Subthreshold K+ production and the nuclear equation-of-stateChristian SturmJohann Wolfgang Goethe-Universitt FrankfurtNUCLEAR MATTER IN HIGH DENSITYHirschegg 2009

Christian Sturm

The compression modulus of nuclear matter at saturation density 0 : Excitation of the giant monopole resonanceinelastic scattering of particles on nuclei measure of the total energy of the outgoing particle Ex Ekin = 240 MeVFrom the measured excitation energy distribution Ex : frequency restoring force (potential) of the oscillation "spring constant" = compression modulusThe energy loss of the particle of about15 25 MeV excites slight density oscillationswith elongations of about 1/100 0 (around saturation density 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

Christian Sturm

The compression modulus of nuclear matter at saturation density 0 : Excitation of the giant monopole resonance"Excitation of the Giant Monopole Resonance by inelastic scattering of particles on nuclei"Youngblood et al. , Phys. Rev. Lett. 82 (1999)691 = 231 5 MeV

Christian Sturm

high density phaseAuAu+QMD , S. Bass , Uni. Frankfurttransport models: max 30 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

Christian Sturm

Au +Au 1.5 AGeVUrQMD

Christian Sturm

The case of moderate beam energiesParticle 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

Christian Sturm

The Kaonspectrometer dedicated to identify rare Kaon eventsKaons are rare at these energy regime:

Christian Sturm

Subthreshold K+ production in nucleus-nucleus collisionsand the equation-of-state of symmetric nuclear matterWhy are Kaons at SIS energies well suited to probe the nuclear equation-of-state ?

brief surveyImportant 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

Associated production of strange mesons in elementary nucleon-nucleon reactionsproduction thresholdin NN collisions :Kaonsproduction thresholdin NN collisions :Antikaons

Christian Sturm

Additional channels in nucleus-nucleus collisions

Christian Sturm

Final state interactionmean free path at 0:K+ no absorption only elastic scattering

Christian Sturm

In-medium modification of Kaons and Antikaons in dense nuclear matterG.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

In-medium modification of Kaons and Antikaonsrepulsive K+ N potentialattractive K- N potential(envelope of several microscopic calculations: all predict the same trend !)This should effect:production yieldpropagation angular distributions

Christian Sturm

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

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 !K+ azimuthal emission pattern from A+A collisions

Christian Sturm

K0 production in Ar + KCl reactionsinvariant mass : Ar + KCl 1.756 GeV / nucleon50% K0S , 50% K0L

Christian Sturm

K0 production in Ar + KCl reactionsrepulsive Kaon-Nucleon Potential : IQMD calculation by C. Hartnack, J. AichelinAr + KCl 1.756 GeV / nucleontransverse mass

Christian Sturm

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 collisionsW. Scheinast et al., (KaoS Collaboration) Phys. Rev. Lett. 96 (2006) 072301 Search for in-medium effects at saturation density !

Christian Sturm

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-Kaon and Antikaon in-medium potentials at 0ratio:

Christian Sturm

M. Poskon, PhD Thesis 2005K+ and K- azimuthal angular distributions in Au + Au collisions 1.5 GeV / nucleonsemi-central collisions (b > 6.4 fm)fit:

Christian Sturm

Elliptic flow of K+ and K- mesons:Comparison to off-shell transport calculations and in-medium spectral functionsData: M. Poskon, PhD Thesis, Univ. Frankfurt 2005Off-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) 547not yet conclusive !

Christian Sturm

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 = - 8020 /0 MeV in-medium K+N potential VK+N = 255 /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

effective NN-Potential (Skyrme)Compression Modulus :The equation-of-state of (symmetric) nuclear matter

Christian Sturm

"Subthreshold" K+ production linked to the nuclear equation-of-state Subthreshold K+ mesonspredominantly produced by collective effects multi step processes(Y=,)production threshold: Elab= 1.58 GeVe.g.

Christian Sturm

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

K+ production in Au+Au and C+C collisions

Christian Sturm

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

Christian Sturm

The compression modulus of nuclear matter at = 2 - 3 0Experiment: C. Sturm et al., Phys. Rev. Lett. 86 (2001) 39Theory: RQMD C. Fuchs et al., Phys. Rev. Lett. 86 (2001) 1974

Christian Sturm

The compression modulus of nuclear matter at = 2 - 3 0Experiment: C. Sturm et al., Phys. Rev. Lett. 86 (2001) 39Theory: RQMD C. Fuchs et al., Phys. Rev. Lett. 86 (2001) 1974 IQMD C. Hartnack, J. Aichelin

Christian Sturm

Robust observable ? Variation of:cross sectionsin-medium KN potentials lifetimeconclusion:calculations using a potential according to a soft nuclear equation-of-state describe the data at best !IQMD C. Hartnack, J. AichelinIQMD

Christian Sturm

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

Christian Sturm

Conclusion Nuclear equation-of-state

23 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)

1 0Excitation of the giant monopole resonance in inelastic -nucleus collisions The compression modulus of nuclear matter K = 231 5 MeV

Christian Sturm

additional slides ...

Christian Sturm

dN/dF (1 + 2v1 cosF + 2v2 cos2F)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(px/A)/d(y/ycm)

Christian Sturm

AcceptancesAu+Au 1.5GeV

Christian Sturm

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 115ToF-2ToF-1

Christian Sturm

Spectral distributions from A+A (cm90) (w/o selection of impact parameter)

Christian Sturm

Spectral distributions as a function of the centralityA. Frster et al. PRL 91(2003)152301F.Uhlig PhD Thesis,TU DarmstadtAu+Au, 1.5AGeVNi+Ni, 1.93AGeV

Christian Sturm

Spectral distributions as a function of the centrality 5% r

15% r 15% r 25% r

40% rcentralperipheralAu+Au, 1.5AGeV1.5AGeV

Christian Sturm

Spectral distributions of PionsAu + Au , 1.5AGeV

Christian Sturm

Azimuthal particle emissionp,d,t,Fourier expansion of the dN/d distribution:mid rapiditythe coefficients quantify : v1 the in-plane and v2 the elliptic emission pattern

Christian Sturm

Directed flow of protons and fragments and the nuclear equation-of-stateAu + Au , 400 AMeV , M4transport calculation (IQMD) by C. HartnackA. Andronic et. al. Phys. Rev. C 67 (2003) 034907 best description of Au and Xe data at 400AMeVwith a soft EoS + MDIFourier coefficient v1 :directed flow (in-plane)

Christian Sturm

Azimuthal particle emission+Bi+Bi 0.7AGeV, semi centralD. Brill et al. ZPA355 (1996) 61ZPA357 (1997) 207out-of-plane

Christian Sturm

K+ sideward flowK+preaction planetop view K+-Mesons show an antiflow" caused by a repulsive K+N potential

Christian Sturm

The in-medium spectral function of AntikaonsCoupled channels calculationM. Lutz GSI resonant state close to theK-N threshold: (1405)

Christian Sturm

K+ and K- production in p+p and A+A collisions

Christian Sturm

Christian Sturm

FOPI and KaoS were designed as complementary experiments:FOPI ... emphasis on the study of global observables ... reaction dynamics like elliptic flow of protons and fragments cover 4 in case of protons and fragments ... beautiful data! ... remarkable are the results

KaoS ... a spectrometer especially designed to detect rare Kaon events small solid angle (quadruple enlarges the solid angle) Kaon trigger based on ToF (stop wall positioned in the focal plane)measure under different lab angles: the spectrometer can be turned around the target pointIn elementary nn-reactions Due to Strangeness conservation in the strong interaction ... production of ssbar pairsadditional channels in A+A collisions available e.g. multi step processes involving 3 or more particles like 1.) first forming a -resonance ... store energy in a second step ... the -resonance collides with a nucleon and the production threshold can be overcome representation: linear dependence gives a flat distribution K+ production and multi step processes - stronger than proportional increase multi step processes collective effects pions show a simple linear dependence 2.) absorption : Pions ... dominant -Resonance K+ ... only elastic scattering K- inelastic channels

Allow me a brief introduction ... the theoreticians may excuse that simplified picture that I'm going to present ...The nuclear equation-of-state of course is a thermodynamical concept ... which requires equilibrium ... but the nuclear matter in a HI reaction is not necessarily in an thermodynamical equilibrium !

end: Usually in this context with EoS is meant the interaction ... effective NN-Potential ... not thermodynamical state a set of parameters of the Skyrme pot. which is used in transport models determines kappa ! How does the EoS effect the subthreshold Kaon production? ... 1.) baryon density 2.) for particle production available energy ...

end: in real life one can not change the stiffness of the EoS and look whether the Kaon yield differs ... like it's possible in theory! as a experimentalist one can vary the size of the reaction system and the bombarding energy ...FOPI measures Kaons more in the backward hemisphere ... whereas KaoS around midrapidity KaoS ... a spectrometer especially designed to detect rare Kaon events small solid angle (quadruple enlarges the solid angle) Kaon trigger based on ToF (stop wall positioned in the focal plane)measure under different lab angles: the spectrometer can be turned around the target pointInclusive spectral distributions measured around midrapidity - in a light , medium and heavy symmetric reaction system K+ identified down to 0.56 AGeV Au+Au !... let me briefly introduce ...

end: what could one expect in case of the K+ mesons ... in comparison with the pions a large mean free path ...... let me briefly introduce ...

end: what could one expect in case of the K+ mesons ... in comparison with the pions a large mean free path ...

end: "offshell" transport under construction ... at least A+A collisions is a difficult issue ... we had measured p+A collisions too ...