Hadron Correlations and Parton Recombination

1
Hadron Correlations and Parton Recombination

• Rainer Fries
• University of Minnesota

Hard Probes 2006 Asilomar
June 11, 2006
2
Hard Probes

• Hard processes as well controlled probes to
  measure properties of the QGP.
• Hard probes ? high momentum transfer, high quark
  mass, high temperature
• Careful which value of our scale is sufficiently
  high depends strongly on the question we ask.

3
Hard Probes

• Careful which value of our
  scale is sufficiently high depends
  strongly on which question we ask.
• Single inclusive pion spectrum in
  pp pQCD works
  from PT ? 1 GeV
• But single inclusive spectra in
  AA dont work up to 5 GeV,
  
• Maybe not even at 10 GeV ??

4
Why Recombination B/M

• Enhanced baryon yield
• p/? 1 in AuAu (for PT 2 4 GeV/c)
• p/? 0.3 in pp,
• p/? 0.1.0.2 in ee-

PHENIX
5
Why Recombination RAA

• No jet quenching for baryons? (RAA RCP 1)
• In the range PT 1.5 5 GeV/c.
• Jet quenching not on the parton level?

PHENIX
6
Why Recombination v2 scaling

• Different v2 saturation for mesons and baryons

7
Baryon/Meson Anomaly

• General baryon/meson pattern p, ?, ?, ? versus
  K, ?, ?, K In the region PT ? 1.5 6 GeV/c

8
Baryon/Meson Anomaly

• General baryon/meson pattern p, ?, ?, ? versus
  K, ?, ?, K In the region PT ? 1.5 6 GeV/c
• No mass effect ? behaves like a pion (m? ? mp ,
  m? gtgt m?)

STAR Preliminary
9
Baryon/Meson Anomaly

• General baryon/meson pattern p, ?, ?, ? versus
  K, ?, ?, K
• No mass effect ? behaves like a pion (m? ? mp ,
  m? gtgt m?)
• v2 of ? lt v2 of proton behaves like meson

10
Baryon/Meson Anomaly

• General baryon/meson pattern p, ?, ?, ? versus
  K, ?, ?, K
• No mass effect ? behaves like a pion (m? ? mp ,
  m? gtgt m?)
• Hadron properties do not matter in this kinematic
  region.
• Only the number of valence quarks!
• We catch a glimpse of hadronization

11
Hadron Correlations

• Away-side jets vanishes
• Ridge on the near side

Away side gone/diffuse
Wiedemann et al.
STAR
AA
pp
?
Broadeningpedestal on near side
?
12
Signatures in Correlations

• Deviations from jet shapes below PT 5 GeV/c
• E.g. ? broadening of the near-side jet cone

Width of the peak in ??
STAR preliminary
13
Fragmentation?

• Hard processes vacuum fragmentation are ruled
  out below 4 6 GeV/c because of RHIC results on
• hadron chemistry
• elliptic flow v2
• Recombination idea hadrons at intermediate PT
  from recombination of soft partons

14
Recombination!

• Fragmentation limit of hadronization for very
  dilute systems (parton density ? 0)
• Recombination hadronization in the opposite
  limit thermalized phase of partons just above Tc

15
Recombination revisited

• Basic assumptions
• Recombine valence quarks
• Instantaneous projection of quark states on
  hadron states
• For simplicity factorize 2-parton distribution
  in 1-parton distributions
• No correlations assumed!

16
Recombination revisited

• Conspiracy of thermal distributions and large P
• i. e. P gtgt M, kT (collinear situation) Boltzmann
  w
• No dependence on shape of ?!
• Baryon meson
• Reco ? Frag competition

fragmenting parton ph z p, zlt1
recombining partons p1p2ph
17
Recombination Fragmentation

• Dual model of hadron production
• Recombination pQCD/fragmentation to describe
  hadron production at RHIC for PT gt 12 GeV/c
• With B. Muller, C. Nonaka, S. A. Bass
• For RHIC
• T 175 MeV
• Radial flow ? 0.55
• Constituent quark masses
• Fit to pion data ? predictive power for all other
  hadron species

18
Spectra Ratios

• Good description of spectra, ratios, RAA for all
  measured hadron species

RJF, Muller, Nonaka, Bass
19
Elliptic Flow Scaling

• Assume universal elliptic flow v2p of the partons
  before the phase transition
• Recombination prediction
• Scaling works for all hadrons
• Deviations for pions arise
  mostly from resonance decays
  (Greco et al.)

20
How robust is v2 scaling?

• Scaling law uses the most primitive
  approximations
• Momentum shared equally between constituents
• Expect correction for realistic wave function ?
  with finite width.
• Numerically effects are small

Momentum shared fractions x and 1-x
21
Fate of the Gluons?

• Are there gluons or sea quarks?
• No effect on particle yields for thermal spectra!
• Resulting elliptic flow for hadrons does not obey
  scaling
• For equally shared momenta

22
Zooming in on v2 Scaling

• We proposed a new variable baryon/meson v2
  asymmetry (B-M)/(BM) for scaled v2.
• First results
• Size and sign of the
  effect predicted
  correctly.
• Gluons could be
  accommodated.

P. Sorensen, QM 05
23
Hadron Correlations

• How can hadrons at intermediate PT show jet-like
  structure?

24
Hadron Correlations

• How can hadrons at intermediate PT show jet-like
  structure?
• Naturally through soft-hard recombination
• Soft-hard hadrons and jet hadrons correlated
• Rudy Hwas talk
• Naturally if the recombining partons are
  correlated

25
2-Particle Correlations

• Recombination of mesons A, B from partons 1,2,3,4
• New permit 2-particle correlations
• Possible ansatz

26
Hot Spots

• Strong energy loss (dE/dx up to 14 GeV/fm)
• a lot of quenched/partially thermalized jets
• Localized deposition of energy and momentum
• Hot Spots?
• Hot spot can be correlated
  with remaining jet
• Partons in the hot spot can
  be correlated
  with themselves
• Add collective effects Mach cone?

27
Associated Yield

• List of assumptions
• Only near side integrate rapidity
• Small correlations, keep only terms linear in c0
  and v2
• Narrow wave functions
• Correlations constant over volume Vc
• Associated yield
• Here

28
Amplification of Correlations

• Q Amplification factor
• Count 2-parton pairs between
  the 2 hadrons for
  effects linear
  in c0, only 1 correlation allowed.
• Uncorrelated background (for meson-meson)

Q4 Meson-meson
Q6 Meson-baryon
Q9 Baryon-baryon
4 pairings that lead to meson correlations
2 pairings without correlating the mesons
29
Numerical Example

• Using Duke parametrization
• consistent with spectra and ratios!
• Consistency with PHENIX data can be reached.

Baryon trigger
Meson trigger
Large correlations from Frag-Frag.
F-F and SS-SS with C00.08x100/Npart (Vcconst.)
Lower associated yield when adding SS-SS without
correlations (C00), especially for baryon
triggers.
RJF, Muller, Bass Phys. Rev. Lett. 94, 122301
(2005)
30
Identified Particles
31
Hadrochemistry in Jet Cones

• The baryon/meson ratio can be an indicator for
  the amount of thermalization in a jet
• Far side produces more baryons than near side

32
Where is Fragmentation?

• Below PT 4 6 GeV/c no go for (hadronic) hard
  probes
• Problems for pQCD fragmentation even above PT
  6 GeV/c ??
• Baryon/meson ratio still too large above 5 GeV/c
  ??

33
Where is Fragmentation?

• Below PT 4 6 GeV/c no go for (hadronic) hard
  probes
• Problems for pQCD fragmentation even above PT
  6 GeV/c ??
• Baryon/meson ratio still too large above 5 GeV/c
  ??
• v2 from jet quenching ??

34
Where is Fragmentation?

• Below PT 4 6 GeV/c no go for (hadronic) hard
  probes
• Problems for pQCD fragmentation even above PT
  6 GeV/c ??
• Baryon/meson ratio still too large above 5 GeV/c
  ??
• v2 from jet quenching ??
• No difference between quark and gluon jets ??
• It may be soft-hard recombination.
• Pick-up of soft quarks by jets

35
Soft/Hard Recombination

• Attempt to treat reco fragmentation
  consistently
• Hwa and Yang jets as cones of parton showers at
  late times fitted to fragmentation functions
• Majumdar, Wang and Wang 2- and 3- quark
  constituent quark fragmentation recombination
  (? Q2 evolution)
• Recombine all partons
• Partons soft/thermal showers from jets
• Two parton distribution function

Partons from 1 jets
soft-soft
Partons from 2 jets
soft-shower
36
Soft/Hard Recombination

• Soft/Hard Reco could be important.
• Signatures in the p/?, ?/K ratio at large PT.
• Produces hadron correlations.

Hwa and Yang
37
Intermediate PT

• Naively expected behavior of observables
• What is found at RHIC
• Some soft physics extends up to 4-6 GeV/c
• But above 2 GeV/c not described by ideal
  hydrodynamics
• Soft-hard region of phase space new phenomena

Soft/Hydro
pQCD
Hydro
ReCo/soft-hard
pQCD
38
Jets Medium

• Recombination alone is not sufficient to
  understand the soft-hard region.
• Uses parameterizations of effects on the parton
  phase
• Need understanding of the mechanisms behind
  jet-medium interaction
• Still much to learn
• LHC will the soft/hard region be larger?

Jets ? Medium
39
Summary

• Soft-hard regime at intermediate PT extends up
  to 6 GeV/c, maybe more.
• Recombination describes hadronization in this
  regime.
• Recombination translates parton correlations into
  hadron correlations possible origin of jet
  correlations
• Hot spots from jet-medium interactions create
  such correlations.
• Soft-Hard correlations are an additional mechanism

40
Backup
41
Recombination Fragmentation

• Competition of hadronization mechanisms
• Fragmentation dominates for power
  law spectra
  in the limit PT ? ?
• Recombination dominates for
  
  exponential spectra
• Note thermal recombination statistical model
  for PT ? ?

Power law
for mesons
Exponential
42
Jets vs Medium

• Apparent question what is a jet, what is the
  medium?
• Possible (not unique) definition
• Jets dominate when the hadron chemistry matches
  expectation for jets in the vacuum
• No pure jet scenario when partons from the
  medium contribute to hadron production
• We compare vacuum fragmentation with
  recombination
• Medium influence on jets effectively
  
  taken into account via energy loss
• Everthing that does not belong to a
  vacuum
  jet, e.g. additional gluon
  radiation,
  is assumed to be part of
  the
  medium (thermalized or not)

43
Correlations from Fragmentation

• Simple model for correlations from fragmentation
• Dihadron fragmentation (Majumder Wang) here
  factorized in single hadron fragmentation
• Gaussian azimuthal dependence
• Note
• Contributions from soft-hard are small in our
  parametrization
• Correlations from soft-hard negligible because of
  the small yields
• Different from other groups.

u thermal
?-
d
Fragmentation u ? ?
d
?
u minijet
44
Identified Particles!

• Again no prediction about the input
  (correlations) on the parton side.
• If predictive power, then for comparison of
  different hadron species.

45
Higher Fock States

• Tower of Fock states, ?th state with n? partons
• Probability for ejection of a very fast cluster
  with n partons from a thermal source at fixed P
  is independent of n!
• Elliptic flow
• scaling violated even for very narrow wave
  functions (xi ? 1/n?)

46
Conical Flow?

• Preliminary data suggest
  double peak
  away side
  correlation
• Mach cone?
• More conservative scenario
  flowing hot spots?
• Defocussing through radial flow
• Supported by PT,trig dependence?
• Has to be ruled out before any more daring
  conclusion

47
Summary

• Jets deviate in shape and hadrochemistry from
  vacuum for values below 6 GeV/c
• Exact definition needed.
• To study jets and energy loss PT,trigger gt 6
  GeV/c mandatory, maybe more