Dileptons from Strongly Coupled
quark-gluon plasma (sQGP)
Edward Shuryak
Department of Physics and Astronomy
State University of New York
Stony Brook NY 11794 USA
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Background:
Motivations:
 Reduced scale
=> enhanced
coupling
 Hydro works and
QGP seem to
have remarkably
small viscosity
 Lattice bound
states and large
potentials
New spectroscopy of
sQGP
•Multiple bound states,
90% of them colored. If
so, it explains several
puzzles related to lattice
results:
•Why resonances in
correlators (J/ from
MEM)?
•How rather heavy
quasiparticles can
create high pressure
already at T= 1.5-2 Tc?
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Outline – main ideas
Vectors in QGP and
dileptons:
Bound states (,,) in
L and T forms, and a
near-threshold bump
can tell us what are
the quasiparticle
masses and
interaction strength in
QGP
(Jorge Casalderrey +ES)
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Jet quenching
due to
``ionization”
of new bound
states
(I.Zahed+ES)
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Can we verify existence of bound
states at T>Tc experimentally?
Dileptons from sQGP: an idea
M=1.5-2 GeV
M=.5-.8 GeV
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Motivation 1: RHIC produces ``matter”, not a
fireworks of partons, =>
hydro and
thermodynamics work
l << L
(the micro scale) << (the macro scale)
(the mean free path) << (system size)
(relaxation time) << (evolution duration)
I
•Good equilibration (including strangeness)
is seen in particle rations (as at SPS)
• the zeroth order in l/L , an ideal hydro,
works well (except in hadroic phase)
•Viscosity is the O(l/L) effect, » velocity gradients. Note
that l» 1/( n) and hydro is (the oldest) strong
coupling expansion tool. /s =.1 -.2
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How strong is strong
interaction and where?
How large can s be in
QGP ?
ES,Nucl.Phys.A717:291,2003
In a QCD vacuum the domain of perturbative QCD (pQCD) is
limited by non-pert. phenomena, e.g. by the Q> 1 GeV as well
as by confinement: so s< 0.3
 At high T we get weak coupling because of screening
<(gT) << 1 (the Debye mass Md sets the scale)
 In between, Tc<T<few Tc, there is no chiral/conf. scales
While Md=2T= 350-400 MeV is not yet large: can
s(Md) be .5-1 (?). If so, binding appears. (ES-Zahed,03)

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T
New QCD Phase
Diagram, which
includes ``zero
binding lines”
(ES+I.Zahed hepph/030726)
The lines marked RHIC and SPS show the
adiabatic cooling paths
Chemical potential B
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lattice puzzles
Since Matsui-Satz and subsequent papers
it looked like even J/,c dissolves in QGP
(thus it was a QGP signal)
And yet recent works (AsakawaHatsuda,Karsch et al) have found, using
correlators and MEM, that they survive up
to about T=2Tc . What was wrong?
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New ``free energies” for static
quarks (from Bielfeld)
•Upper figure is
normalized at small
distances: one can
see that there is
large ``effective
mass” for a static
quark at T=Tc.
•Both are not yet
the potentials!
•The lower figure
shows the effective
coupling constant
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
From Bielefld heplat/0406036
•Note that the Debye
radius
produces ``normal” coupling,
but the coeff. is larger
•It becomes still larger if V is used
instead of F, see later
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For a screened Coulomb potential, a
simple condition for a bound state
(4/3)s (M/MDebye) > 1.68
 M(charm) is large, Md is only about 2T
 If (Md) indeed runs and is about ½-1, it is
large enough to bind charmonium till about
T=3Tcor about 500 MeV
(which is above the highest T at RHIC)
 Since q and g quasiparticles are heavy,
M appr. 3T, they all got bound as well !

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Digression:
Relativistic eqns have a critical Coulomb coupling
for falling onto the center
(known since 1920’s)

(4/3)s=1/2 is a critical value for Klein-Gordon eqn, at which
falling onto the center appears. (It is 1 for Dirac).
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New potentials (cont):
after the entropy term is subtracted,
potentials become much deeper
this is how potential I got look like for T = 1; 1.2; 1.4; 2; 4; 6; 10Tc,
from right to left, from ES,Zahed hep-ph/0403127
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Here is the binding and |psi(0)|^2
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If a Coulomb coupling is too strong,
falling onto the center may occur:
but it is still rather difficult to get a binding
comparable to the mass
But we need massless pion/sigma at T=>Tc !
Brown,Lee,Rho,ES hepph/0312175 : near-local
interaction induced by the
``instanton molecules”
(also called ``hard glue” or
``epoxy”, as they survive
at T>Tc
 Their contribution is »
|(0)|2 which is calculated
from strong Coulomb
problem

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Solving for the bound states
ES+I.Zahed, hep-ph/0403127

In QGP there is no confinement =>
Hundreds of colored channels may have
bound states as well!
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The pressure puzzle
(GENERAL)
Well known lattice prediction (numerical
calculation, lattice QCD, Karsch et al) the
pressure as a function of T (normalized to
that for free quarks and gluons)
•This turned out to be the
most misleading picture we
had, fooling us for nearly 20
years
•p/p(SB)=.8 from about .3 GeV to very
large value. Interpreted as an argument
that interaction is relatively weak (0.2)
and can be resumed, although pQCD
series are bad…
BUT: we recently learned that
storng coupling leads to about 0.8
as well!
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(The pressure puzzle, cont.)
How quasiparticles, which according to
direct lattice measurements are heavy
(Mq,Mg = 3T) (Karsch et al) can provide
enough pressure? (exp(-3) is about 1/20)
(The same problems appears in N=4
SUSY YM, where it is parametric,
exp(-1/2) for large =g2Nc>>1)
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The pressure puzzle is
resolved!
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Other observables at T>Tc?
Viscosity, charm diffusion coefficient
=> are binary resonances enough? Chains
\bar q g … g q?
 Succeptibilities at nonzero mu have large
peaks (Karsch et al, mu/T^6 paper):
=> is N bound at T>Tc? Or only diquarks?
 V.Koch et al: what about <SB>/<S^2>?
=> (strange B)/(strange B+M) or
(qs vs \bar q s bound states)(T)

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Can we verify existence of bound
states at T>Tc experimentally?
Dileptons from sQGP:
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Quark mass and the interaction
strength (“s”) via dileptons


Three objects can be
seen at nonzero p,
T,L bound states (at
fixed T<Tz.b.about 2 Tc)
and the near-threshold
enhancement
(``bump”), at any T
Why bump? Because
attraction between antiq q in QGP enhances
annihilation
Example:
pp(gg) -> t t at
Fermilab has a bump near
threshold (2mt) due to gluon
exchanges.
The Gamow parameter
for small velocity
z= (4/3)s/v; can be > 1,
Produces a bump (or
jump): the
Factor z/(1-exp(-z))
Cancels v in phase space
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a nonrelativistic approach with realistic
potentials (Jorge Casalderrey +ES,2004)
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Following the methods developed
for t quark



Khose and Fadin: sum over states, then
Strassler and Peskin: Green function can be
formed of 2 solutions
We get 2 solutions numerically and checked
that published t-pair production for Coulomb
is reproduced up to .2 percent!
Then we used it for ``realistic” potentials
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Study of near-endpoint annihilation rate
using non-rel. Green function, for lattice-based
potential (+ instantons) Im(M) for T=1… 2 Tc
(a warning: very small width)
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Total width is 20,100 or 200
MeV
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Karsch-Laerman, T=1.5 and 3 Tc
Width is not to be
trusted !
Asakawa-Hatsuda
T=1.4Tc
,
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Scattering amplitudes
for quasiparticles
M. Mannarelli. and R. Rapp hep-ph/05050080
\bar q q scattering no q - gluon scattering yet
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QUARK-HADRON DUALITY AND BUMPS IN QCD:
A simple exercise with all M scaling as T
(the worse case scenario)
Operator product expansion tells us that the integral
Under the spectral density should be conserved
(Shifman, Vainshtein, Zakharov 78).
Three examples which satisfy it (left) the same after realistic time integral
Over the expanding fireball (as used in Rapp+ES paper on NA50), divided
by a ``standard candle” (massless quarks) (right)
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Summary on dileptons





In general, 3*3 objects (for each rho, omega and phi
states):L,T vectors plus a near-threshold bump
Most observable is probably T=Tc when Vs are
about .5-.8 GeV in mass
Possibly observable enhancement is in the region
1.5-2 GeV, where 2Mq is about constant in a wide T
interval. Not to be present at SPS but at RHIC
Realistic potential predicts quite interesting shapes,
but the width (and resolution) issue is so far not
quite quantitive.
Sound waves became narrow in strong coupling:
can this mix with omega and produce dileptons?
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Jet quenching by ``ionization”
of new bound states in QGP?
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Calculation of the ionization rate
ES+Zahed, hep-ph/0406100




Smaller than radiative
loss if L>.5-1 fm
Is there mostly near the
zero binding lines,
Thus it is different from
both radiative and elastic
looses, which are simply
proportional to density
Relates to non-trivial
energy dependence of jet
quenching (smaller at 62
and near absent at SPS)
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dE/dx in GeV/fm vs T/Tc for a
gluon 15,10,5 GeV.
Red-elastic, black -ionization
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Conclusions:



Lattice EoS is about
confirmed,
 Dileptons is a
QGP seems to be
way to measure
the most ideal fluid
known
masses of qs and
/s = .1-.2
the strength of
=> QGP at RHIC is
their
in a strong coupling
interactions, via
regime => New
resonances and
spectroscopy: many
old mesons plus
near-threshold
hundreds of exotic
bumps
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colored binary
states
Additional slides
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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, similar
to the well known
sonic boom from
supersonic planes.
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
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Distribution of radial velocity v_r
(left) and modulus v (right).
(note tsunami-like features, a positive and
negative parts of the wave)
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Is such a sonic boom already observed?
Mean Cs=.33 time average over 3 stages=>
= +/-1.23=1.91,4.37
M.Miller, QM04
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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
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Away <pT> vs centrality
STAR,Preliminary
Away core <pT> drops with centrality faster than corona <pT>.
Core hadrons almost identical to medium in central collisions.
A punch-thorugh at the highest trigger?
39
away <pT> dependence on angle
(STAR,preliminary)
Preliminary
<pT> (phi) has a dip structure in central AA.
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Mach shock wave?