Hadron Correlations from Recombination

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Hadron Correlations from Recombination
Fragmentation
Rainer J. Fries University of Minnesota
Workshop Hot Quarks Taos NM, July 23 2004
In Collaboration with S.Bass, C.Nonaka, B. Müller
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But first
a Short Tour of the ReCo Universe
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Hadronization

• Partons created in a high energy collision have
  to be converted to hadrons. We don't know the
  dynamics non-perturbative QCD!
• From ee- collisions fragmentation.
  single parton ? hadrons
• Generally works for pp etc.
  
  at large transverse momentum.
• What happens with the bulk of
  the partons in a HI collision?

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From Fragmentation to ReCo

• Fragmentation 1 parton has to hadronize
• With more partons around multiple parton
  fragmentation (higher twist)
• If phase space is filled with partons
  recombine/coalesce them into hadrons!

Dilute parton system High virtualities
Dense parton system Low virtualities
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Recombination

• Ideas going back to the 70s (BjorkenFarrar,
  Anisovich, Hwa)
• Leading particle effect recombination in very
  forward direction (Hwa et al., Braaten et al.)
• Recombination is dominated by the valence quark
  structure (n2,3).
• Are we dealing with constituent quarks?
• Where is chiral symmetry breaking?
• Baryons (3 x pT) pushed out
• further than mesons (2 x pT)
• ? baryon enhancement
• (compared to fragmentation)

fragmenting parton ph z p, zlt1
recombining partons p1p2ph
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ReCo Formalism

• ReCo of hadrons convolution of Wigner functions
• assuming thermal parton distributions
• minijets/showers or independent fragmentation
• Implementations by different groups available
• ReCo is very effective for thermal spectra
• Fragmentation is more effective for power law
  spectra.

Parton
Meson
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Solving RHIC puzzles

• Recombining thermalized
• parton phase pQCD
• Transition between 4 (mesons)
• and 6 GeV/c (baryons)
• Consistent description of all
• measured hadron species,
• RAA, ratios.

Duke
Greco et al.
Duke
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Elliptic flow

• Suppose partons have elliptic flow v2 before
  hadronization
• Meson/baryon elliptic flow (Voloshin, LinKo)

• Does it work?
• Yes
• Quark counting holds
• for K, p, ?, ?, ?, d (?),
• ? ( res correction ??)

P. Sorensen
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The Bigger Picture

• For single particle spectra recombination is
  just a microscopic realization of the statistical
  model!
• (for PT ? ? and exponential spectra masses,
  shapes of wave functions are negligible)
• But who would believe the statistical model at 4
  GeV/c?
• ReCo pushes out soft physics
• by factors x2 and x3 !
• Clearly visible in RAA and v2
• measurements at RHIC.
• It is not a mass effect (?, K!).

STAR P. Sorensen
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Why can it work?

• (Non-perturbative) QCD dynamics drops out
• if the partons are (quasi) thermalized.
• if process is dominated by kinetic energies (PT
  gtgt M).
• Then recombination counting quantum numbers
  momentum conservation.
• Works from PT 2 GeV/c on, however obscured by
  fragmentation at higher PT.
• One can make it more complicated to extend the
  range of validity ...

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Where is the QGP?

• Quark counting rules were once very useful to
  convince us that there is a substructure in
  hadrons.
• RHIC 2003 A quark counting rule for an
  observable that describes a collective
  effect!
• System must have reached state with detailed
  balance at the time of hadronization ?
  thermalization?
• Parton deg of freedom collective behavior
  thermalization ??

A classic example
counting constituent quarks!
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Some Final Thoughts

• We only see the lowest Fock state constituent
  quarks?
• Deep inelastic scattering average parton
• configuration, lots of sea quarks and gluons
• Exclusive processes hard scattering as a filter
  in favor of low Fock states
• Recombination is there a filter for low Fock
  states?
• Remember very low scale
• set by T!
• Where is chiral symmetry
• breaking?

Diakonov Petrov Bowman et al.
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Recent Developments

• Higher order harmonics (P. Kolb, Ko et al.)
• Hadron correlations Jets at intermediate PT?

No simple scaling!
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And now, correlations
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Associated yields

• Trigger hadron A, associated hadron B. Measure
  pairs uncorrelated pairs (including flow) per
  trigger. Associated yield as a function of
  relative azimuthal angle
• PT window for trigger gt PT for associated hadrons
  (down to 1.7 GeV/c)
• Clear jet-like structure at
• intermediate PT. Very similar
• to pp (jet fragmentation).

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ReCo and Correlations

• Claim hadrons coming from recombination are
  always uncorrelated jets are seen down to 2
  GeV/c.
• This is true if we choose thermalized
  uncorrelated quark distributions as input for
  ReCo hadronization.
• But we don't know these distributions. ReCo is
  there to help us understand them.
• So can there be correlations in the parton phase?
  We know the answer YES
• v2 is a good example for correlations in momentum
  space.
• From v2 ReCo even enhances the correlation
  effect!

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Jets Correlations

• Fast partons in the medium experience strong
  interactions ? energy loss, jet quenching
• Wang, Gyulassy, Vitev, BDMPS, Zakharov,
  Wiedemann and many more...
• What happens to the medium?
• X.N. Wang 10 GeV quark loses 14 GeV/fm!
• Large energy deposition ? local heating
• Large momentum transfer ? directional information
• Jet quenching is followed by a phase of
  dissipation.
• Are the hot spots completely washed out?
• How global is thermal equilibrium?
• The hot spot is correlated with the remaining
  jet.
• Even if the hard parton is completely stopped,
  the partons in the spot will be correlated.

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Experimental Evidence

• Strong jet quenching is established fact
• Entangling of medium and jets can be seen in
  correlation measurements. STAR nucl-ex/0407001
• Hot spots from jets
• participate in the strong
• longitudinal expansion
• of the medium.

T. Trainor
STAR 2-point velocity correlations
hD h1-h2
away-side same-side
fD f1-f2
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Expanding the formalism

• Formalism so far factorize n-parton Wigner
  function into 1-particle phase space
  distributions
• Sufficient to describe single hadron spectra!
• We take it one order further and introduce
  2-particle correlations.

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Modeling parton correlations

• Our factorized ansatz for the correlation
  function
• Gaussian correlations in azimuthal angle ? and
  rapidity y.
• The two terms correspond to correlations from the
  same jet and correlations from the recoil jet.
• Widths and correlation strength can be different
  for near and far side correlations
• No attempt to have a microscopic theory. It's an
  ansatz, but it is compatible with the jets hot
  spots picture.

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Correlations from SS-SS ReCo

• 2-hadron yield
• Associated yield as a function of relative
  azimuthal angle at midrapidity near-side only
• using some simplification like narrow wave
  function approximation, flat PT correlations,
  only terms linear in v2 and c0 etc.)
• Ni are single particle spectra
• C0 c0 Vc / V? rescaled normalization factor
  Vc correlation volume
• Q amplification factor

(SS-SS)
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Amplification and Background

• Amplification factor larger for
• baryons.
• Count possible 2-parton correlations between the
  2 hadrons for effects linear in c0, only 1
  correlation is allowed.
• Background for NAYAB from SS-SS (for meson-meson)

4 pairings that lead to meson correlations
2 pairings without correlating the mesons
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Correlations from Fragmentation

• The correct way dihadron fragmentation (Majumder
  Wang)
• We estimate the contribution by a simple model
• factorization in 1-hadron fragmentation functions
  D(z)
• Gaussian smearing of the collinear limit in y and
  ?.
• Associated yield for F-F
• Background from independent fragmentation (2
  minijets!)

(F-F)
Minijet spectrum
?E average energy loss of parton a
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Soft-Hard Recombination

• Recombination of a medium parton and a
  minijet/shower parton.
• Is it necessary to explain measured hadron
  correlations?
• In the Duke reco model S-H contribution is very
  small. Different for parametrizations by Greco et
  al., Hwa et al.!
• Simplest possible process for fragmentation
  soft-hard recombination (F-SH)
• There are even more processes for dihadron
  production, e.g. F-SS, SH-SH, SH-SS ...

u thermal
?-
d
d
Fragmentation u ? ?
?
u minijet
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The F-SH Process

• Our model for a?Ab (F) bc?B (Reco)
• v Vc/V? lt 1
• We calculate this process only for ?-?
  production.
• The process where the SH meson is the trigger
  meson has to be taken into account as well.

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Numerical example
Baryons
Mesons
F-F and SS-SS with C00.08, VcNpart.
Large correlations from F-F, favoring baryon
triggers.
F-F and SS-SS with C00.08x100/Npart (Vcconst.)
Lower associated yield when adding SS-SS without
correlations (C00), especially for baryon
triggers.
F-SH (?-? only) v0.5
Calculations done using the Duke
parametrization.
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Baryons vs Mesons

• Non-trivial baryon/meson behavior by mixing of
  F-F and SS-SS contributions.
• But are there jet cones
• for baryon triggers?
• Centrality dependence given
• by the scaling of Vc.
• Yields for F-SH are
• negligible (using Duke
• parameters).

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Conclusions

• Recombination provides an excellent description
  of single hadron spectra, ratios, nuclear
  modification factors and elliptic flow for all
  measured hadron species.
• Recombination enhances correlations in the parton
  phase, similar to the amplification of elliptic
  flow.
• Jets dumping energy and momentum into the medium
• are good candidates for the origin of such
  correlations.
• There is a non-trivial interplay of different
  hadronization mechanisms that can determine
  flavor dependence and centrality dependence.