flow
How does the system respond to initial spatial anisotropy?
Dense or dilute?
If dense, thermalization?
If thermalized, EoS?
)
The coolest thing on Earth, T=10 nK or
10^(-12) eV can actually produce a
Micro-Bang ! (O’Hara et al,
Duke )
Elliptic flow with ultracold trapped
Li6 atoms, a=> infinity regime
The system is extremely dilute, but
can be put into a hydro regime, with
an elliptic flow, if it is specially tuned
into a strong coupling regime via the
so called Feshbach resonance
Similar mechanism was proposed (Zahed and myself) for
QGP, in which a pair of quasiparticles is in resonance
with their bound state at the “zero binding lines”
2001-2005: hydro describes radial and elliptic flows for all
secondaries , pt<2GeV, centralities, rapidities, A (Cu,Au)…
Experimentalists were very sceptical but were
convinced and ``near-perfect liquid” is now official,
=>AIP declared this to be discovery #1 of 2005 in physics
proton
v_2=<cos(2 phi)>
pion
PHENIX,
Nucl-ex/0410003
red lines are for
ES+Lauret+Teaney
done before RHIC data,
never changed or fitted,
describes SPS data as well!
It does so because of the
correct hadronic matter
/freezout via (RQMD)
One more surprise from RHIC: strong jet
quenching and flow of heavy quarks
nucl-ex/0611018
Heavy quark quenching as
strong as for light gluon-q
jets!
Radiative energy loss only
fails to reproduce v2HF.
Heavy quark elliptic flow:
v2HF(pt<2GeV) is about the
same as for all hadrons!
=>
Small relaxation time t or
diffusion coefficient DHQ
inferred for charm.
Sonic boom from quenched jets
Casalderrey,ES,Teaney, hep-ph/0410067; H.Stocker…
• the energy deposited by
jets into liquid-like
strongly coupled QGP
must go into conical
shock waves
• We solved relativistic
hydrodynamics and got
the flow picture
• If there are start and
end points, there are
two spheres and a cone
tangent to both
Wake effect or “sonic boom”
Two hydro modes can be excited
(from our linearized hydro solution):
a ``diffuson”
a sound
2 Mach cones
in strongly
coupled
plasmas
(thanks to B.Jacak)
PHENIX jet pair distribution
Note: it is only
projection of a
cone on phi
Note 2: more
recent data from
STAR find also a
minimum in
<p_t(\phi)> at
180 degr., with
a value
Consistent with
background
The most peripheral bin, here no matter
AdS/CFT
from gravity in
AdS5 to strongly
coupled CFT
(N=4 SYM)
plasma
what people dream about for LHC
experments -- a black hole formation -does happen, in each and every RHIC
AuAu event =>
thermalization, All info is lost except
the overall entropy=area of newly
formed b.h.horizon
viscosity from AdS/CFT
(Polykastro,Son, Starinets 03)
Kubo formula <Tij(x)Tij(y)>=>
 /s  hbar /4
•
Left vertical line is our 4d Universe,
(x,y are on it)
• Temperature is given by position of
a horizon (vertical line, separationg
 /s
 /s

hbar
1/4/4

• From interier of``black brane”
T=T(Howking radiation) (Witten 98)
a graviton
• Correlator needed is just
propagator G(x,y)
• Blue graviton path does not
contribute to Im G, but
the red graviton path (on which it is
absorbed) does
Both viscosity and entropy are
proportional to b.h. horizon, thus
such a simple asnwer

Heavy quark diffusion
J.Casalderrey+ D.Teaney,hep-ph/0605199,hep-th/0701123
One quark
(fisherman) is
In our world,
The other (fish) in
Antiworld
(=conj.amplitude)
String connects them and
conduct waves in one
direction through the
black hole
A
N
T
I
W
O
R
L
D
W
O
R
L
D
subsonic
supersonic
Left: P.Chesler,L.Yaffe
Up- from Gubser et al
Both groups made
Amasingly detailed
Description of the
conical flow from
AdS/CFT=> not much
is diffused
Gravity dual to the whole collision:
“Lund model” in AdS/CFT
• Expanding/cooling fireball=
departing Black Hole
(Nastase 03, Sin,ES and Zahed 04,Janik-Peschanski 05…)
If colliding objects made of heavy quarks
• Stretching strings -- unlike Lund model those are
falling under the AdS gravity and don’t break
(Lin,ES hep-ph/0610168)
• The falling membrane is created which separate
two regions of two different metrics: it is
becoming a b.h. horizon
Now linearized version in progress
(field from a static Maldacena string recently done
Lin,ES arXiv:0707.3135, T00 ->1/r7 )
AdS5
Center=
Extremal b.h.
AdS/CFT suggests completely new
pictures of gauge theory topology
• Instantons = D-1 brane=point in the bulk,
at large Nc coalesce together (Mattis,Khose,Dorey 90’s)
• Monopoles = endpoints of D1 (string-like) branes
• Electric-magnetic duality includes
duality between baryons and calorons
(finite T instantons) as Nc monopoles
(known before ads <= Kraan,van Baal ….)
Explaining transport in sQGP:
electric/magnetic fight
“Classical QGP” and its
Molecular Dynamics
Electrons have the same charge -e all the time,
but our quasiparticles (quarks, gluons,…) have colors
which is changing
in time
Fraction of quasiparticles are magnetically
Charged (monopoles and dyons) which
fight each other
At T<Tc they somehow (?) make a
“dual superconductor”
An example of ``dyonic baryon”=finite T instanton
top.charge Q=1 config.,
dyons identified via fermionic zero modes
Berlin group - Ilgenfritz
et al
Red, blue and
green U(1) fields
3 dyons with corresp.
Field strengths, SU(3),
Each (1,-1,0) charges
Electric and magnetic scrrening
Masses, Nakamura et al, 2004
My arrow shows the ``self-dual” E=M point
Me<Mm
Magnetic
Dominated
At T=0 magnetic
Screening mass
Is about 2 GeV
(de Forcrand et al)
(a glueball mass)
Other data
(Karsch et al)
better show how
Me
Vanishes at Tc
Me>Mm
Electrric
dominated
ME/T=O(g)
ES 78
MM/T=O(g^2)
Polyakov 79
New (compactified) phase diagram
describing an electric-vs-magnetic competition
Dirac condition (old QED-type units e^2=alpha, deliberately no Nc yet)
<- n=2 adjoint
Thus at the e=g line
Near deconfinement line g->0 in IR
(Landau’s U(1) asymptotic freedom)
e-strong-coupling
because g in weak!
=>
Why is this diagram better? =>
There are e-flux tubes in all blue region, not only in the
confined phase! In fact, they are maximally enhanced at Tc
Energy and entropy
associated with 2
static quarks
is very large near Tc
from lattice potntials BielefeldBNL
• R->infinity means there
are 2 separate objects
• Entropy=20 implies
exp(20) states
• At R=(.3-1.2)fm both are
about linear in R <=
What object is that?
pQCD
predicts
a negative U
Energy and entropy
associated with 2
static quarks
is very large near Tc
from lattice potntials BielefeldBNL
• R->infinity means there
are 2 separate objects
• Entropy=20 implies
exp(20) states
• At R=(.3-1.2)fm both are
about linear in R <=
What object is that?
pQCD
predicts
a negative U
e-flux tubes above Tc?
(with J.F.Liao, archive 0706.4465 [hep-ph])
• Dual superconductivity at T<Tc as a confinement
mechanism (‘tHooft, Mandelstam 1980’s) =>
monopole Bose condensation =>
electric flux tubes (dual to Abrikosov-Nielsson-Olesen vortices)
• Can uncondenced MQPs do the same at T>Tc ?
MQPs are reflected from a region with E field =>
pressure => flux tubes compression in plasma
• We solve quantum mechanics of motion in each partial wave
magnetic flux tubes at the Sun,
(work without any superconductor!): so we need
to work out the exact conditions
where classical electrons rotate
around it
• B: about 1 kG,
• Lifetime: few months
Classical and quantum
mechanics of the flux tube
Red trajectory A => nu=0
(velocity at large r directed to the center)
Black one B => m=0
(which goes through
the center because no m^2/r^2 barrier)
Self-consistent solution => stability
condition of the flux tube
Z=exp(-mu/T)
dissolution of the tube
roughly at T>1.4Tc
(lattice Bielefeld-BNL)
• Assuming this is the case
and using our criterion we
get density of magnetic
QPs=>
• n(magnetic,T=1.3Tc)=
(4-6)fm-3
• Twice less than about 10
fm^-3 at T=0 (Bali et al,
from vacuum confining
strings)
Is sQGP full of flux tubes?
evolution with T:
• T=0, dual Meissner =>ANO
• At T<Tc complicated shape can produce
entropy=o(L) but it is Nc independent => no
electric objects, no color changed
• At T>Tc heavy gluon (and quark) quasiparticles
first appear as ``beads”
S=(L/a)log7+(L/b)log(Nc)
• As T grows further => less monopoles of higher
energy => no electric field flux suppression
=>``electric polymers”
•
Very high T => wQGP, electric plasma, no bound
states
(Presumably gluons-in-the-tube correspond to AdS/CFT
Minahan string solutions and are also dual
to monopoles-in-the-tube solutions recently
Worked out by Tong et al,Shifman et al)
Bose-Einstein condensation of interacting
particles (=monopoles)
(with M.Cristoforetti,Trento)
• Feynman theory (for liquid He4): polygon jumps
BEC if exp(-∆S(jump))>.16 or so (1/Nnaighbours)
We calculated ``instantons” for particles
jumping paths in a liquid and
solid He4 incuding realistic atomic potentials
and understood 2 known effects:
(i) Why Tc grows with repulsive
interaction<= because a jump proceeds
faster under the barrier
(ii) no supersolid He => density too large
and action above critical
Marco is doing Path Integral simulations with
permutations numerically, to refine conditions
when BEC transitions take place
Jumping
paths:
Feynman,
interacting
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)
∆S=M sqrt(d2+(1/Tc)2)+ ∆S(interaction) = Sc
=1.65-1.89
(first value from Einstein ideal gas, second from liquid He)
provides the monopole mass M at Tc
M Tc approx 1.5 =>
M as low as 300 MeV
Strong coupling in plasma physics:
Gamma= <|Epot|>/<Ekin> >>1
gas => liquid => solid
• 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
<pot>/<kin>=O(60), about 3-10 in sQGP)
Wong eqn
can be rewritten as x-p canonical pairs,
1 pair for SU(2), 3 for SU(3), etc. known as
Darboux variables. We did SU(2) color => Q is a unit
vector on O(3)
Gelman,ES,
Zahed,nuclth/0601029
With a non-Abelian color => Wong eqn
Gas,
liquid
solid
So why is such plasma a good liquid?
Because of magnetic-bottle trapping:
static eDipole+MPS
Note that Lorentz force is O(v)!
E+
+
V
E-
-
M
We found that two charges play pingpong by a monopole without even
moving!
Chaotic, regular
and escape trajectories
for a monopole, all
different in initial
condition by 1/1000
only!
Dual to Budker’s
magnetic bottle
MD simulation for plasma with monopoles
(Liao,ES hep-ph/0611131)
monopole admixture M50=50% etc
again diffusion decreases indefinitely, viscosity does not
D 1/^( 0.6  0.8)

It matters: 50-50 mixture
makes the best liquid, as it
creates ``maximal confusio
short transport summary
log(inverse viscosity s/eta)- vs. log(inverse heavy q
diffusion const D*2piT) (avoids messy discussion of couplings)
->Stronger coupled ->
•
•
RHIC data: very small
viscosity and D
vs theory - AdS/CFT and
MD(soon to be explained)
Most perfect liquid
4pi
MD results, with
specified
monopole fraction
Weak coupling end =>
(Perturbative results shown here)
Both related to mean free path
50-50% E/M is the most ideal liquid
From RHIC to LHC:
(no answers, only 1bn$ questions)
Will ``perfect liquid” be still there?
 Is jet quenching as strong, especially for
c,b quark jets and much larger pt?
 Is matter response (conical flow at
Mach angle) similar? (This is most
sensitive to viscosity…)

From SPS to LHC
• lifetime of QGP phase nearly doubles, but v2 grows only a
little, to a universal value corresponding to EoS p=(1/3)epsilon
• radial flow grows by about 20% => less mixed / hadronic
phase (only 33% increase in collision numbers of hadronic
phase in spite of larger multiplicity)
(hydro above
from S.Bass)
Conclusions



Strongly coupled
QGP is produced
at RHIC T=(1-2)Tc
This is the region
where transition
from magnetic to
electric
dominance
happen
at T<1.4 Tc still
Lots of magnetic
objects =>
E-flux tubes

RHIC data on
Good liquid
transport (eta,D),
because of
ADS/CFT and
magnetic-bottle
trapping
classical MD all
Classical MD is qualitatively agree
being done,
!
lowest viscosity
for 50-50%
electric/magnetic
plasma

•AdS/CFT => natural
applications of
string theory
N=4 SYM is
nonconfining and
Strongly coupled!
Are these two
pictures
related?
reserve
Effective coupling is large!
alphas=O(1/2-1) (not <0.3 as in pQCD applications)
tHooft lambda=g2Nc=4piNc=O(20)>>1-1
Bielefeld-BNL lattice group: Karsch et al

At e=m line both effective gluons and
monopoles have masses M about 3T exp(3)<<1 is our classical parameter
(Boltzmann statistics is good enough)
 At T=Tc monopoles presumably go into BoseEinsetein condensation => new semiclassical
theory of it for strongly interacting Bose
gases, tested on He4
 (M.Cristoforetti, ES, in progress)