Particle Production from Soft Processes

1
Particle Production from Soft Processes
P. Fachini Brookhaven National Laboratory
2
Outline

• (Local) Thermal Equilibrium
• Spectra
• Statistical Model, Blast-Wave and Hydro
• Further Test of (Early) Thermalization and Hydro
• Particle Elliptic Flow v2
• Coalescence and Recombination
• Elliptic Flow v2 Scaling
• Freeze-outs (Late Stages)
• Resonances
• Late stages of the collision
• Modification of ?0 Spectral Shape
• Conclusions

3
Spectra
?sNN 200 GeV
4
Baryon Enhancement

• Models qualitatively describe the ratios at
  intermediate pT and underpredict the ratios at
  higher pT
• Above pT 6 GeV/c ? ratio is the same in dAu
  and central AuAu ? limit of the coalescence
  domain?

5
Spectra Strangeness
AuAu 200 GeV
6
Spectra Strangeness
AuAu 62 GeV
?
7
Thermal Model
H. Caines, SQM2006

• Reproduce well stable particles

pp Tch 171 9 MeV ?S 0.53 0.04
AuAu Tch 168 6 MeV ?S 0.92 0.06
Preliminary
Preliminary
Canonical Ensemble
8
Blast-Wave Parameterization
The picture thermal random motion
collective motion
Flow profile used ?r ?s (r/R)n
9
Tkinetic x Transverse velocity (ltßTgt)

• Temperature Tkinetic higher for baryons with
  higher strange quark content for Blast-wave fits
• Spectral shapes different

T100 MeV
T132 MeV

• p, K, p ltßTgt at 200 GeV gt 62 GeV Tkin at
  200 GeV 62 GeV
• ?, O ltßTgt at 200 GeV 62 GeV Tkin at
  200 GeV gt 62 GeV

Most Central Collisions

• ? ? Tkinetic from Blast-Wave is not same as
  Temperature from Hydro Model

10
Elliptic Flow
Early Stages
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Elliptic Flow ? v2
Overlap region
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Flow ? p, K, p, d, F
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Flow ? KS, ?, F, ?, O
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Elliptic Flow

• Every particle flows
• Large v2 of heavier particles ? F, ?, O, d
• Even open charm flows ? measured through single
  electrons
• Strong interactions at early stage ? Early
  Thermalization!

15
? dependence of v2
0-40 centrality
PHOBOS 200 GeV Statistical errors only

• Elliptic flow has strong ? dependence ? not
  Bjorken assumption of rapidity invariant!

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v2 ? Hydrodynamics

• Hydro works at low pT

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v2 ? Hydrodynamics

• Hydro breaks down at intermediate pT

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Coalescence and Recombination
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v2 Scaling
AuAu ?sNN 200 GeV solid? STAR open ? PHENIX
Coalescence works at intermediate pT
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v2 ? Hydro x Coalescence

• Hydro works at low pT
• Hydro breaks down at intermediate pT
• Coalescence works at intermediate pT
• ?All this strengthens the case for sQGP with
  early thermalization of partonic matter in which
  constituent quark degree of freedom may be
  relevant at hadronization

21
Nuclear Modification Factor
If no effects R lt 1 in regime of soft
physics R 1 at high-pt where hard
scattering dominates
22
RCP Splitting/Scaling
?sNN 200 GeV

• Clear baryon/meson separation at intermediate pT
• ? K and F have mass proton, but RCP of a meson

23
Late Stages
Freeze-Outs
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Time Between Freeze-Outs

• If resonance decays before kinetic freeze-out ?
  not reconstructed due to rescattering of
  daughters
• K0 (c? 4 fm) survival probability ? time
  between chemical and kinetic freeze-out, source
  size and pT of K0
• Chemical freeze-out ? elastic interactions pK ?
  K0? pK regenerate K0(892) until kinetic
  freeze-out
• K0/K may reveal time between chemical and
  kinetic freeze-out

25
Time Between Freeze-Outs

• If rescattering is the dominant process,
• And the time between chemical and kinetic
  freeze-out should be ?t 2 1 fm
• If no regeneration is present ? ?t 2 1 fm
• Blast-Wave fit to p, K, p, and p ? ?t gt 6 fm

26
Time Between Freeze-Outs
Thermal Models
Chemical freeze-out
Kinetic freeze-out
Chemical Kinetic freeze-out

• K/K- ? pp ratio reproduced by thermal model at
  chemical freeze-out ? AuAu reproduced by thermal
  model at kinetic freeze-out

27
Thermal Models
Chemical freeze-out
Chemical Kinetic freeze-out

• F/K- ? ratio reproduced by thermal model ? F has
  long lifetime! ? not affected by rescattering (or
  regeneration)

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Modification of ?0 Spectral Shape
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Why measure the ?0 meson?

• Medium modification of mass and/or width ? Chiral
  Symmetry Restoration, Collision Broadening and/or
  Phase Space?
• Leptonic decay channel ? probes all stages of the
  collision

R. Rapp and J. Wambach, Adv. Nucl. Phys. 25, 1
(2000) G. E. Brown and M. Rho, Phys. Rev. Let.
66 2720 (1991) P. Braun-Munzinger, GSI Internal
Report
?0 c? 1.3 fm

• Hadronic decay channel ? probes late stages of
  the collision

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?0 ? Dimuons channel ? NA60 (SPS)
Hees and Rapp, hep-ph/0603084

• Probing all stages of the collisions
• Mass broadening

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?0 ? Hadronic channel ? STAR (RHIC)

• Probing late of the collisions
• Mass shift 70 MeV

32
Mass Shift in AA
Hees and Rapp, hep-ph/0603084
SPS
RHIC

• 70 MeV mass shift measured by STAR in peripheral
  AuAu collisions and no apparent broadening
• Broadening measured by NA60 in central In-In
  collisions and no mass shift
• Are these measurements in agreement?
• RHIC ? di-lepton measurements!

33
Mass Shift in AA
Hees and Rapp, hep-ph/0603084
SPS
RHIC

• NA60 ? Models in the market that reproduce the
  data quantitatively
• STAR ? Models in the market that reproduce the
  data qualitatively
• STAR ? Go back and look at reference system

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Modification of ?0 Spectral Shape
in pp
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?0 Mass in pp

• 40 MeV shift position ?0 peak measured by STAR
  in minimum bias pp

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Phase Space
T 160 MeV
M Invariant Mass pT transverse momentum T
Inverse Slope
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What about other measurements?
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Previous Measurements?

• ?0
• No detailed mass measurements
• Mass integrated in pT, xF, xp
• STAR measurement ? ?0 mass shifted 40 MeV in
  minimum bias pp
• Considerably large mass shift
• Mass shift observed before!
• Previous ?0 mass measurements ? NA27, OPAL,
  DELPHI, and ALEPH

NOTE Previous experiments interested in
cross-sections and NOT in mass!
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?0-meson Measured in pp ? NA27

• vs 27.5 GeV
• The ?0 mass obtained by fitting same event
  distribution of pp- to
• BG PS x BW BG BGxBW BG(1 BW)
• BW Breit-Wigner
• BG Background
• PS Phase Space

pp-
pT gt 0
xF gt 0
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?0-meson Measured in pp ? NA27

• CERN ? vs 27.5 GeV
• ?0 mass 762.6 2.6 MeV/c2 ? only pp
  measurement used in average by PDG
• PDG average other reactions hadroproduced ? ?0
  mass 769.0 0.9 MeV/c2
• PDG average ee- (exclusive) ? ? mass 775.9
  0.5 MeV/c2
• ? The position of the ?0 peak is clearly below
  reported value

762.6 MeV/c2
775.9 MeV/c2
scanned version
41
?0-meson Measured in pp ? NA27
Fitting to a p-wave BW function ? M 747.6 2.0
MeV
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?0-meson Measured in ee- ? LEP
vs 90 GeV

• OPAL ? ?0 mass shifted by 70 MeV/c2 at low xp
  and no shift at high xp (xp 1)
• OPAL ? -10 to -30 MeV/c2 shift in the position of
  the maximum of the resonance ? ? consistent with
  ?0 measurement
• DELPHI ? 0.1 lt xp lt 0.4 ? ?0 peak fit to (BWxBG)
  BG ? ?0 mass 757 2 MeV/c2 ? five standard
  deviations below PDG value
• ALEPH ? same ?0 mass shift observed by OPAL

?0
?0
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?0-meson Measured in pp and ee-

• Measurements in pp and ee- observe a mass shift
  in the position of the peak of the ?0 meson
• The phase space does not account for the mass
  shift observed
• Phase Space

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Discussing Phase Space
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What is the meaning of Phase Space in AuAu?

• Hadrons scattering ? forming resonances ?
  modifying mass distributions
• Check ? Transport Model Calculations ? UrQMD

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Transport Model - UrQMD
AuAu
AuAu
b 3 fm
b 3 fm
?0
?0
vsNN 200 GeV
1.2 pT lt 1.4 GeV/c y 0.5
0.2 pT lt 0.4 GeV/c y 0.5
M? 769 MeV/c2

• UrQMD ? Only imaginary part ? No medium
  modification
• Central AuAu ? ?0 mass shifted 30 MeV at low pT
• ?0 shape reproduced by p-wave Breit-Wigner
  Phase Space
• M? 765.6 MeV for 0.2 pT lt 0.4 GeV/c
• M? 761.2 MeV for 1.2 pT lt 1.4 GeV/c
• M? 769 MeV/c2 input

? 150 MeV
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What is the meaning of Phase Space in pp?

• Particles born at hadronization according to
  phase space
• No final state interaction expected
• Particle spectra
• No need to be thermodynamically equilibrated
• Multiparticle production saturates available
  phase space
• Valid for pp and ee-
• MT scaling

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?0 Spectra in pp at ?sNN 200 GeV

• p- Minimum bias pp
• Tslope 160 MeV
• ?0 Minimum bias pp
• Tslope 180 MeV
• ?0 High Multiplicity pp
• Tslope 180 MeV
• ?0 Tslope multiplicity independent!

ylt 0.5
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?0 Mass in pp at ?sNN 200 GeV
10 of minimum bias pp for ?lt0.5
Systematic errors ? common and correlated for pp
and peripheral AuAu
ylt 0.5

• ?0 mass pT dependent!
• ?0 mass multiplicity dependent!

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Show that ?0 mass multiplicity dependent ?
Evidence for pp- Rescattering
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Quantum Mechanics

• A resonance at rest is described by
• The probability amplitude

E0 is energy at rest
?
is the lifetime
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Quantum Mechanics
G h/?
P(E) Breit-Wigner distribution
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Adding Phase Space

• String fragmentation
• Multiplicity independent
• Data
• Multiplicity dependent! ? Inconsistency!

?
Necessary!
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String Fragmentation
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Phase Shift Analysis

• Interference ? Partial-wave analysis pp-
  scattering
• M? 779.1 MeV/c2 ? 150
  MeV/c2
• Distance of interaction in pp- scattering ? 1/3
  fm

56
Phase Shift Analysis
D2 is the direct production ?0
d1 is the p-wave phase shift
A2 is the PS overlap of di-pions in l1 partial
waves
r is the radius
r0 1.0 fm
q0 200 MeV/c
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p p- Rescattering
Minimum bias pp 0.6 pT lt 0.8 GeV/c
Good Agreement with Data!
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Modification of the ?0 Spectral Function
Minimum bias pp 0.6 pT lt 0.8 GeV/c
40-80 AuAu 0.6 pT lt 0.8 GeV/c

• pp ? 40 MeV shift due to pp- rescattering
  forming ?0
• AuAu ? 70 MeV shift
• Difference ? Further modification of the ?0 meson
  in the medium

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Conclusions

• (Early)Equilibration
• Early time ? v2
• Chemical ? Ratios
• Strangeness ? ?S
• Thermal ? T, ß
• Constituent quark degrees of freedom may be
  relevant at hadronization ? Recombination and
  Coalescence
• ? Signatures of sQGP
• Measurement mass and width wide resonances in the
  vacuum ? exclusive reactions ONLY! ? ee- ? pp-
• ?0 mass shift multiplicity dependent ? Evidence
  for pp- Rescattering in pp collisions

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Elliptic Flow ? v2

• Coordinate-space-anisotropy ? Momentum-space-aniso
  tropy
• Nuclei Non-central Collisions ? Hot System
  Elliptic Shape

?
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Söding Model
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Quark or Hadron Combination
Number of constituent quarks
Constants extracted by fitting the K0s and ? v2