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Subthreshold K + production and the nuclear equation-of-state

This study investigates subthreshold K+ production and its implications for the equation-of-state of symmetric nuclear matter. It explores the in-medium properties of Kaons and their production in nucleus-nucleus collisions. The findings are compared with transport model calculations to identify a robust observable.

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Subthreshold K + production and the nuclear equation-of-state

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  1. Subthreshold K+ production and the nuclear equation-of-state Christian Sturm Johann Wolfgang Goethe-Universität Frankfurt NUCLEAR MATTER IN HIGH DENSITY Hirschegg 2009

  2. α α 90Zr The compression modulus of nuclear matter at saturation density ρ0: Excitation of the giant monopole resonance Youngblood et al. , Phys. Rev. Lett. 82 (1999)691 inelastic scattering of α particles on nuclei measure of the total energy of the outgoing α particle → Ex Ekin = 240 MeV "resonance phenomenon" The energy loss of the α particle of about 15 – 25 MeV excites slight density oscillations with elongations of about 1/100 ρ0 (around saturation density ρ0 ). It is a collective excitation of the nucleus and calls the Giant Monopole Resonance or the "breathing mode" of nuclei. From the measured excitation energy distribution Ex : → frequency → restoring force (potential) of the oscillation → "spring constant" κ = compressionmodulus Christian Sturm

  3. The compression modulus of nuclear matter at saturation density ρ0: Excitation of the giant monopole resonance "Excitation of the Giant Monopole Resonance by inelastic scattering of α particles on nuclei" Youngblood et al. , Phys. Rev. Lett. 82 (1999)691 κ = 231 ± 5 MeV Christian Sturm

  4. nucleons resonances mesons t ≈ 10-22 s To investigate high baryon densities in the laboratory: Relativistic Heavy Ion Collisions Au + Au QMD , S. Bass , Uni. Frankfurt high density phase 1.5 GeV/nucleon transport models:ρmax≅ 3ρ0 • high density and temperature on a very short time scale • thermodynamical equilibrium not necessarily achieved Christian Sturm

  5. Au +Au 1.5 AGeV UrQMD Christian Sturm

  6. NN → NΔ πN πN → K+Λ multi step processes: i.e. ≈ 10 fm/c 30 10 20 t [fm/c] The case of moderate beam energies • Particle production at or below threshold : • co-operative processes • (i.e. multi step processes) • production confined to the • high density phase ! Enhancement of baryon density : Dt (r/r0 > 2) ≈ 10 fm/c → comparatively long life-time at moderate densities ! Christian Sturm

  7. FOPI: Light vector mesons at SIS18: Dilepton spectroscopy with HADES Christian Sturm

  8. The Kaonspectrometerdedicated to identify rare Kaon events Kaons are rare at these energy regime: Christian Sturm

  9. Subthreshold K+ production in nucleus-nucleus collisionsand the equation-of-state of symmetric nuclear matter Why are Kaons at SIS energies well suited to probe the nuclear equation-of-state ? brief survey Important for transport models: what are the experimental findings according the in-medium properties of Kaons ? What is the conclusion of the subthreshold K+ production in comparison with transport model calculations ? Could we identify a robust observable ? Christian Sturm

  10. u d u u d s p L u d d u d d n s u n K+ s u K+ s u u d u K- p u d u d d u d d u p n n Associated production of strange mesons in elementary nucleon-nucleon reactions Kaons Antikaons production threshold in NN collisions : production threshold in NN collisions : Christian Sturm

  11. “Subthreshold” K+ production e.g. (Y=Λ,Σ) multi step processes ! Au + Au 1 GeV / nucleon : Kaons are predominantly produced during the high density phase of the collision! central collisions peripheral M: multiplicity = number / per collision Apart : number of participating nucleons Additional channels in nucleus-nucleus collisions Christian Sturm

  12. Final state interaction mean free path at ρ0: • K+ • no absorption • only elastic scattering Christian Sturm

  13. L(1405) K- K- N-1 In-medium modification of Kaons and Antikaons in dense nuclear 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) self-consistent coupled channel calculation with mean field (s,p,d waves) Christian Sturm

  14. In-medium modification of Kaons and Antikaons (envelope of several microscopic calculations: all predict the same trend !) repulsive K+ N potential attractive K- N potential This should effect: production→ yield propagation→ angular distributions Christian Sturm

  15. 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 Christian Sturm

  16. K+ azimuthal emission pattern from A+A collisions 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 Evidence for a repulsive K+N interaction ! Christian Sturm

  17. 69% , cτ ≈ 2.7 cm 68% , cτ ≈ 15.5 m K0 production in Ar + KCl reactions Ar + KCl 1.756 GeV / nucleon 50% K0S , 50% K0L invariant mass : Christian Sturm

  18. K0 production in Ar + KCl reactions Ar + KCl 1.756 GeV / nucleon repulsive Kaon-Nucleon Potential : IQMD calculation by C. Hartnack, J. Aichelin transverse mass Christian Sturm

  19. Strangeness production in proton - nucleus collisions Search for in-medium effects at saturation density ! 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) W. Scheinast et al., (KaoS Collaboration) Phys. Rev. Lett. 96 (2006) 072301 Christian Sturm

  20. In-medium KN potentials used: Kaon and Antikaon in-medium potentials at ρ0 ratio: Transport calculation: H. W. Barz et al., Phys.Rev. C68 (2003) 041901 contributing channels: p + N → K++  p + N → N + N + K+ + K-  + N  N + N + K- Christian Sturm

  21. K+ and K- azimuthal angular distributions in Au + Au collisions 1.5 GeV / nucleon fit: semi-central collisions (b > 6.4 fm) M. Płoskon, PhD Thesis 2005 Christian Sturm

  22. 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 not yet conclusive ! Christian Sturm

  23. Conclusion In-medium modification of Kaons and Antikaons Yield and elliptic flow of Kaons in A+A collisions: The in-medium Kaon-Nucleon potential is repulsive Yield of Kaons and Antikaons in proton-nucleus collisions:  in-medium K-N potential VK-N = - 8020/0 MeV in-medium K+N potential VK+N = 255/0 MeV Yield and elliptic flow of Antikaons in A+A collisions: Quantitative interpretation of data requires off-shell transport calculations (dealing with spectral functions !) Christian Sturm

  24. nuclear equation-of-state at T = 0 : "compressional" energy stiff EoS soft EoS α [MeV] β [MeV] γ κ = 380 MeV -124 70.5 2 κ = 200 MeV -356 303 7/6 The equation-of-state of (symmetric) nuclear matter effective NN-Potential (Skyrme) Compression Modulus : Christian Sturm

  25. Probability of multi step processes increases nonlinearly with the baryon density IQMD: Au+Au 1AGeV stiff EoS ρmax / ρ0≅ 2.7 soft EoS ρmax / ρ0≅ 3.1 "Subthreshold" K+ production linked to the nuclear equation-of-state production threshold: Elab= 1.58 GeV “Subthreshold” K+ mesons predominantly produced bycollective effects → multi step processes e.g. (Y=Λ,Σ) Christian Sturm

  26. IQMD C. Hartnack What could be a sensitive observable ? Idea: measure K+ production in Au+Au and C+C collisions ! The light collision system serves as a “reference” system because there is almost no compression expected ! Christian Sturm

  27. K+ production in Au+Au and C+C collisions Christian Sturm

  28. Production excitation functions in Au+Au and C+C collisions C. Sturm et al., Phys. Rev. Lett. 86 (2001) 39 enhanced K+ production in Au+Au reactions Christian Sturm

  29. soft nuclear equation-of-state: κ≈ 200 MeV The compression modulus of nuclear matter at ρ = 2 - 3 ρ0 Experiment: C. Sturm et al., Phys. Rev. Lett. 86 (2001) 39 Theory: RQMD C. Fuchs et al., Phys. Rev. Lett. 86 (2001) 1974 Christian Sturm

  30. IQMD C. Hartnack, J. Aichelin The compression modulus of nuclear matter at ρ = 2 - 3 ρ0 Experiment: C. Sturm et al., Phys. Rev. Lett. 86 (2001) 39 Theory: RQMD C. Fuchs et al., Phys. Rev. Lett. 86 (2001) 1974 IQMD C. Hartnack, J. Aichelin Christian Sturm

  31. Robust observable ? Variation of: IQMD IQMD C. Hartnack, J. Aichelin cross sections in-medium KN potentials conclusion: calculations using a potential according to a “soft” nuclear equation-of-state describe the data at best ! Δ lifetime Christian Sturm

  32. The equation-of-state of (symmetric) nuclear matter C. Fuchs, Prog. Part. Nucl. Phys. 56 (2006) 1 Christian Sturm

  33. Conclusion Nuclear equation-of-state ρ≈ 1 ρ0 Excitation of the giant monopole resonance in inelastic α-nucleus collisions  The compression modulus of nuclear matter K = 231± 5 MeV ρ≈ 2–3 ρ0 Double ratio of the K+ production excitation functions in Au+Au and C+C  Robust observable  The nuclear matter equation-of-state is soft ( K  200 MeV) Christian Sturm

  34. additional slides ... Christian Sturm

  35. Probing the nuclear equation-of-state: proton collective flow P. Danielewicz, R. Lacey, W.G. Lynch, Science 298 (2002) 1592 Transverse in-plane flow: Elliptic flow: F = d(px/A)/d(y/ycm) dN/dF  (1 + 2v1cosF + 2v2 cos2F) Christian Sturm

  36. Θlab= 60o K+ 48o 40o 71o 32o Acceptances Au+Au 1.5GeV Christian Sturm

  37. Θlab= K+ 60o 48o 71o 40o 32o The Kaon Spectrometer •  = 15 – 35 msr • p/p  2 • lab: 0 – 115 ToF-2 ToF-1 • compact size: path length 5 – 7.5 m • Kaon Trigger (ToF + Cherenkov) • efficient background reduction by 2xToF measurement Christian Sturm

  38. fit: Spectral distributions from A+A (Θcm≈90º) (w/o selection of impact parameter) Christian Sturm

  39.  5% σr  15% σr  15% σr  25% σr  40% σr central peripheral Spectral distributions as a function of the centrality Ni+Ni, 1.93AGeV Au+Au, 1.5AGeV A. Förster et al. PRL 91(2003)152301 F.Uhlig PhD Thesis,TU Darmstadt Christian Sturm

  40. Spectral distributions as a function of the centrality 1.5AGeV Au+Au, 1.5AGeV central 5% σr 15% σr 15% σr 25% σr 40% σr peripheral Christian Sturm

  41. Spectral distributions of Pions Au + Au , 1.5AGeV Christian Sturm

  42. out off planeemission semi central collisions out off plane emission Azimuthal particle emission mid rapidity p,d,t,α Fourier expansion of the dN/dϕdistribution: • the coefficients quantify : • v1 the in-plane and • v2 the elliptic emission pattern Christian Sturm

  43. Directed flow of protons and fragments and the nuclear equation-of-state A. Andronic et. al. Phys. Rev. C 67 (2003) 034907 Au + Au , 400 AMeV , M4 Fourier coefficient v1 : directed flow (in-plane) best description of Au and Xe data at 400AMeVwith a soft EoS + MDI transport calculation (IQMD) by C. Hartnack Christian Sturm

  44. semi central collisions Pions are enhanced emitted perpendicular to the reaction plane. What would you expect how the K+ emission pattern look like ? Azimuthal particle emission out-of-plane Bi+Bi 0.7AGeV, semi central π+ D. Brill et al. ZPA355 (1996) 61 ZPA357 (1997) 207 Christian Sturm

  45. -1.2  y0  -0.5 P. Crochet et al., Phys. Lett. B 486 (2000) 6 RBUU: E. Bratkovskaya , W. Cassing K+ sideward flow reaction plane K+ top view p K+-Mesons show an “antiflow" – caused by a repulsive K+N potential Christian Sturm

  46. L(1405) K- K- N-1 The in-medium spectral function of Antikaons Coupled channels calculation M. Lutz GSI resonant state close to the K-N threshold: Λ(1405) Christian Sturm

  47. Parameterizations: A. Sibirtsev, W. Cassing, C.M. Ko, ZPA 258 (1997) 101 F. Laue, C. Sturm et al. PRL 82 (1999) 1640 M. Menzel et al. PLB 495 (2000) 26 K-/ K+≪ 1 F. Laue, C. Sturm et al. PRL 82 (1999) 1640 M. Menzel et al. PLB 495 (2000) 26 dropping K- mass ? K+ and K- production in p+p and A+A collisions Christian Sturm

  48. ρ/ρ0 PK Nb + Nb , 0.7 AGeV soft EoS stiff EoS t [fm/c] Christian Sturm

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