1. Countrate estimates

2. Particle production in heavy ion collisions

3. Particle multiplicities for central Au+Au collisions from UrQMD calculations Au+Au 6 AGeV central minimum bias 0.00072 0.00018 Example Ω production Direct production: NN   +  - NN (E thr = 12.7 GeV) Production via multiple collisions: NN  K+ΛN, NN  K+K-NN, ΛK-   -  0,  -K-   -  -

4. R = reactions/sec N B = beam particles/sec  = cross section [barn = 10 -24 cm 2 ] N T /F = target atoms/cm 2 = N A ·  ·d/A with Avogadros Number N A = 6.02·10 23 · mol -1, material density  [g/cm 3 ], target thickness d [cm] atomic number A Reaction rate: R = N B ·  · N T /F

5. Reaction cross section and target thickness Reaction cross section:  R =  · (2 ·R) 2 = 4  ·(r 0 ·A 1/3 ) 2 with r 0 =1.2 fm Au+Au collisions: A=197   R = 6.1 barn, 1 barn = 10 -24 cm 2 Reaction probability for Au+Au collisions: R/N B =  R · N T /F = 6.1 b · 6.02·10 23 ·  ·d/A = 6.1 ·10 -24 cm 2 · 6.02·10 23 ·19.3 g/cm 3 ·d/197 = 1% target thickness d = 0.027 cm

6. Production cross sections for min. bias Au+Au collisions at 6 AGeV:  (Ω) = M(Ω) x  R = 1.8·10 -4 x 6.1 b = 1.1·10 -3 b Particle production probabilities for min. bias Au+Au at 6 AGeV: R (Ω)/N B =  (Ω)·N A ·  ·d/A =  (Ω) [b]·1.6·10 -3 = 1.8·10 -6 recorded particles: R( Ω )/N B ·  = ? Experimental efficiencies?

7. 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

8. Typical Ω detection probabilities in Au+Au at 5 AGeV: R (Ω)/N B ·  = 1.8·10 -6 ·0.05 = 9·10 -8 Recorded Ω rates for a Au-beam intensity of 10 8 /sec: R (Ω) = 10 8 /sec x 9·10 -8 = 9/sec Recorded Ω yield after 1 week beam on target: Y = 9 x 3600 x 24 x 7 = 5.4·10 6 These numbers refers to one collision system and one beam energy only. Systematic studies require excitation functions (several beam energies) with different collision systems !

9. Observables U+U 23 AGeV

10. Pion multiplicities per participating nucleons RHIC

11. meson-baryon interaction

12. SIS: KaoS AGS: E802,E866 SPS: NA49 Production of K + und K - mesons in central AuAu/PbPb collisions NN  K +  N: E lab  1.6 GeV NN  K + K - NN: E lab  2.5 GeV RHIC

13. GSI Meson production in central Au+Au collisions W. Cassing, E. Bratkovskaya, A. Sibirtsev, Nucl. Phys. A 691 (2001) 745

14. Rapidity distributions Rapidity: y (0) = y-y m with y =0.5 ln [(E+p z )/(E-p z )] Central Pb+Pb collisions at SPS energies C. Blume for the NA49 Collaboration, J.Phys. G31 (2005) S685-S692

15. Particle yields in midrapidity from central A+A collisions

16. Partition function Particle density g i = (2J i +1) spin degeneracy factor, temperature T, and E i =  (p 2 + m 2 ) i the total energy. net baryon density:  B  4 ( mT/2  ) 3/2 x [exp((  B -m)/T) - exp((-  B -m)/T)] baryons - antibaryons

17. Central Au+Au collisions (midrapidity): statistical model results E = 2 AGeV E = 4 AGeV E = 6 AGeV E = 8 AGeV A. Andronic, P. Braun-Munzinger, J. Stachel, Nucl.Phys. A772 (2006) 167-199

18. E = 10.7 AGeV E = 40 AGeVE = 80 AGeV Central Au+Au collisions (midrapidity): statistical model results

19. E = 158 AGeV Central Au+Au collisions (midrapidity): Statistical model results

25. Strangeness/pion ratios Decrease of baryon-chemical potential: transition from baryon-dominated to meson-dominated matter ? C. Blume for the NA49 Collaboration, J.Phys. G31 (2005) S685-S692

26. Strangeness = 2 × (K + + K − ) + 1.54 × (Λ + Λ¯) Entropy = 1.5 × (π + + π − ) + 2 × p¯

27. The freeze-out curve in the QCD phase diagram A. Andronic, P. Braun-Munzinger, J. Stachel, Nucl.Phys. A772 (2006) 167-199

28. J. Randrup and J. Cleymans, hep-ph/0607065

29. Particle yields

31. Pion production in Au + Au collisions at 1.5 AGeV Data: T. Schuck, Dipl. Thesis 2003, GSI/Uni Frankfurt

32. "Boltzmann" parameterisation: d 3  /dp 3 = C 1 exp(-E/T 1 ) + C 2 exp(-E/T 2 )

33. Kinetic energy of a particle: E k = E th + E flow = 3/2 kT + m/2  flow  2 The explosion of the fireball Blast wave model: isotropically expanding System with temperature T P.J. Siemens and J.O. Rasmussen, Phys. Rev. Lett. 42 (1979) 880 dotted line:  f = const. solid line: Hubble expansion  f = rH

34. N. Xu, Int. J. Mod. Phys. E16 (2007) 715

36. Participan t s Spectator s Determination of collision centrality Number of participating nucleons in A+A collisions : A part = 2 x A/Z x (Z – Z spec ) or Zero Degree Calorimeter: E ZDC = E beam A Pro-Spec and A part = 2 ( A - E ZDC /E beam )

37. Determination of the reaction plane Transverse Momentum Method: P. Danielewicz & G. Odyniec, Phys. Lett. 157 B (1985) 146 Q =    p   = 1 für y>y cm  R = arctan(Q y /Q x ) Dispersion of the reaction plane: Sub-Event-Method:  =  1 -  2

38. N π proj /N π targ The pion clock: in-plane emission in Au+Au collisions at 1.0 AGeV A. Wagner et al., Phys. Rev. Lett. 85 (2000) 18 High-energy pions freeze-out early

39. Expect Large Pressure Gradients  Hydro Flow The Flow Probe

41. Dense baryonic matter up to 3 ρ 0: Probing the nuclear equation-of-state with heavy ions

42. Observable in HI collisions: collective flow (driven by pressure) The equation-of-state of (symmetric) nuclear matter  E/A(   ) = -16 MeV  (E/A)(   )/   Compressibility:     (E/A)/    = 200 MeV: "soft" EOS  = 380 MeV: "stiff" EOS C. Fuchs, Prog. Part. Nucl. Phys. 56 (2006) 1 Equation of state: PV  T  E P  E/V  E/A

43. Definition of the potentials in transport codes Bethe Weizsaecker –mass formula: Volume term (with eos) +Surface term+Coulomb term +symmetry term (+pairing term not included) 2 and 3 body interactions (no equilibrium required)

44. The eos in IQMD after the convolution of the Skyrme type potentials supplemented by momentum dependent interactions (mdi) for infinite nuclear matter at equilibrium hard soft

45. Energy per nucleon in nuclear matter (Skyrme potential): E/A = 3k F 2 /(10M) +  /2   /(1 +  ) The nuclear matter equation of state Conditions:  E/A(   ) = -16 MeV  (E/A)(   )/   Compressibility:     (E/A)/     200 - 400 MeV 

46. Baryon/energy density in central cell (Au+Au, b=0 fm): Transport code HSD: mean field, hadrons + resonances + strings E. Bratkovskaya, W. Cassing Baryon and energy densities at FAIR energies

48. Dynamics of a semi-central Au+Au collision at 2 AGeV (BUU calculation, P. Danielewicz, MSU)

49. Azimuthal angle distribution: dN/d  1 + 2v 1  cos  + 2v 2 cos2  C.Pinkenburg et al., (E895), Phys. Rev. Lett. 83 (1999) 1295 Azimuthal angular distribution of protons measured in Au+Au collisions at 1.15, 2, 4, 6, 8 AGeV Rapidity: y (0) = y-y m with y = 0.5 ln [(E+p z )/(E-p z )] AGeV

50. dN/d  1 + 2v 1  cos  + 2v 2 cos2  P. Danielewicz, R. Lacey, W.G. Lynch, Science 298 (2002) 1592 Probing the nuclear equation-of-state: proton collective flow Transverse in-plane flow: Elliptic flow: F = d(p x /A)/d(y/y cm ) K = 170 – 210 MeV K = 170 – 380 MeV

51. New data: Au + Au collisions at SIS energies A. Andronic et al. (FOPI Collaboration) Phys. Lett. B612 (2005) 173

52. P. Danielewicz, R. Lacey, W.G. Lynch, Science 298 (2002) 1592 pressure P = ρ 2 · ( δ(ε/ρ) / δρ ) with nuclear density ρ and energy density ε Pressure as function of density Independent observable ? particle production Within microscopic transport models the collective flow is sensitive to:  The nuclear matter equation of state  In-medium nucleon-nucleon cross sections  Momentum dependent interactions

53. Probing the equation-of-state of symmetric nuclear matter: Kaon production in Au+Au collisions at 1 AGeV K + mesons probe high densities udsuds n dudu  uddudd susu  K+K+ pp → K + Λp (E thres = 1.6 GeV) K + reabsorption negligible

54. NN  K +  N reduced (E beam = 1.6 GeV)  N  K + ,  N  K +  N enhanced M K    ( A part ) 1.8 M    A part Kaon production in Au+Au collisions at subthreshold beam energies

55. The creation of strange mesons udsuds n dudu  uddudd susu  K+K+ uduudu  uuuu  udsuds susu p K-K- K - absorption udsuds n p uddudd susu  K+K+ dduddu n uduudu uduudu uduudu n p uddudd susu K+K+ susu p KK dduddu n

56. Probing the nuclear equation-of-state (ρ = 1 – 3 ρ 0 ) by K + meson production in C+C and Au+Au collisions Transport model (RBUU) Au+Au at 1 AGeV: κ = 200 MeV  ρ max  2.9 ρ 0  K +  κ = 380 MeV  ρ max  2.4 ρ 0  K +  Reference system C+C: K + yield not sensitive to EOS Idea: K + yield  baryon density ρ  compressibility κ Experiment: C. Sturm et al., (KaoS Collaboration), Phys. Rev. Lett. 86 (2001) 39 Theory: Ch. Fuchs et al., Phys. Rev. Lett. 86 (2001) 1974

57. The compressibility of nuclear matter Experiment: C. Sturm et al., (KaoS Collaboration) Phys. Rev. Lett. 86 (2001) 39 Theory: QMD Ch. Fuchs et al., Phys. Rev. Lett. 86 (2001) 1974 IQMD Ch. Hartnack, J. Aichelin, J. Phys. G 28 (2002) 1649 soft equation-of-state:  ≤ 200 MeV Au/C ratio: cancellation of systematic errors both in experiment and theory

59. Exploring the "nuclear" EOS at 3ρ 0 < ρ < 7ρ 0 Measure excitation function of (multi-strange) hyperon production in heavy-ion collisions from 2 - 15 AGeV (no data yet): Direct production: NN  Λ 0 Λ 0 NN (E thr = 7.1 GeV) NN   +  - NN (E thr = 9.0 GeV) NN   +  - NN (E thr = 12.7 GeV) Production via multiple collisions: NN  K + Λ 0 N, NN  K + K - NN, Λ 0 K -   -  0,  - K -   -  - Λ 0 K +   +  0,  + K +   +  +.

60. The in-medium properties of strange mesons

61.  (1232)  (1600)  k,    p,n N (1440) N (1520) M [GeV] 0 1 a1a1 Vakuum  0 Mesonen Baryonen Chiral Symmetry of QCD: Quarks are massless. In natur chiral symmetry is broken: Spontaneous: Parity-Doubletts are not degenerated Explicit: small pion mass (Goldstone Boson) Explicit breaking: m u  5 MeV, m d  10 MeV, m s  150 MeV Spontaneos/dynamical breaking: quarks couple to the virtual quark-antiquark pairs of the chiral condensate

62.  B  3-8  0, T  130 MeV

63. K mesons in dense matter G.E Brown, C.H. Lee, M. Rho, V. Thorsson, Nucl. Phys. A 567 (1994) 937 T. Waas, N. Kaiser, W. Weise, Phys. Lett. B 379 (1996) 34 J. Schaffner-Bielich, J. Bondorf, I. Mishustin, Nucl. Phys. A 625 (1997) How to measure in-medium modifications of kaons in heavy-ion collisions?  yield at subthreshold beam energies  repulsive K + N and attractive K - N potential: angular distributions

64. In-medium modifications of K + mesons Data: M. Menzel et al., (KaoS Collab.), Phys. Lett. B 495 (2000) 26 K. Wisniewski et al., ( FOPI Collab.), Eur. Phys. J A 9 (2000) 515 Reduced K + yield due to increased in-medium K + mass

65. Au + Au at 1 AGeV, b = 7 fm Azimuthal angle distributions dN/d  (“flow”) Target rapidity K + around midrapidity  particle emission angle with respect to the reaction plane

66. Data: Y. Shin et al., (KaoS Collaboration), Phys. Rev. Lett. 81 (1998) 1576 F. Uhlig et al., (KaoS Collaboration), Phys. Rev. Lett. 95 (2005) 012301 Calculations see A. Larionov, U. Mosel, nucl-th/0504023 Data show evidence for repulsive K + N interaction ! K + azimuthal emission pattern from A+A collisions K + mean free path in nuclear matter at ρ 0 : λ ~ 5 fm

67. F. Uhlig et al., (KaoS Collaboration), Phys. Rev. Lett. 95 (2005) 012301 Ni+Ni at 1.93 AGeV: π, K + and K - azimuthal distributions 3.8 fm < b < 6.4 fm 0.4 < y/y beam <0.6 0.2 GeV < p ┴ < 0.8 GeV IQMD Calculation: C. Hartnack et al.

68. dN(φ)/φ  1 + 2v 1 cos(φ) + 2v 2 cos(2φ) +... Au+Au 1.5 AGeV semi-central collisions (b > 6.4 fm) K + and K - azimuthal angular distributions M. Płoskon, PhD Thesis 2005

69. Antikaon spectral function in nuclear matter self-consistent coupled channel calculation with mean field (s,p,d waves)  (1405) K-K- K-K- N -1

70. dN(φ)/φ  1 + 2v 1 cos(φ) + 2v 2 cos(2φ) +... Elliptic flow of K + and K - mesons: Comparison to off-shell transport calculations and in-medium spectral functions Data: M. Płoskon, PhD Thesis, Univ. Frankfurt 2005 Off-shell transport calculations: W. Cassing et al., NPA 727 (2003) 59, E. Bratkovskaya, priv. com. Coupled channel G-Matrix approach (K- spectral functions): L. Tolos et al., NPA 690 (2001) 547

71. p + C  K + + X (1.6, 2.5, 3.5 GeV) p + C  K - + X (2.5, 3.5 GeV) p + Au  K + + X (1.6, 2.5, 3.5 GeV) p + Au  K - + X (2.5, 3.5 GeV) Strangeness production in proton - nucleus collisions W. Scheinast et al., (KaoS Collaboration) Phys. Rev. Lett. 96 (2006) 072301

72. Transport calculation: H. W. Barz et al., Phys.Rev. C68 (2003) 041901 U K ≈ - 80  /  0 MeV Important channel: Strangeness exchange  + N  N + N + K — Comparison of p+A data to transport calculations K+K+ K-K-

73. Summary Kaon production Excitation function of K + production in A+A collisions (ρ = 1–3 ρ 0 ):  The nuclear matter equation-of-state is soft ( K  200 MeV) Yield and elliptic flow of K + mesons in A+A collisions:  The in-medium potential of K + mesons is repulsive (i.e. the effective K + mass is increased) Yield and elliptic flow of K - mesons in A+A collisions:  Quantitative interpretation of data requires off-shell transport calculations and in-medium spectral functions