Dileptons from Strongly Coupled quarkgluon plasma sQGP

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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

• 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?

• Motivations
• Reduced scale gt enhanced coupling
• Hydro works and QGP seem to have remarkably small
  viscosity
• Lattice bound states and large potentials

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Outline main ideas
Jet quenching due to ionization of new bound
states (I.ZahedES)

• 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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Can we verify existence of bound states at TgtTc
experimentally?Dileptons from sQGP an idea
M1.5-2 GeV
M.5-.8 GeV
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Motivation 1 RHIC produces matter, not a
fireworks of partons, gt hydro and
thermodynamics work

• l ltlt L
• (the micro scale) ltlt (the macro scale)
• (the mean free path) ltlt (system size)
• (relaxation time) ltlt (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.A717291,2003

• In a QCD vacuum the domain of perturbative QCD
  (pQCD) is limited by non-pert. phenomena, e.g. by
  the Qgt 1 GeV as well as by confinement so ?slt
  0.3
• At high T we get weak coupling because of
  screening
• ?lt?(gT) ltlt 1 (the Debye mass Md sets the scale)
• In between, TcltTltfew Tc, there is no chiral/conf.
  scales
• While Md2T 350-400 MeV is not yet large can
• ?s(Md) be .5-1 (?). If so, binding appears.
  (ES-Zahed,03)

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New QCD Phase Diagram, which includes zero
binding lines(ESI.Zahed hep-ph/030726)
T
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 (Asakawa-Hatsuda,Karsch et
  al) have found, using correlators and MEM, that
  they survive up to about T2Tc . 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 TTc.
• Both are not yet the potentials!
• The lower figure shows the effective coupling
  constant

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Fitting F to screened Coulomb

• From Bielefld hep-lat/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) gt 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
  T3Tcor 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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DigressionRelativistic eqns have a critical
Coulomb coupling for falling onto the center
(known since 1920s)

• (4/3)?s1/2 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 occurbut it is still rather
difficult to get a bindingcomparable to the
massBut we need massless pion/sigma at TgtTc !

• Brown,Lee,Rho,ES hep-ph/0312175 near-local
  interaction induced by the instanton molecules
  
• (also called hard glue or epoxy, as they
  survive
• at TgtTc
• Their contribution is ?(0)2 which is
  calculated from strong Coulomb problem

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Solving for the bound statesESI.Zahed,
hep-ph/0403127

• In QGP there is no confinement gt 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 N4 SUSY YM, where
  it is parametric, exp(-?1/2) for large
  ?g2Ncgtgt1)

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The pressure puzzle is resolved!
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Other observables at TgtTc?

• Viscosity, charm diffusion coefficient
  gt are binary resonances enough? Chains \bar q g
  g q?
• Succeptibilities at nonzero mu have large peaks
  (Karsch et al, mu/T6 paper) gt is N
  bound at TgtTc? Or only diquarks?
• V.Koch et al what about ltSBgt/ltS2gt? gt
  (strange B)/(strange BM) or
• (qs vs \bar q s bound states)(T)

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Can we verify existence of bound states at TgtTc
experimentally?Dileptons from sQGP
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Quark mass and the interaction strength (?s)
via dileptons

• Example pp(gg) -gt 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 gt 1,
• Produces a bump (or jump) the
• Factor z/(1-exp(-z))
• Cancels v in phase space

• Three objects can be seen at nonzero p, T,L
  bound states (at fixed TltTz.b.about 2 Tc) and the
  near-threshold enhancement (bump), at any T
• Why bump? Because attraction between anti-q q in
  QGP enhances annihilation

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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 rateusing
non-rel. Green function, for lattice-based
potential ( instantons) Im?(M) for T1 2 Tc (a
warning very small width)
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Total width is 20,100 or 200 MeV
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Width is not to be trusted ! Asakawa-Hatsuda,
T1.4Tc
Karsch-Laerman, T1.5 and 3 Tc
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Scattering amplitudesfor quasiparticlesM.
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
RappES paper on NA50), divided by a standard
candle (massless quarks) (right)
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Summary on dileptons

• In general, 33 objects (for each rho, omega and
  phi states)L,T vectors plus a near-threshold
  bump
• Most observable is probably TTc 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 ionizationof new bound
states in QGP?
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Calculation of the ionization rateESZahed,
hep-ph/0406100

• Smaller than radiative loss if Lgt.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)

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,
• QGP seems to be the most ideal fluid known
• ?/s .1-.2
• gt QGP at RHIC is in a strong coupling regime gt
  New spectroscopy many old mesons plus hundreds
  of exotic colored binary states

• Dileptons is a way to measure masses of qs and
  the strength of their interactions, via
  resonances and near-threshold bumps

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Additional slides
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Sonic boom from quenched jets Casalderrey,ES,Teane
y, 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 stagesgt
?? /-1.231.91,4.37
flow of matter normal to the Mach cone seems to
be observed! See data from STAR,
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 ltp_t(\phi)gt at 180 degr., with a
value Consistent with background
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Away ltpTgt vs centrality
STAR,Preliminary
Away core ltpTgt drops with centrality faster than
corona ltpTgt. Core hadrons almost identical to
medium in central collisions. A punch-thorugh at
the highest trigger?
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away ltpTgt dependence on angle (STAR,preliminary)
ltpTgt (phi) has a dip structure in central AA.
Mach shock wave?