Recombination Models Hadronization of a dense parton system

1
Recombination ModelsHadronization of a dense
parton system

• Rainer Fries
• University of Minnesota
• Plenary Talk at QM 2004
• Oakland CA --- January 15, 2004

2
Outline

• Hadronization and fragmentation
• The ReCo (recombination/coalescence) idea
• The leading particle effect
• What can ReCo do for RHIC?
• Azimuthal anisotropy v2
• ReCo implementations
• Myths and facts
• Conclusions
• Thanks to my collaborators B. Müller, S. A.
  Bass, C. Nonaka

3
Hadronization

• We produce "free" partons in high energy
  collisions like ee-, ep, pp, AA.
• Partons in the final state have to be converted
  into hadrons.
• Can we learn about the parton phase from a theory
  of hadronization?

Non-Perturbative QCD
4
Fragmentation

• There is a theory at large PT pQCD
  factorization.
• Long- and short-distance contributions separated
  for single parton fragmentation.

• Fragmentation functions D are not
• calculated determined from ee- data.
• Works well for pion production in pp
• at RHIC.

5
Limitations of Fragmentation

• Fragmentation is not working
• in central heavy ion collisions at RHIC.
  Fragmentation
• energy loss seem to work above 6 GeV/c. But
  below
• ? Baryon enhancement, dependence of RAA on
  hadron species
• in the low PT/forward region ? Leading particle
  effect
• when the single parton picture breaks down.

FF modified in the medium by parton energy loss
(Wang, Guo Gyulassy, Levai, Vitev ...)
RCP from PHENIX
6
From Fragmentation to Recombination

• With more partons around multiple parton
  fragmentation (higher twist)
• If phase space is filled with partons,
  recombine/coalesce them into hadrons.
• Use just the lowest Fock state, i.e. valence
  quarks
• qqq?B qq?M

7
The Leading Particle Effect

• K.P. Das R.C. Hwa Phys. Lett. B68, 459 (1977)
  Quark-Antiquark Recombination in the
  Fragmentation Region
• Braaten, Jia, Mehen Phys. Rev. Lett. 89, 122002
  (2002)

Recombination of beam partons in forward
direction.
Asymmetry of D mesons in forward direction, ?0
from LO fragmentation.
E791 ?- beam hard cc production recombine c
with d valence quark from ?- reco of c with d
8
RHIC puzzles

• Anomalous baryon enhancement.
• Difference in baryon and meson v2.

PHENIX
p/?1
PHENIX
RCP1 for protons
Saturation of v2 at different PT and on
different levels.
9
Recombination for a dense parton system

• ReCo of hadrons convolution of Wigner functions
• Where does ReCo win?

Wab(12) wa(1)wb(2)
Exponential
fragmenting parton ph z p, z
Power law
recombining partons p1p2ph
10
Azimuthal anisotropy v2

• Anisotropy v2
• Voloshin, Lin Ko, Molnar, Nonaka v2 from ReCo
• v2 scaling law
• v4, v6 from ReCo Chen, Ko, Lin

11
v2 Scaling
P. Sorensen
Perfect scaling for all measured hadrons, some
deviation for pions (from ? decays)
P. Sorensen
Baryons are pushed further in PT
12
ReCo Challenges

• Current formalism not suitable at very low PT
• Particle number scaling.
• Hadronic rescattering?
• Energy conservation, particles off the mass shell
• (2?2, 3?2 instead of 2?1, 3?1 processes)
• Decreasing entropy?
• ? include resonances, ???? etc.
• Correlations in the hadron spectrum.

13
Duke ReCo

• Duke/Minnesota/Kyoto (Fries, Müller,Nonaka,Bass,As
  akawa)
• Recombine thermal ensemble of massive quarks
  (constituent quarks) at the phase transition.
• Add pQCD calc. using fragmentation and energy
  loss.
• No soft-hard ReCo resonances studied, but no ?.
• Many different hadron species b dependence.

Hadr. hypersurface ? T175 MeV Radial flow v0.55c
14
Texas ReCo / Ohio ReCo

• Texas AM/Budapest (Greco, Ko, Levai, Chen)
• Monte Carlo implementation (using also spatial
  overlap)
• Soft (thermal/AMPT) and hard (minijet) partons
• Soft-hard coalescence is allowed.
• Effects of resonances studied ? ? significantly
  increases the low PT yield of pions solution to
  the entropy problem?
• Resonances don't destroy the v2 scaling law.
• Ohio State (Lin, Molnar)
• ReCo as a solution to the opacity puzzle input
  MPC.
• ? Denesh Molnar's talk

15
Results for RHIC
Duke
ReCo dominates up to 4..6 GeV/c fragmentation
and energy loss takes over above.
Texas
FragCoal
Frag
????
FragCoalSH
Texas
Texas
Duke
Good description of the different hadron species
16
Elliptic flow results
Duke
Texas
When does v2 from pQCD take over?
????
Ohio
Experimental result v2(s) v2(u,d) What about
charm?
? Chiho Nonaka's poster
17
Back to Fragmentation

• Oregon (Hwa, Yang)
• Fragmentation function is a black box.
• Early attempts to calculate FF with ReCo
• Migneron, Jones, Lassila PRD 26, 2235 (1982)
• Let jet partons shower and recombine.
• (Convert gluons to quark antiquark pairs)
• Thermal-Thermal, Thermal-Shower,
• Shower-Shower ReCo for a meson.

18
Results on fragmentation
Oregon
Oregon
Shower distributions from ?, K FF check proton
FF.
Oregon shower-thermal is very important at RHIC.
? Rudy Hwa's talk
19
Myths about ReCo
Facts about ReCo

• ReCo makes pQCD jet quenching obsolete.
• pQCD has to dominate for PT??.
• Without large jet quenching, ReCo might be
  invisible.
• ReCo contradicts hydrodynamics (v2 scaling).
• v2 mass splitting at low PT is perfectly
  explained by hydro, no scaling there.
• ReCo is free of particle correlations.
• Wrong. Hadron correlations reflect parton
  correlations.

20
Mass vs valence quark number

• Pure hydro pQCD descriptions associate
  anomalous hadron behavior at intermediate PT with
  mass effects (Hirano, Nara)

K. Schweda
STAR ? and K behave like mesons, despite of the
large mass ReCo prediction!
21
Correlations I
2-meson production
Partons with pairwise correlations
Using narrow width appr.
Meson-meson, baryon-baryon, baryon-meson
correlations
22
Correlations II

• Parton correlations trivially translate into
  hadron correlations.
• Modelling of correlations on the parton side
  baryon/meson difference quark/antiquark
  difference.
• Soft-hard/thermal-shower ReCo gives such
  correlations.
• Parton correlations even in
• the "thermal" regime?

T. Trainor
STAR 2-point velocity correlations
hD h1-h2
away-side same-side
fD f1-f2
23
A Glance at LHC
More hard partons, but stronger energy loss.
Thermal phase will be pushed out further!
Fries, Müller Proc. for LHC 2003 CERN Yellow
Rep. "Hard probes..."
24
Conclusions

• Hadronization of a dense phase space of partons
  can be described by ReCo.
• ReCo is the dominant hadronization mechanism for
  central AuAu collisions at RHIC for PT GeV/c.
• ReCo naturally explains differences between
  hadron species baryon enhancement, v2 scaling,
  RAA/RCP...
• All observed hadron species seem to obey the ReCo
  systematics (?0, ??, K0, K?, ?, p, ?, ?, ?, d
  etc.)
• Different implementations agree on basic
  concepts dense parton phase with collective
  properties.
• The future explore the soft-hard region, role of
  resonances, v2 scaling violations, charm,
  2-particle correlations ....

25
The End
26
Backup
27
ReCo Hard Scattering

• T. Ochiai, Prog. Theor. Phys. 75 (1986) 1184

28
Is the parton phase accessible?

• How well defined are results for the parton
  phase?
• Results for the parton spectrum can have
  different interpretations (e.g. minijet vs
  shower)
• Consensus (thermalized) dense parton phase with
  collective flow.
• Elliptic flow seems to be an unambiguous property
  of the parton phase

Duke