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Sketch of a competitive experiment on dense nuclear matter in the (future) Nuclotron energy range (2-5 AGeV). Helmholtz Summer School 2006, Dubna, Student Seminar Peter Senger, GSI. 1. The physics case:  Nuclear equation of state at high baryon densities

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Sketch of a competitive experiment on dense nuclear matter

in the (future) Nuclotron energy range (2-5 AGeV)

Helmholtz Summer School 2006, Dubna, Student Seminar

Peter Senger, GSI

1. The physics case:

 Nuclear equation of state at high baryon densities

 Search for a first order phase transition between

hadronic matter and quark matter

2. Observables:

 Yield, spectra and collective flow of hadrons

incl. (multi-) strange particles

 Event-by-event fluctuations of particle yields and

mean transverse momenta

 Excitation functions (1-5 AGeV),

system size and centrality dependence

3. Estimation of feasibility

 Particle production cross sections in heavy ion collisions

 Reaction rates

4. Experimental conditions and requirements

 Beam energy and intensity

 Detectors (tracking, momentum determination, particle identification)

 Efficiencies, signal-to background


Transport calculations: energy densities matter

Baryon density in central cell (Au+Au, b=0 fm):

HSD: mean field, hadrons + resonances + strings

QGSM: Cascade, hadrons + resonances + strings

C. Fuchs, E. Bratkovskaya, W. Cassing



“Trajectories” from UrQMD matter

L. Bravina, M. Bleicher et al., PRC 1998


Event-by-event analysis by NA49: matter5% most central Pb+Pb collisions at 158 AGeV

liquid

gas

coexistence

Below Tc: 1. order phase transition

above Tc: no phase boundary

At the critical point:

Large density fluctuations,

critical opalescence

The critical point


Strangeness production in central Pb+Pb collisions matter

C. Blume et al., nucl-ex/0409008 (CERN NA49)


Multistrange hyperons matter

from p+Be, p+Pb and Pb+Pb at 158 AGeV/c

Strangeness enhancement:

F. Antinori et al, Nucl. Phys. A 661 (1999) 130c



Production processes of multistrange hyperons matter

Production processes and thresholds

pp  K+0p ( Ep 1.6 GeV )

pp  K+K-pp(Ep  2.5 GeV)

pp K+K+-p ( Ep  3.7 GeV )

pp K+K+K+-p ( Ep  7.0 GeV )

0(s d u) m =1116 MeV

- (s s d) m =1321 MeV

- (s s s) m =1672 MeV

pp 0 0pp ( Ep  7.1 GeV )

pp + -pp ( Ep  9.0 GeV )

pp + -pp ( Ep  12.7 GeV )

In heavy ion collisions: “cooking” of multistrange hyperons ?

Strangeness exchange reactions:

2) 0 K-  -00 K+  +0

3) -K-  -- +K+  ++

Enhanced yield at high densities



Particle multiplicities for central au au collisions from urqmd calculations
Particle multiplicities for central Au+Au collisions matterfrom UrQMD calculations

Au+Au 5 AGeV

central minimum bias

8.2 2

0.06 0.015

0.0002 0.00005


Reaction rate: matterR = NB · · NT/F·

  • R = reactions/sec

  • NB = beam particles/sec

  • = cross section [barn = 10-24cm2]

    NT /F= target atoms/cm2 = NA ··d/A

    with Avogadros Number NA = 6.02·1023· mol-1,

    material density  [g/cm3],

    target thickness d [cm]

    atomic number A

     = efficiency


Determination of target thickness matter

Reaction cross section:

R = · (2 ·R)2 = 4 ·(r0·A1/3)2 with r0=1.2 fm

Au+Au collisions:

A=197  R = 6.1 barn, 1 barn = 10-24 cm2

Reaction probability for Au+Au collisions:

R/NB = R· NT/F

= 6.1 b ·6.02·1023··d/A

= 6.1 ·10-24 cm2·6.02·1023·19.3 g/cm3·d/197 = 1%

target thickness d = 0.027 cm


Production cross sections for min. bias Au+Au collisions at 5 AGeV:

(Λ) = M(Λ) x R = 2 x 6.1 b = 12.2 b

(Ξ) = M(Ξ) x R = 0.015 x 6.1 b = 0.09 b

(Ω) = M(Ω) x R = 0.00005 x 6.1 b = 0.0003 b

Particle production probabilities for min. bias Au+Au at 5 AGeV:

R(Λ)/NB = (Λ)·NA··d/A = (Λ) [b]·1.6·10-3 = 2·10-2

R(Ξ)/NB = (Ξ)·NA··d/A = (Ξ) [b]·1.6·10-3 = 1.4·10-4

R(Ω)/NB =(Ω)·NA··d/A = (Ω) [b]·1.6·10-3 = 4.8·10-7

R(Λ)/NB = (Λ)·NA··d/A· = ?


  • Acceptances and Efficiencies 5 AGeV:

  • = · p ·Det · Trigg · DAQ · analysis

    with

  •  = angular acceptance

  • p = momentum acceptance

  • Det = detector efficiencies

  • Trigg = trigger efficiencies

  • DAQ= deadtime correction of DAQ

  • analysis = efficiency of analysis

  • (track finding, cuts for background suppression , ...)

Typical values:

 0.5, p 0.8, Det 0.9, Trigg  0.9,DAQ  0.5,analysis  0.3,

 0.05


Typical particle 5 AGeV:detection probabilities in Au+Au at 5 AGeV:

R(Λ)/NB = (Λ)·NA··d/A· = 2·10-2·0.05=1·10-3

R(Ξ)/NB = (Ξ)·NA··d/A· = 1.4·10-4·0.05 = 7·10-6

R(Ω)/NB =(Ω)·NA··d/A· = 4.8·10-7·0.05 = 2.4·10-8

Required particle yield for a competitive physics analysis:

(differential values like v2 as function of pT): 1 Mio particles

Required number of beam particles (integrated luminosity):

for Λ: NB x sec = 106/ 1·10-3 = 1·109

for Ξ : NB x sec = 106/ 7·10-6 = 1.4·1011

for Ω: NB x sec = 106/ 2.4·10-8 = 4.2·1013

Required beam time for a Au-beam intensity of NB = 106/sec:

for Λ: t = 1·103 sec = 17 min

for Ξ : t = 1.4·105 sec = 1.6 d

for Ω: t = 4.2·107 sec = 500 d

These numbers refer to one

collision system and one

beam energy only.

Systematic studies require

excitation functions

(several beam energies)

with different

collision systems !


Possible experiment layout 5 AGeV:

TOF wall measures

Time-of-flight for

mass determination.

needed:

fast detectors

tracking

chambers

Dipole

magnet

Time-of-flight wall

(RPC)

Silicon

tracker

Tracking chambers

are needed to match

tracks in Silicon detector

to hits in TOF wall

Silicon tracker in magnetic

dipole field measures tracks

(particle numbers) and curvature

(particle momentum).

6 m


Hyperons at ags au au 6 agev
Ξ 5 AGeV: - Hyperons at AGS: Au+Au 6 AGeV

  • Threshold production of Xi measured

  • Main detector: TPC with PID capabilities

  • Measured in 4 centrality bins

  • ~ 250 Xi measured

  • Results consistent with UrQMD

  • Neural network algorithm used for the bgd suppression


Invariant mass distributions
Invariant mass distributions 5 AGeV:Ξ-

After impact parameter cut

Before cuts

  • Invariant mass resolution is improved with the dca cut

  • σ = 1.7 MeV

  • Signal yield: 264

After dca cut

All cuts


Invariant mass distributions1
Invariant mass distributions 5 AGeV:Ω-

After impact parameter cut

Before cuts

  • Invariant mass resolution is improved with the dca cut

  • σ = 2.2 MeV

  • Signal yield: 486

After dca cut

All cuts


Results on without pid
Results on 5 AGeV:Ω- without PID

Statistics: 1.4 108 events


Invariant mass distributions with perfect pid
Invariant mass distributions 5 AGeV:Ω- with perfect PID

After impact parameter cut

Before cuts

After dca cut

All cuts


Results on with perfect pid
Results on 5 AGeV:Ω- with perfect PID

Statistics: 1.4 108 events


Conclusions
Conclusions 5 AGeV:

  • Multistrange hyperon measurements seem feasible in Au+Au collision at 5 AGeV

  • Track reconstruction, momentum determination and particle identification is required

  • Beam intensities of better than NB = 106/sec are needed


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