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

2 / 33Christian SturmHirschegg 2009 The compression modulus of nuclear matter at saturation density ρ 0 : Excitation of the giant monopole resonance 90 Zr α α inelastic scattering of α particles on nuclei measure of the total energy of the outgoing α particle → E x E kin = 240 MeV From the measured excitation energy distribution E x : → frequency → restoring force (potential) of the oscillation → "spring constant" κ = compression modulus The energy loss of the α particle of about 15 – 25 MeV excites slight density oscillations with elongations of about 1/100 ρ 0 (around saturation density ρ 0 ). It is a collective excitation of the nucleus and calls the Giant Monopole Resonance or the "breathing mode" of nuclei. "resonance phenomenon" Youngblood et al., Phys. Rev. Lett. 82 (1999)691

3 / 33Christian SturmHirschegg 2009 The compression modulus of nuclear matter at saturation density ρ 0 : 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

4 / 33Christian SturmHirschegg 2009 high density phase Au + QMD, S. Bass, Uni. Frankfurt transport models: ρ max ≅ 3ρ 0 ≈ s t resonances nucleons mesons high density and temperature on a very short time scale thermodynamical equilibrium not necessarily achieved To investigate high baryon densities in the laboratory : Relativistic Heavy Ion Collisions 1.5 GeV/nucleon

5 / 33Christian SturmHirschegg 2009 Au +Au 1.5 AGeV UrQMD

6 / 33Christian SturmHirschegg 2009 The case of moderate beam energies t [fm/c] ≈ 10 fm/c 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 :  (   > 2) ≈ 10 fm/c → comparatively long life-time at moderate densities ! NN → NΔ πNπN πN → K + Λ multi step processes: i.e.

7 / 33Christian SturmHirschegg 2009 FOPI: Light vector mesons at SIS18: Dilepton spectroscopy with HADES

8 / 33Christian SturmHirschegg 2009 The Kaonspectrometer dedicated to identify rare Kaon events Kaons are rare at these energy regime:

9 / 33Christian SturmHirschegg 2009 Subthreshold K + production in nucleus-nucleus collisions and 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 ?

10 / 33Christian SturmHirschegg 2009 Associated production of strange mesons in elementary nucleon-nucleon reactions uduudu uduudu n p uddudd susu K+K+ susu p KK dduddu n udsuds n p uddudd susu  K+K+ dduddu n uduudu production threshold in NN collisions : Kaons production threshold in NN collisions : Antikaons

11 / 33Christian SturmHirschegg 2009 Additional channels in nucleus-nucleus collisions e.g. (Y=Λ,Σ) multi step processes ! M: multiplicity = number / per collision central collisions peripheral A part : number of participating nucleons “Subthreshold” K + production Au + Au 1 GeV / nucleon : Kaons are predominantly produced during the high density phase of the collision!

12 / 33Christian SturmHirschegg 2009 Final state interaction mean free path at ρ 0 : K + no absorption only elastic scattering

13 / 33Christian SturmHirschegg 2009 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)  (1405) K-K- K-K- N -1 self-consistent coupled channel calculation with mean field (s,p,d waves)

14 / 33Christian SturmHirschegg 2009 In-medium modification of Kaons and Antikaons repulsive K + N potential attractive K - N potential (envelope of several microscopic calculations: all predict the same trend !) This should effect: production → yield propagation → angular distributions

15 / 33Christian SturmHirschegg 2009 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

16 / 33Christian SturmHirschegg 2009 Data: Y. Shin et al., (KaoS Collaboration), Phys. Rev. Lett. 81 (1998) 1576 F. Uhlig et al., (KaoS Collaboration), Phys. Rev. Lett. 95 (2005) Calculations see A. Larionov, U. Mosel, nucl-th/ Evidence for a repulsive K + N interaction ! K + azimuthal emission pattern from A+A collisions

17 / 33Christian SturmHirschegg 2009 K 0 production in Ar + KCl reactions invariant mass : Ar + KCl GeV / nucleon 50% K 0 S, 50% K 0 L 69%, cτ ≈ 2.7 cm 68%, cτ ≈ 15.5 m

18 / 33Christian SturmHirschegg 2009 K 0 production in Ar + KCl reactions repulsive Kaon-Nucleon Potential : IQMD calculation by C. Hartnack, J. Aichelin Ar + KCl GeV / nucleon transverse mass

19 / 33Christian SturmHirschegg 2009 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) Search for in-medium effects at saturation density !

20 / 33Christian SturmHirschegg 2009 Transport calculation: H. W. Barz et al., Phys.Rev. C68 (2003) contributing channels: p + N → K + +  p + N → N + N + K + + K -  + N  N + N + K - Kaon and Antikaon in-medium potentials at ρ 0 ratio: In-medium KN potentials used:

21 / 33Christian SturmHirschegg 2009 M. Płoskon, PhD Thesis 2005 K + and K - azimuthal angular distributions in Au + Au collisions 1.5 GeV / nucleon semi-central collisions (b > 6.4 fm) fit:

22 / 33Christian SturmHirschegg 2009 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 !

23 / 33Christian SturmHirschegg 2009 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 V K - N = - 80  20  /  0 MeV  in-medium K + N potential V K + 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 !)

24 / 33Christian SturmHirschegg 2009 nuclear equation-of-state at T = 0 : " compressional" energy effective NN-Potential (Skyrme) stiff EoS soft EoS Compression Modulus : 7/ κ = 200 MeV κ = 380 MeV γβ [MeV] α [MeV] The equation-of-state of (symmetric) nuclear matter

25 / 33Christian SturmHirschegg 2009 "Subthreshold" K + production linked to the nuclear equation-of-state “Subthreshold” K + mesons predominantly produced by collective effects → multi step processes (Y=Λ,Σ) production threshold: E lab = 1.58 GeV e.g. Probability of multi step processes increases nonlinearly with the baryon density soft EoS ρ max / ρ 0 ≅ 3.1 stiff EoS ρ max / ρ 0 ≅ 2.7 IQMD: Au+Au 1AGeV

26 / 33Christian SturmHirschegg 2009 What could be a sensitive observable ? Idea: measure K + production in Au+Au and C+C collisions ! IQMD C. Hartnack The light collision system serves as a “reference” system because there is almost no compression expected !

27 / 33Christian SturmHirschegg 2009 K + production in Au+Au and C+C collisions

28 / 33Christian SturmHirschegg 2009 Production excitation functions in Au+Au and C+C collisions enhanced K + production in Au+Au reactions C. Sturm et al., Phys. Rev. Lett. 86 (2001) 39

29 / 33Christian SturmHirschegg 2009 The compression modulus of nuclear matter at ρ = ρ 0 Experiment: C. Sturm et al., Phys. Rev. Lett. 86 (2001) 39 soft nuclear equation-of-state: κ ≈ 200 MeV Theory: RQMD C. Fuchs et al., Phys. Rev. Lett. 86 (2001) 1974

30 / 33Christian SturmHirschegg 2009 The compression modulus of nuclear matter at ρ = ρ 0 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

31 / 33Christian SturmHirschegg 2009 Robust observable ? Variation of: cross sections in-medium KN potentials Δ lifetime conclusion: calculations using a potential according to a “soft” nuclear equation-of-state describe the data at best ! IQMD C. Hartnack, J. Aichelin IQMD

32 / 33Christian SturmHirschegg 2009 The equation-of-state of (symmetric) nuclear matter C. Fuchs, Prog. Part. Nucl. Phys. 56 (2006) 1

33 / 33Christian SturmHirschegg 2009 Conclusion Nuclear equation-of-state ρ ≈ 2–3 ρ 0 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) ρ ≈ 1 ρ 0 Excitation of the giant monopole resonance in inelastic α-nucleus collisions  The compression modulus of nuclear matter K = 231± 5 MeV

34 / 33Christian SturmHirschegg 2009 additional slides...

35 / 33Christian SturmHirschegg 2009 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 )

36 / 33Christian SturmHirschegg 2009 K+K+ 32 o 40 o 48 o 60 o 71 o Θ lab = Acceptances Au+Au 1.5GeV

37 / 33Christian SturmHirschegg 2009 K+K+ 32 o 40 o 48 o 60 o 71 o Θ lab = The Kaon Spectrometer  compact size: path length 5 – 7.5 m  Kaon Trigger (ToF + Cherenkov)  efficient background reduction by 2xToF measurement   = 15 – 35 msr   p/p  2   lab : 0  – 115  ToF-2ToF-1

38 / 33Christian SturmHirschegg 2009 Spectral distributions from A+A (Θ cm ≈90 º ) (w/o selection of impact parameter) fit:

39 / 33Christian SturmHirschegg 2009 Spectral distributions as a function of the centrality A. Förster et al. PRL 91(2003) F.Uhlig PhD Thesis,TU Darmstadt Au+Au, 1.5AGeV Ni+Ni, 1.93AGeV  5% σ r  15% σ r  15% σ r 25% σ r  40% σ r central peripheral

40 / 33Christian SturmHirschegg 2009 Spectral distributions as a function of the centrality  5% σ r  15% σ r  15% σ r 25% σ r  40% σ r central peripheral Au+Au, 1.5AGeV 1.5AGeV

41 / 33Christian SturmHirschegg 2009 Spectral distributions of Pions Au + Au, 1.5AGeV

42 / 33Christian SturmHirschegg 2009 Azimuthal particle emission out off plane emission semi central collisions p,d,t,α Fourier expansion of the dN/d ϕ distribution: mid rapidity the coefficients quantify : v 1 the in-plane and v 2 the elliptic emission pattern

43 / 33Christian SturmHirschegg 2009 Directed flow of protons and fragments and the nuclear equation-of-state Au + Au, 400 AMeV, M4 transport calculation (IQMD) by C. Hartnack A. Andronic et. al. Phys. Rev. C 67 (2003) best description of Au and Xe data at 400AMeVwith a soft EoS + MDI Fourier coefficient v 1 : directed flow (in-plane)

44 / 33Christian SturmHirschegg 2009 semi central collisions Azimuthal particle emission π+π+ Bi+Bi 0.7AGeV, semi central D. Brill et al. ZPA355 (1996) 61 ZPA357 (1997) 207 Pions are enhanced emitted perpendicular to the reaction plane. What would you expect how the K + emission pattern look like ? out-of-plane

45 / 33Christian SturmHirschegg 2009 K + sideward flow K+K+ p reaction plane top view RBUU: E. Bratkovskaya, W. Cassing P. Crochet et al., Phys. Lett. B 486 (2000) 6 K + -Mesons show an “antiflow" – caused by a repulsive K + N potential -1.2  y 0  - 0.5

46 / 33Christian SturmHirschegg 2009 The in-medium spectral function of Antikaons  (1405) K-K- K-K- N -1 Coupled channels calculation M. Lutz GSI resonant state close to the K - N threshold: Λ(1405)

47 / 33Christian SturmHirschegg 2009 K + and K - production in p+p and A+A collisions F. Laue, C. Sturm et al. PRL 82 (1999) 1640 M. Menzel et al. PLB 495 (2000) 26 dropping K - mass ? F. Laue, C. Sturm et al. PRL 82 (1999) 1640 M. Menzel et al. PLB 495 (2000) 26 Parameterizations: A. Sibirtsev, W. Cassing, C.M. Ko, ZPA 258 (1997) 101 K - / K + ≪ 1

48 / 33Christian SturmHirschegg 2009 soft EoS stiff EoS Nb + Nb, 0.7 AGeV ρ/ρ0ρ/ρ0 PKPK t [fm/c]