Sketch of a competitive experiment on dense nuclear matter in the (future) Nuclotron energy range (2-5 AGeV)

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

Helmholtz Summer School 2006, Dubna, Student Seminar Peter Senger, GSI

Baryon density in central cell (Au+Au, b=0 fm): HSD: mean field, hadrons + resonances + strings QGSM: Cascade, hadrons + resonances + strings

Transport calculations: energy densities

C. Fuchs, E. Bratkovskaya, W. Cassing

Ch. Fuchs, Tübingen

“Trajectories” from UrQMD

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

The critical point

gasliquid

coexistence

Below Tc: 1. order phase transitionabove Tc: no phase boundary

At the critical point:Large density fluctuations,critical opalescence

Event-by-event analysis by NA49: 5% most central Pb+Pb collisions at 158 AGeV

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

Strangeness production in central Pb+Pb collisions

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

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

Thermal production of multistrange hyperons ?

Production processes of multistrange hyperons

0 (s d u) m =1116 MeV

- (s s d) m =1321 MeV

- (s s s) m =1672 MeV

Production processes and thresholds

pp K+ 0 p ( 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 )

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

pp 0 0 pp ( Ep 7.1 GeV )

pp + - pp ( Ep 9.0 GeV )

pp + - pp ( Ep 12.7 GeV )

Hyperon properties

Particle Quark content

Mass (GeV/c2)

Lifetime

c (cm)

Multiplicity at 6 GeV

Decay channel

BR

uds 1.116 7.89 9.7 p - 63.9%

- dss 1.321 4.91 0.118 - 99.9%

- sss 1.672 2.46 ~710-4 K- 67.8%

Particle multiplicities for central Au+Au collisionsfrom UrQMD calculations

Au+Au 5 AGeV central minimum bias 8.2 2

0.06 0.015 0.0002 0.00005

R = reactions/secNB = 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

Reaction rate: R = NB · · NT/F ·

Determination of target thickness

Reaction cross section: R = · (2 ·R)2 = 4 ·(r0·A1/3)2 with r0=1.2 fmAu+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

= · 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 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 minfor Ξ : t = 1.4·105 sec = 1.6 dfor 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 !

Dipolemagnet

tracking chambers

6 m

Possible experiment layout

Silicontracker

Time-of-flight wall(RPC)

needed: fast detectors

Tracking chambers are needed to match tracks in Silicon detector to hits in TOF wall

Silicon tracker in magneticdipole field measures tracks (particle numbers) and curvature (particle momentum).

TOF wall measures Time-of-flight for mass determination.

Ξ - 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 Ξ-

• Invariant mass resolution is improved with the dca cut

• σ = 1.7 MeV

• Signal yield: 264

Before cutsAfter impact

parameter cut

After dca cut

All cuts

Invariant mass distributions Ω-

• Invariant mass resolution is improved with the dca cut

• σ = 2.2 MeV

• Signal yield: 486

Before cutsAfter impact

parameter cut

After dca cut

All cuts

Results on Ω- without PIDStatistics: 1.4 108 events

Invariant mass distributions Ω- with perfect PID

Before cutsAfter impact

parameter cut

After dca cut

All cuts

Results on Ω- with perfect PID

Statistics: 1.4 108 events

Conclusions

• 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