Analysis of preliminary BoseEinstein correlation HBT data in Pb Pb collisions at CERN SPS energies

1
Analysis of preliminary Bose-Einstein correlation
(HBT) data in PbPb collisions at CERN SPS
energies
A. Ster1,2, T. Csörgo2
1 KFKI-RMKI, 2 KFKI-MFA, Hungary

• BudaLund analitical hydro formulas for
  observables
• Fits to preliminary NA49 data of 20, 30, 40, 80,
  158 AGeV
• Results
• Conclusion

2
The BudaLund fluid model

• Observables

3
The BudaLund fluid model

• A general form
• With probability distribution for fluids

4
The BudaLund fluid model

• Buda-Lund solutions of the 5 differential fluid
  equations

5
The BudaLund fluid model

• Where (in case of axial symmetry)

(Ht rt Ht transverse Hubble constant)
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The BudaLund fluid model

• Final form of Invariant Momentum Distribution

7
BudaLund old fits to old SPS PbPb
NA49
NA44
A. Ster, T.Csörgo, B. Lörstad , Nucl.Phys. A661
(1999) 419-422, nucl-th/9907338
8
BudaLund fits to RHIC AuAu data
A. Ster, et al., Acta Phys.Polon. B35 (2004)
191-196, nucl-th/0311102
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BudaLund fits to RHIC AuAu data
http//www.kfki.hu/csorgo/budalund/budalund1.5.qm
04.tar.gz
M. Csanád, et al., J.Phys.G30 S1079-S1082, 2004,
nucl-th/0403074
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BudaLund fits to old NA49 data
New code
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Status of BudaLund fits to NA49 data

• Old (Torino QM 1999) results reproduced
• Confidence level of the Torino QM 99 data fits is
  acceptable, CL gt 0.1
• Conf. level of the new preliminary NA49 data
  with stat errors of 0.1 fm -gt only CL lt 0.1 ,
  not acceptable
• Good CL is obtained if error on radii x 4 tried
• All forthcoming numbers work in progress
• Missing dn/dy, Routlong, hyperon spectra fits

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BudaLund fits to NA49 data (preliminary HBT)
NA49 Collaboration (preliminary data), A.
Ster, T. Csörgo and M. Csanád (work in progress)
13
BudaLund fits to NA49 data (preliminary HBT)
NA49 Collaboration (preliminary data), A.
Ster, T. Csörgo and M. Csanád (work in progress)
14
BudaLund fits to NA49 data (preliminary HBT)
NA49 Collaboration (preliminary data), A.
Ster, T. Csörgo and M. Csanád (work in progress)
15
BudaLund fits to NA49 data (preliminary HBT)
NA49 Collaboration (preliminary data), A.
Ster, T. Csörgo and M. Csanád (work in progress)
16
BudaLund fits to NA49 data (preliminary HBT)
NA49 Collaboration (preliminary data), A.
Ster, T. Csörgo and M. Csanád (work in progress)
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BudaLund, excitation functionof central T from
preliminary NA49 PbPb
Central temperature increases with increasing
bombarding energy
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BudaLund, excitation functionof T(post evap)
from preliminary NA49 PbPb
Post-evaporation temperature increases also with
increasing E, similar to central T.
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BudaLund, excitation function of geometrical
radius from preliminary NA49 PbPb
Geometrical size decreases or nearly flat with
increasing Elab!
20
BudaLund, excitation function of Rs, T(Rs)
T0/2 from preliminary NA49 PbPb
Rs is large temperature is nearly constant in
the transverse plane.
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BudaLund, excitation function of Hubble constant
Htr from preliminary NA49 PbPb
Transverse expansion rate nearly saturates. Htr
ltutgt/Rg
22
BudaLund, excitation function of Hubble constant
Hlong from preliminary NA49 PbPb
Longitudinal expansion rate slightly increases.
Hlong 1/t0
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BudaLund, excitation functionof Dh from
preliminary NA49 PbPb
Longitudinal extension slightly increases.
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BudaLund, excitation functionof D? from
preliminary NA49 PbPb
Emission time width fluctuates within errors .
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BudaLund fit results of preliminary NA49 data
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Analysis of NA49 data

• Torino QM 99 fit reanalized, CL gt 0.1
• New preliminary NA49 data
• analysed with stat errors only, order of 0.1 fm
  
• only CL lt 0.1 , not acceptable
• all fits look good but fits are only work in
  progress
• Missing dn/dy, Routlong, hyperon spectra fits
• Monotonic increase with energy T0, Tevap, Dh,
• Within errors, independent of energy Htr, Hlong,
  Rg, Rs, D?
• Temperature is constant of (r,t) at freeze
  in
  PbPb_at_CERN SPS

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Conclusions on NA49 data

• Buda-Lund model describes single particle
  distributions, and preliminary HBT radii w/o HBT
  puzzle
• PbPb _at_SPS,
• Elab 20, 30, 40, 80, 158 AGeV
• But the CL is good only on the previously
  published NA49 data, errors on new preliminary
  data stat only and very small (0.1 fm)
• T0 lt Tc in PbPb _at_SPS
• T0 gt Tc in AuAu _at_RHIC
• IF Tc1723MeV