Dynamics of Hadronization

1
Dynamics of Hadronization Interplay of
Fragmentation and Recombination
Steffen A. Bass
Duke University RIKEN-BNL Research Center

• The baryon puzzle at RHIC
• Recombination Fragmentation Model
• Results single particle observables,
  correlations entropy

• R.J. Fries, C. Nonaka, B. Mueller S.A. Bass,
  PRL 90 202303 (2003)
• R.J. Fries, C. Nonaka, B. Mueller S.A. Bass,
  PRC 68 044902 (2003)
• C. Nonaka, B. Mueller, M. Asakawa, S.A. Bass
  R.J. Fries, PRC 69 031902 (2004)
• R.J. Fries, S.A. Bass B. Mueller, PRL in print
  (nucl-th/0407102)
• C. Nonaka, B. Mueller, S.A. Bass M. Asakawa,
  nucl-th/0501028

2
Standard Model of Hadronization
?

• low pt
• hadron yields ratios fit with a SM
• spectra via Hydro
• high pt
• pQCD is applicable, hadronization via
  fragmentation
• a fast parton fragments via a color string a ?
  hX
• hadron spectrum is given by

3
The baryon puzzle _at_ RHIC

• where does the large proton over pion ratio at
  high pt come from?
• why do protons not exhibit the same suppression
  as pions?
• fragmentation yields Np/Np
• fragmentation starts with a single fast parton
  energy loss affects pions and protons in the same
  way!

ratio of KKP fragmentation functions for p and p
from u quarks
4
Species dependent saturation of elliptic flow

• hyperon v2 saturates later and higher than kaon
  v2.
• same effect observed for protons and pions.
• at low pT the phenomenology seems better
  described in mT m0 than pT , indicating hydro
  scaling, yet scaling breaks down for high pT
• what drives the different pT scales for KS and ?
  v2?
• novel mechanism of baryon formation?

5
RecombinationFragmentation Model

• basic assumptions
• at low pt, the quarks and antiquark spectrum is
  thermal and they recombine into hadrons locally
  at an instant
• features of the parton spectrum are shifted to
  higher pt in the hadron spectrum
• at high pt, the parton spectrum is given by a
  pQCD power law, partons suffer jet energy loss
  and hadrons are formed via fragmentation of
  quarks and gluons

6
Recombination Pros Cons

• Pros
• for exponential parton spectrum, recombination
  is more effective than fragmentation
• baryons are shifted to higher pt than mesons,
  for same quark distribution
• understand behavior of protons!
• Cons

fragmenting parton ph z p, z
recombining partons p1p2ph

• simple recombination may violate entropy
  conservation
• gluons at hadronization need to be converted

7
Recombination new life for an old idea

• High Energy Physics Phenomenology
• K.P. Das R.C. Hwa, Phys. Lett. B68, 459 (1977)
• Quark-Antiquark Recombination in the
  Fragmentation Region
• description of leading particle effect
• T. Ochiai, Prog. Theo. Phys. 75, 1184 (1986)
• E. Braaten, Y. Jia T. Mehen, Phys. Rev. Lett.
  89, 122002 (2002)
• R. Rapp E.V. Shuryak, Phys. Rev. D67, 074036
  (2003)
• Heavy-Ion Phenomenology
• T. S. Biro, P. Levai J. Zimanyi, Phys. Lett.
  B347, 6 (1995)
• ALCOR a dynamical model for hadronization
• yields and ratios via counting of constituent
  quarks
• R.C. Hwa C.B. Yang, Phys. Rev. C66, 025205
  (2002)
• R. Fries, B. Mueller, C. Nonaka S.A. Bass,
  Phys. Rev. Lett. 90
• V. Greco, C.M. Ko and P. Levai, Phys. Rev. Lett.
  90
• Anisotropic flow
• S. Voloshin, QM2002, Nucl. Phys. A715, 379
  (2003)
• Z.W. Lin C.M. Ko, Phys. Rev. Lett 89, 202302
  (2002)
• D. Molnar S. Voloshin, Phys. Rev. Lett 91,
  092301 (2003)

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Recombination nonrelativistic formalism

• use thermal quark spectrum given by w(p)
  exp(-p/T)
• for a Gaussian meson wave function with momentum
  width ?M, the meson spectrum is obtained as

• similarly for baryons

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Recombination relativistic formalism

• choose a hypersurface S for hadronization
• use local light cone coordinates (hadron
  defining the axis)
• wa(r,p) single particle Wigner function for
  quarks at hadronization
• ?M ?B light-cone wave-functions for the meson
  baryon respectively
• x, x (1-x) momentum fractions carried by the
  quarks
• integrating out transverse degrees of freedom
  yields

10
Recombination vs. Fragmentation
Fragmentation
never competes with recombination for a thermal
(exponential) spectrum
but it wins out at large pT, when the spectrum
is a power law (pT)-b
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Hadron Spectra
12
Hadron Ratios vs. pt
13
Flavor Dependence of high-pt Suppression

• RF model describes different RAA behavior of
  protons and pions
• in the fragmentation region all hadron flavors
  exhibit jet-quenching

14
Elliptic Flow

• anisotropic or elliptic flow is sensitive to
  initial geometry

low pt domain
high pt domain
more flow in collision plane than perpendicular
to it
less absorption in collision plane than
perpendicular to it

• total elliptic flow is the sum of both
  contributions

r(pt) relative weight of the fragmentation
contribution in spectra
15
Parton Number Scaling of v2

• in leading order of v2, recombination predicts

• smoking gun for recombination
• measurement of partonic v2 !

16
Resonance v2 scaling violations

• QGP resonances
• hadronizing QGP, no rescattering
• HG resonances
• hadronic phase, h-h rescattering

Key v2 is additive for composite particles
17
Two-Particle Correlations a Challenge?

• PHENIX STAR measure associated yields in pT
  windows of a few GeV/c.
• trigger hadron A, associated hadron B associated
  yield as a function of relative azimuthal angle
• clear jet-like structure observed at
• intermediate pT
• very similar to pp jet fragmentation?
• analyze as function of integrated yield
• simple recombination of uncorrelated
  thermal quarks cannot reproduce two
  particle correlations

18
Recombination Inclusion of Correlations

• Recombination approach allows for two particle
  correlations, provided they are contained in the
  parton source distributions
• Three distinct types are conceivable F-F, SH-F
  and SS-SS
• Ansatz for SS-SS for two mesons, use product of
  correlated parton distributions
• Which results in a correlated two hadron yield

19
Correlations Proof of Principle
Meson-trigger
Baryon-trigger

• strong correlations from fragmentation, but
  suppressed by soft triggers
• combination of hard fragmentation and soft
  recombination correlations with a fixed
  correlation volume is compatible with data

20
Recombination Entropy Puzzle

• Does recombination violate the 2nd law of
  thermodynamics ?
• particle number decreases drastically in
  hadronization via reco
• restrict reco approach to intermediate momenta,
  ignore bulk
• decay of hadronic resonances as possible solution
  (Greco et al.)
• need estimate of entropy at hadronization

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Entropy in the Hadronic Phase

• 1) resonance gas model
• massless particles
• massive particles

2) final state entropy from data
bosons
Pal Pratt, PLB578,310 (2004)
fermions
STAR PRC68, 044905 (2003)
MeV

• HydroUrQMD calculations indicate a 5 increase
  in multiplicity due to rescattering in the
  hadronic phase

4.72
5.15

• entropy content is larger than often assumed!

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Entropy in the Deconfined Phase

• Lattice QCD CP-PACS with Nt6 Nf2

• entropy content of the deconfined phase near TC
  is strongly reduced due to interactions!

systematic uncertainties include thermodynamic
limit, continuum limit, unphysically large quark
mass
23
Entropy Puzzle resolved?
Quark Phase
Hadron Phase

• No direct comparison of the entropy content of
  both phases
• Volume at hadronization ?
• Number of quarks on the lattice ?

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Summary Outlook

• The Recombination Fragmentation Model
• provides a natural solution to the baryon puzzle
  at RHIC
• describes the intermediate and high pt range of
• hadron ratios spectra
• jet-quenching phenomena
• elliptic flow
• leading / next-to-leading particle correlations
• issues to be addressed in the future
• treatment of gluons higher Fock states (work
  in progress)
• realistic space-time dynamics of parton source
• need improved data of identified hadrons at high
  pt

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The End
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Connecting the dots
jet production
fragmentation
jet quenching
parton recombination
HBT
radial flow
reco/SM?
shattered color-glas
hydrodynamic evolution
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Parton Number Scaling of Elliptic Flow

• in the recombination regime, meson and baryon v2
  can be obtained from the parton v2 in the
  following way

• neglecting quadratic and cubic terms, one finds a
  simple scaling law