Energy Dependence of Soft Hadron Production

1
Energy Dependence of Soft Hadron Production
2
The QCD Phase DiagramThe Simplified Version
Phase boundary separating QGP and hadronic world
3
The QCD Phase DiagramHeavy Ion Reactions
4
The QCD Phase DiagramExperimental Observables

• SPS energy regime allows to explore an essential
  part of the phase diagram
• Transition to QGP is likely to happen at SPS
  energies
• Ebeam 20 - 158 AGeV (?sNN 6.3
  - 17.3 GeV)
• Use hadronic observables to pin down phase
  transition
• Systematic studies ? Energy dependence
• of central AA reactions

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OutlineSoft Hadron Production

• Soft physics regime
• pt lt 2 GeV/c
• Bulk properties of particle production
• Rapidity Spectra
• Longitudinal expansion
• Particle Yields
• Strangeness
• Chemical freeze-out conditions
• Transverse Mass Spectra
• Transverse expansion (? EOS?)
• Thermal freeze-out conditions
• Fluctuations
• K/? (p/?) fluctuations

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Rapidity Spectra
Central PbPb 7 (20-80) 5/10 (158) NA49
Change of shape only for L Others
Gaussians
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Rapidity SpectraPions
Central PbPb/AuAu
Comparison AGS, SPS, and RHIC
Single Gaussians!
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Rapidity SpectraEnergy Dependence of Widths
Pion widths are close to Landau prediction, but
not perfectly
But Perfect agreement to linear dependence on
ybeam
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Rapidity SpectraEnergy Dependence of Widths
Linear dependence on ybeam
Clear hierarchy for Gaussian-like particles at
SPS (p, ?, ? excluded) ? gt K gt K-, ? gt
? Seems to break down at AGS
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Rapidity SpectraMass Dependence of Widths
? negatives
Approx. linear dependence on particle mass
Similar slope at all SPS energies
? Thermal component of longitudinal flow
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Rapidity SpectraDependence on Strangeness Content
Central PbPb, 158 AGeV NA49
Net protons 3 valence quarks (uud )
Net ?s 2 valence (ud ) 1 produced quark (s )
Net ?s 1 valence (d ) 2 produced quarks
(ss )
Omegas 3 produced quarks (sss )
Net protons difficult to reconcile with pure
Landau !
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Particle Yields
AGS
NA49
BRAHMS
Central AuAu, PbPb
4? multiplicities only!
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Particle YieldsStatistical Hadron Gas Model
Becattini et al., Phys. Ref. C69 (2004) 024905
Assumption of chemical equilibrium at the
freeze-out point
? Particle production can be described with a
few parameters V, T, ?B, ?s
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Particle YieldsPhase Diagram (II) Chemical
Freeze-Out
Chemical freeze-out points approach phase
boundary at top SPS energies
Does the system cross the phase boundary ? And
if yes, where ?
Freeze-out curve at ?E ?/N 1GeV Cleymans and
Redlich PRL 81 (1998) 5284
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Particle YieldsEnergy Dependence
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Particle YieldsEnergy Dependence
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Particle YieldsEnergy Dependence
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Particle YieldsEnergy Dependence
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Particle YieldsComparison s- and s-Carriers
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Particle Yields(Anti-)Strangeness to Pion Ratio
Difficult to model Solid line Statistical
hadron gas model with ?s 1 K. Redlich, priv.
comm. Predicted as signal for the onset of
deconfinement M. Gazdzicki and M.I. Gorenstein,
Acta Phys. Polon. B30 (1999), 2705
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Transverse Mass Spectra
Central (7) PbPb NA49
Radial flow fit (Blast Wave)
20 AGeV
30 AGeV
Here ?t independent of r
Schnedermann, Sollfrank, and Heinz, Phys. Rev. C46
22
Transverse Mass Spectra
?-
p
K-
Model U. Wiedemann and U. Heinz,
Phys. Rev. C56 (1997) 3265 B.
Tomasik, nucl-th/0304079
Data E895 nucl-ex/0306033 NA49
Phys. Rev. C66 (2002) 054902, nucl-ex/0403023
PHENIX Phys. Rev. C69 (2004) 024904,
nucl-ex/0307022
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Transverse Mass SpectraEnergy Dependence of Fit
Parameter
Fit to ?-, K- and p
Tch
Box-shaped source profile and linear velocity
profile Fit range 0.1 lt mt-m0 lt 0.8 GeV
Energy dependence of Tf seems to change around 30
AGeV Thermal and chemical freeze-out different?
Single freeze-out model? Continous increase of
??T?
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Transverse Mass SpectraPhase Diagram (III)
Thermal Freeze-Out
Thermal freeze-out seems to be at lower
temperature than chemical freeze-out from top AGS
energies on
Strongly model dependent ! Single freeze-out
models ?

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Transverse Mass SpectraInverse Slope Parameters
of Kaons
Step in energy dependence
Seems to be absent in pp
How about other particle types?
pp compilation from M. Kliemant, B. Lungwitz,
and M. Gazdzicki, PRC 69 (2004) 044903
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Transverse Mass SpectraEnergy Dependence of
?mt?-m0
? negatively charged
Energy dependence of transverse activity seems to
change around 30 AGeV. General feature for
pion, kaons and protons
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Transverse Mass SpectraInverse Slope Parameters
of Kaons
Feature cannot be described by transport models
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Transverse Mass SpectraInverse Slope Parameters
of Kaons
Hydro calculation
Y. Hama et al. Braz. J. Phys. 34 (2004), 322,
hep-ph/0309192
Assuming 1st order phase transition Initial
conditions from NeXus
? Change of EOS seen?
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Elliptic FlowEnergy Dependence
Initial spatial anisotropy ? different pressure
gradients ? momentum anisotropy v2
Mid-rapidity data, pt integrated
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Elliptic FlowEnergy Dependence Transport Model
Data show saturation of scaled v2
Points to an initial QGP pressure from 30 AGeV
on !
M. Bleicher, SQM04
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FluctuationsThe Critical Point
Endpoint of the first order phase transition line
? crossover on left side
Position quite uncertain But recent lattice
calculations by Fodor and Katz predicts position
at ?B 360 MeV using physical quark masses
It might be accessible in the SPS energy
range Observables Event-by-event fluctuations
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FluctuationsParticle Ratios
Event-by-event fluctuations of e.g. K/?

• Compare to mixed event
• reference
• Resolution
• Finite number statistics

NA49
? Extraction of dynamical fluctuations
NA49
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FluctuationsEnergy Dependence of K/p Fluctuations
Data wider than mixed events reference
Clear energy dependence of K/p fluctuations
observed ? Decrease with energy
Fluctuation from UrQMD independent of
energy Non-zero value due to energy and
strangeness conservation
preliminary
Promising, but no clear evidence for critical
point yet
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FluctuationsEnergy Dependence of p/p Fluctuations

• Data narrower than reference
• Can be caused by resonances

Clear energy dependence of p/p fluctuations
observed ? Increase with energy
preliminary

• Similar trend seen in UrQMD
• Resonance contribution changes
• with beam energy

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Summary

• Systematic study of energy dependence (still
  ongoing)
• Rapidity and transverse mass spectra
• Particle Yields
• Fluctuations
• A variety of interesting features have been
  revealed
• Mass dependence of rapidity widths, seemingly
  independent of beam energy at SPS
• Clear change of the energy dependence of
  mt-spectra at 30 AGeV ? Evidence
  for a change of EOS?
• Maximum in the strangeness to pion ratio at 30
  AGeV ? Evidence for deconfinement?
• Outlook Search for critical point
• No clear evidence yet (K/? fluctuations)
  ? dedicated search with future projects
  (SPS, FAIR)

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The End
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Particle YieldsEnergy Dependence
Central PbPb/AuAu
Mid-rapidity ratios
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Transverse Mass SpectraBlast Wave Model

• Basic blast wave model
• Common freeze-out of all particle types
• Boost invariant longitudinal expansion
• Transverse expansion is modelled by a velocity
  profile
• Standard version

Schnedermann, Sollfrank, and Heinz, Phys. Rev. C46

• Extended version
• Resonance contribution included
• Baryonic resonances introduce dependence on ?B
• Chemical freeze-out Tch and ?B taken from
  freeze-out curve
• Thermal freeze-out System cools down,
  therefore assume
• Conservation of entropy
• Conservation of effective particle numbers

U. Wiedemann and U. Heinz, Phys. Rev. C56
(1997) 3265 B. Tomasik, nucl-th/0304079
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Rapidity DistributionsLandau Scenario in pp
Pion production Entropy Isentropic
expansion Description of the pion gas as a 3D
relativistic fluid
L. D. Landau, Izv. Akad. Nauk. SSSR 17 (1953)
52 P. Carruthers and M. Duong-Van, Phys. Ref. D8
(1973) 859
Prediction dN/dy is Gaussian of a width ? 2L
given by (simplified model)
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Rapidity SpectraKaons
Single Gaussian works reasonably well for K-
Does not really work for K at lower SPS
energies ? Use RMS
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Particle YieldsEnergy Dependence
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Transverse Mass SpectraThe Omega
Evidence for early freeze-out of the Omega from
blast wave fits?
NA49 publication C. Alt et al., nucl-ex/0409004
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Rapidity SpectraRapidty Shift ?y
Baryon number distributions at
lower energies
higher energies
How does the rapidity shift ?y evolve with beam
energy?
Determines the energy available in the produced
fireball
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Rapidity SpectraEnergy Dependence of ??y ?
BRAHMS, I.G. Bearden et al. PRL 93 (2004), 102301
Rapidity shift
Seems to increase linearly at AGS and SPS
??y ?/ybeam ? 0.27
But Weaker increase to RHIC energies!
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Rapidity Spectra Energy Dependence of Net-Protons
BRAHMS, I.G. Bearden et al. PRL 93 (2004), 102301
The shape of the distributions changes
dramatically with energy
AGS baryonic system ? RHIC mesonic system ?
Large implications in the hadronic sector
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Transverse Mass SpectraInverse Slope Parameters
of Kaons
Model comparisons
M. Bleicher, SQM04
Additional resonances? UrQMD 2.1 Initial QGP
pressure?