Aman Sood, Christoph Hartnack, Elena Bratkovskaya

Transcription

1 What strange particles can tell us about hadronic matter and what hadronic matter tells us about strange particles Aman Sood, Christoph Hartnack, Elena Bratkovskaya Strangeness production at threshold: The nucleus can act as detector Strangeness can probe nuclear properties K + and the nuclear Eq.of state

2 How one can solve physics questions with HI experiments? 2 Not directly: one measures spectra but no observable gives direct information on cross sections, potentials, equation of state. For the physics one needs comparison with theory: One simulates the complete heavy ion reaction on the computer using different eqs. of state different KN potentials (+ other unknown quantities) and compares the results with experiment -> One has to assure that the results are robust This requires a lot of systematics (different AA, different energies) 1/m t 2 d 2 N/(dm t dy c.m. ) ((GeV/c 2 ) -3 ) <y c.m. <0.05(x10 0 ) -0.15<y c.m. <-0.05(x10-1 ) -0.25<y c.m. <-0.15(x10-2 ) -0.35<y c.m. <-0.25(x10-3 ) -0.45<y c.m. <-0.35(x10-4 ) -0.55<y c.m. <-0.45(x10-5 ) HADES HSD w pot HSD wo pot m t - m 0 (GeV/c 2 )

3 The tools: Isospin-Quantum Molecular Dynamics (IQMD) Hadron String Model (HSD) (Differences here not important) -Semiclassical dynamical N(1)-body model - with quantum features -based on 2- and 3-body interactions -- Microscopic calculation of heavy ion collisions on an event-by-event-basis 3 -includes N,Δ,p with isospin d.o.f. -- strange particles treated virtually Allows for a «photo» of the high density phase and for a look inside

4 Strangeness is complicated: Many combinations are possible - Many channels have to be implemented Each channel contains isospin subdivisions Only few channels (like pp pλk + ) are measured by experiment (even incomplete infos) Significant incertainties from parametrization of unknown channels or isospin subdivisions 4

5 Subthreshold kaon production Production of kaons at energies below the kinetic threshold for K production in elementary pp collisions Fermi momenta may contribute to of the collisions 5 Multi-step processes (especially with a Δ) can cumulate the energy needed for kaon production. Short Δ lifetime enhances production at high densities Repulsive KN potential cause a penalty factor at high density The ρ dependence of both yields a sensitivity to the eq. of state and KN potential

6 Condition: The yield depends of the EOS Multistep processes require high densities, but medium effects of kaons penalize the high density production No KN potential soft Incl. KN potential K= compressibility modulus at ρ 0 Soft : K =200 MeV Hard: K=380 MeV 6 hard Effect of repulsive KN potential and multistep processes compensate to a large extend but sensitivity to the eos still survives. However, the absolute yield depends on many details and is not conclusive.

7 Ratio K + in Au/C yields robust observables Variation of σ NΔ Variation of U KN 7 σ ND Tsushima σ ND =.75 σ NN Robust versus effects of production cross sections, KN-potential, less stopping (reduced σ NN ), lifetime of the Δ,

8 Verification by second independent observable: Centrality dependence of the K + yield Different cross sections and potential parameters may change the global yield. 8 peripheral Experimental value: >1.19 central However, the parameter α for the increase of the kaon yield N with the number A of participating nucleons (raising with centrality) N(K)=N 0 A partα depends on the eos. A soft eos yields higher values than a hard eos.

9 Three independent variables Centrality dependence of the K + yield Energy dependence of the K + yield (A dependence of the K + yield) allow for the conclusion that hadronic equation of state is soft K at ρ 0 around 200 MeV or even smaller 9

10 What nuclei tell us about K + properties According to the theoretical calculations the spectral form at low m t is the only observable which depends exclusively on the KN interaction ( and not on the σ(nn(δ) K + ΛN)) IQMD HSD 10

11 transverse momentum spectra in A+A,depend on K + N potential 0.06 Ar+KCl, 1.75 A GeV, b< 6 fm, y cm <0.07 ) dn/(dp t dy cm ) [(GeV/c) -1 ] U(ρ 0 )=α40mev 0.01 HADES: K 0 S =(K0 +K 0 bar)/2 HSD: K 0 /2 U( )=0 U( )=+20 MeV U( )=+40 MeV 11 U(ρ 0 )=α 40MeV p t [GeV/c] IQMD and HSD models describe the HADES Ar+KCl at 1.75 AGeV data with a repulsive K + N potential U K ~ 40 MeV at ρ 0. Shape of the p T -spectra is sensitive to the in-medium potential! 11

12 Transverse momentum spectrum of K + is compatible with a linear K + - nucleus potential of U(ρ/ρ 0 )=40ρ/ρ 0 [MeV] as predicted by nuclear matter calculation (nucl-th/ ) Conclusions HI reactions can measure K + properties K + can measure nuclear matter properties 12 K + are presently the best tool to measure the nuclear equation of state Compressibility modulus K around 200 MeV K + - nucleus potential is close to that predicted by theory (around 40 MeV at ρ 0 ) Independent models (HSD and IQMD) agree