Strangeness Production as a Probe for the Nuclear Equation of State
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1 Strangeness Production as a Probe for the Nuclear Equation of State Christian Fuchs Institut für Theoretische Physik Christian Fuchs - Uni Tübingen p.1/28
2 Key Questions Christian Fuchs - Uni Tübingen p.2/28
3 Key Questions Where does the mass of matter come from? Christian Fuchs - Uni Tübingen p.2/28
4 Key Questions Where does the mass of matter come from? QCD: massless quarks = chiral symmetry m u = 5 MeV, m d = 8 MeV (m s = 150 MeV ) = spontanously broken by vacuum condensate qq 98% of our mass comes from QCD vacuum Christian Fuchs - Uni Tübingen p.2/28
5 Key Questions Where does the mass of matter come from? QCD: massless quarks = chiral symmetry m u = 5 MeV, m d = 8 MeV (m s = 150 MeV ) = spontanously broken by vacuum condensate qq 98% of our mass comes from QCD vacuum How behaves a strongly interacting medium? Christian Fuchs - Uni Tübingen p.2/28
6 Key Questions Where does the mass of matter come from? QCD: massless quarks = chiral symmetry m u = 5 MeV, m d = 8 MeV (m s = 150 MeV ) = spontanously broken by vacuum condensate qq 98% of our mass comes from QCD vacuum How behaves a strongly interacting medium? Nuclear matter at high densities? E Nuc (ρ) =? What happens with ρ qq ρ? Christian Fuchs - Uni Tübingen p.2/28
7 Key Questions Where does the mass of matter come from? QCD: massless quarks = chiral symmetry m u = 5 MeV, m d = 8 MeV (m s = 150 MeV ) = spontanously broken by vacuum condensate qq 98% of our mass comes from QCD vacuum How behaves a strongly interacting medium? Nuclear matter at high densities? E Nuc (ρ) =? What happens with ρ qq ρ? Duality : ρ qq ρ = qq de Nuc (ρ) dm q Christian Fuchs - Uni Tübingen p.2/28
8 Scaling of Hadron Masses Chiral symmetry of QCD: m u, m d 0 = spontanous symmetry breaking by condensate qq : m 2 π m N = m u + m d 2f 2 π = 8π2 Λ 2 B qq qq m 2 ρ = 8π 2(m u + m d ) m 2 π GOR QCD sum rules qq f π = 93MeV Borel mass : Λ B 1GeV Christian Fuchs - Uni Tübingen p.3/28
9 Hadrons in the Medium Gas approximation: ρ qq ρ = qq + ρ N qq N +... = qq (1 Σ πn ρ) +... fπm 2 2 π T [MeV] 300 <qq> - ρ,t 5 ρ 0 ρ But : f π(ρ) =? qγ µ q ; qq qq =? +... =? NJL: Klimt, Lutz, Weise, PLB 249 (1990) 386 Christian Fuchs - Uni Tübingen p.4/28
10 Nuclear Equation of State E/A [MeV] nuclear matter EOS DBHF Bonn A, K=230 DBHF Bonn B, K=150? Skyrme soft, K=200 Skyrme hard, K=380 SIS E(ρ), ρ 0 from 208 P b finite nuclei: ρ/ρ 0 1 heavy ions: ρ/ρ 0 3? neutron stars: ρ/ρ 0 10 ρ/ρ Pb Protons -5 Energy [MeV] s 1/2 2d 3/2 1h 11/2 2d 5/2 1g 7/2 1g 9/2-20 exp. Bonn A Bonn B Bonn C Christian Fuchs - Uni Tübingen p.5/28
11 Nuclear Equation of State E/A [MeV] nuclear matter EOS DBHF Bonn A, K=230 DBHF Bonn B, K=150? Skyrme soft, K=200 Skyrme hard, K=380 SIS HICs: Non-Equilibrium ρ/ρ 0 E(ρ), ρ 0 from 208 P b finite nuclei: ρ/ρ 0 1 heavy ions: ρ/ρ 0 3? neutron stars: ρ/ρ Pb Protons Energy [MeV] s 1/2 2d 3/2 1h 11/2 2d 5/2 1g 7/2 = Equilibrium = -15 1g 9/2-20 exp. Bonn A Bonn B Bonn C Christian Fuchs - Uni Tübingen p.5/28
12 Saturation of Nuclear Matter Microscopic approach, realistic NN force, no parameter E B [MeV] V K=? ρ/ρ 0 correlated uncorrelated wave r E/A [MeV] Tuebingen (Bonn) BM (Bonn) Bonn A, ps Reid CD Bonn Bonn AV k F [fm 1 ] see e.g. nucl-th/ Coester line = relativistic! Christian Fuchs - Uni Tübingen p.6/28
13 Hadronic many-body theory Relativistic Brueckner: N+OBEP ( V = σ, ω, π, ρ, η, δ) = 2-N correlations in hole-line expansion = self-consistent sum of ladder diagrams Dyson-Equation: G = G0 + G0ΣG = + Σ Bethe-Salpeter-Equation: T = V + i V GGQT T T = + Self Energy (Hartree-Fock): Σ(ρ, k) = qɛf < q T (q, k) q >= ΣS γ0σ0 + γ kσv = T T Σ Christian Fuchs - Uni Tübingen p.7/28
14 Results for nuclear matter E/A [MeV] Tuebingen Groningen BM C B A k F [fm 1 ] m * /M in medium nucleon mass Bonn A BM (Bonn A) Groningen QHD QCD sum rule+chpt ρ / ρ 0 Christian Fuchs - Uni Tübingen p.8/28
15 Results for nuclear matter E/A [MeV] Tuebingen Groningen BM C B A k F [fm 1 ] m * /M in medium nucleon mass Bonn A BM (Bonn A) Groningen QHD QCD sum rule+chpt ρ / ρ 0 = microscopic EOS is soft (K=230 MeV, Bonn A) = strongly dropping nucleon mass (model independent!) Gross-Boelting, C.F., Faessler, NPA 648 ( 99) 105 Christian Fuchs - Uni Tübingen p.8/28
16 Models for heavy ion collisions initial final thermal + expansion hydro thermal model?? transport Christian Fuchs - Uni Tu bingen p.9/28
17 Non-Eq.-QFT: Kinetic Theory (s s )G < [ReΣ +, G < ] [Σ >, G + ] = 1 2 ({Σ>, G < } {Σ <, G > }) [ t + p U x x U p ] f( x, p, t) = I coll [f, σ, Γ] (BUU) T = V + iv QGGT (Bethe Salpeter) Re U opt [MeV] mean field 2.0 [ρ 0 ] exp E lab [MeV] dσ/dω [mb/sr] U = Re tr[t f] = m E Σ S Σ in medium cross section free 0.5ρ 0 ρ 0 3ρ 0 E lab =250 MeV Θ c.m. [deg] dσ = T 2 dω P(ω,p) p 2 [fm 2 ] E E ω [GeV] p [fm -1 ] 4.0 Γ Im tr[t f] Lehr, Mosel et al. ( 99) C.F. et al. PRC 58 ( 97) 2022, PRC 64 ( 01) Christian Fuchs - Uni Tübingen p.10/28
18 Transport is a coupled channel problem [ t + p U N x x U N p ] f N = I coll [f N, σ N, Γ N, f π, f K, ] [ t + p U π x x U π p ] f π = I coll [f π, σ π, Γ π, f N, f K, ] [ t + p U K x x U K p ] f K = I coll [f K, σ K, Γ K, f N, f π, ] [ ]f Λ,Σ =,, In-medium cross sections: K close to Λ 1405 resonance = strong medium dependence M. Lutz, NPA700 Christian Fuchs - Uni Tübingen p.11/28
19 Transport is a coupled channel problem [ t + p U N x x U N p ] f N = I coll [f N, σ N, Γ N, f π, f K, ] [ t + p U π x x U π p ] f π = I coll [f π, σ π, Γ π, f N, f K, ] [ t + p U K x x U K p ] f K = I coll [f K, σ K, Γ K, f N, f π, ] [ ]f Λ,Σ =,, In-medium cross sections: K close to Λ 1405 resonance = strong medium dependence M. Lutz, NPA700 Use all possible exp. & theor. hadronic input Christian Fuchs - Uni Tübingen p.11/28
20 Good probes for dense matter Dileptons: ρ, ω e + e = CERES, HADES Kaons: K + (u s): NN NΛK + E thr = 1.58 GeV πn ΛK + K (ūs): NN NNK + K E thr = 2.5 GeV Subthreshold Kaon Production (E Lab < E thr ): Do kaons change their properties in dense matter? = Chiral Symmetry of QCD restored? Christian Fuchs - Uni Tübingen p.12/28
21 Good probes for dense matter Dileptons: ρ, ω e + e = CERES, HADES Kaons: K + (u s): NN NΛK + E thr = 1.58 GeV πn ΛK + K (ūs): NN NNK + K E thr = 2.5 GeV Subthreshold Kaon Production (E Lab < E thr ): Do kaons change their properties in dense matter? = Chiral Symmetry of QCD restored? Sensitivity to collective effects = Can kaons provide information on the nuclear EOS? (Aichelin & Ko 85) Christian Fuchs - Uni Tübingen p.12/28
22 Good probes for dense matter Dileptons: ρ, ω e + e = CERES, HADES Kaons: K + (u s): NN NΛK + E thr = 1.58 GeV πn ΛK + K (ūs): NN NNK + K E thr = 2.5 GeV Subthreshold Kaon Production (E Lab < E thr ): Do kaons change their properties in dense matter? = Chiral Symmetry of QCD restored? Sensitivity to collective effects = Can kaons provide information on the nuclear EOS? (Aichelin & Ko 85) Christian Fuchs - Uni Tübingen p.12/28
23 Good probes for dense matter Dileptons: ρ, ω e + e = CERES, HADES Kaons: K + (u s): NN NΛK + E thr = 1.58 GeV πn ΛK + K (ūs): NN NNK + K E thr = 2.5 GeV Subthreshold Kaon Production (E Lab < E thr ): Do kaons change their properties in dense matter? = Chiral Symmetry of QCD restored? Sensitivity to collective effects = Can kaons provide information on the nuclear EOS? (Aichelin & Ko 85) Christian Fuchs - Uni Tübingen p.12/28
24 Chiral Lagrangian L K = µ Φ K µ Φ K 3 8f 2 π ( m 2 K Σ ) KN ΨΨ fπ 2 iψγ µ ΨΦ K µ Φ K + O((1/f 2 π )2 ) Φ K Φ K Kaplan & Nelson 86 Klein-Gordon equation: [ µ µ ± 3i ( j 4fπ 2 µ µ + m 2 K Σ )] KN ρ fπ 2 s φ K ± = 0 Christian Fuchs - Uni Tübingen p.13/28
25 Chiral Lagrangian L K = µ Φ K µ Φ K 3 8f 2 π ( m 2 K Σ ) KN ΨΨ fπ 2 iψγ µ ΨΦ K µ Φ K + O((1/f 2 π )2 ) Φ K Φ K Kaplan & Nelson 86 Klein-Gordon equation: [ µ µ ± 3i ( j 4fπ 2 µ µ + m 2 K Σ )] KN ρ fπ 2 s φ K ± = 0 V µ = 3 8f 2 π j µ nuclear matter at rest = j µ µ = ρ B t = V µ = V 0 Christian Fuchs - Uni Tübingen p.13/28
26 Quasi-particle picture ω K / m K "in medium mass" Waas et al. Li/Ko Brown/Rho ρ/ρ 0 m* K / m K quasiparticle mass Wass et al. Li/Ko Brown/Rho ρ/ρ 0 [ ( µ ± iv µ ) 2 ] + m 2 K φk ± = 0 m K = m 2 K Σ KN ρ fπ 2 s + V µ V µ [ ] k 2 m 2 K φk ± = 0 dispersion relation : ω = k 2 + m 2 K ± V 0 Christian Fuchs - Uni Tübingen p.14/28
27 Quasi-particle picture ω K / m K "in medium mass" Waas et al. Li/Ko Brown/Rho ρ/ρ 0 m* K / m K quasiparticle mass Wass et al. Li/Ko Brown/Rho ρ/ρ 0 [ ( µ ± iv µ ) 2 ] + m 2 K φk ± = 0 m K = m 2 K Σ KN ρ fπ 2 s + V µ V µ [ ] k 2 m 2 K φk ± = 0 dispersion relation : ω = k 2 + m 2 K ± V 0 How good is mean field? Christian Fuchs - Uni Tübingen p.14/28
28 Quasi-particle picture ω K / m K "in medium mass" Waas et al. Li/Ko Brown/Rho ρ/ρ 0 m* K / m K quasiparticle mass Wass et al. Li/Ko Brown/Rho ρ/ρ 0 [ ( µ ± iv µ ) 2 ] + m 2 K φk ± = 0 m K = m 2 K Σ KN ρ fπ 2 s + V µ V µ [ ] k 2 m 2 K φk ± = 0 dispersion relation : ω = k 2 + m 2 K ± V 0 How good is mean field? for K + Christian Fuchs - Uni Tübingen p.14/28
29 Quasi-particle picture ω K / m K "in medium mass" Waas et al. Li/Ko Brown/Rho ρ/ρ 0 m* K / m K quasiparticle mass Wass et al. Li/Ko Brown/Rho ρ/ρ 0 [ ( µ ± iv µ ) 2 ] + m 2 K φk ± = 0 m K = m 2 K Σ KN ρ fπ 2 s + V µ V µ [ ] k 2 m 2 K φk ± = 0 dispersion relation : ω = k 2 + m 2 K ± V 0 How good is mean field? for K + for K = Λ 1405 resonance = coupled channels Christian Fuchs - Uni Tübingen p.14/28
30 Collective flow in HICs Px squeeze-out Pz bounce-off θ reaction plane Christian Fuchs - Uni Tübingen p.15/28
31 Collective flow in HICs Px squeeze-out Pz bounce-off θ reaction plane In-plane flow = scattering angle = repulsion Out-of-plane flow = compression & absorption Christian Fuchs - Uni Tübingen p.15/28
32 K + In-Plane Flow <p x >/m K 0,15 0,1 0,05 0 K + (p t /m>0.5) Ni+Ni, 1.93 AGeV Equations of motion: dk dt = m K m K E q V 0 q + t V -0,05-0,1 FOPI, new reflected w/o kaon pot. with kaon pot kaon pot, w/o LF FOPI, old Y (0) Christian Fuchs - Uni Tübingen p.16/28
33 K + In-Plane Flow <p x >/m K 0,15 0,1 0,05 0-0,05-0,1 K + (p t /m>0.5) Ni+Ni, 1.93 AGeV Y (0) FOPI, new reflected w/o kaon pot. with kaon pot kaon pot, w/o LF FOPI, old Equations of motion: dk dt = m K m K E q V 0 q + t V + k E ( ) q V = Lorentz Force C.F. et al., PLB 434 (1998) 358 Christian Fuchs - Uni Tübingen p.16/28
34 K + In-Plane Flow <p x >/m K 0,15 0,1 0,05 0-0,05-0,1 K + (p t /m>0.5) Ni+Ni, 1.93 AGeV Y (0) FOPI, new reflected w/o kaon pot. with kaon pot kaon pot, w/o LF FOPI, old Equations of motion: dk dt = m K m K E q V 0 q + t V + k E ( ) q V = Lorentz Force C.F. et al., PLB 434 (1998) 358 = K + flow consistent with repulsive K + potential Christian Fuchs - Uni Tübingen p.16/28
35 K + Out-Off-Plane Flow dn/dφ K +, Au+Au, 1 A.GeV K, Au+Au, 1.8 A.GeV Shadowing: K + N K + N : σ 10 mb K N Y π : σ 50 mb Wang et al., Eur. Phys. J. A5 ( 99) KaoS with pot. without pot with pot. without pot Φ [deg] Φ [deg] Christian Fuchs - Uni Tübingen p.17/28
36 Kaons and the Nuclear EOS Early simulations favor soft EOS. Ko&Li, JPG22( 96) But: Many things have changed! Christian Fuchs - Uni Tübingen p.18/28
37 Kaons and the Nuclear EOS Early simulations favor soft EOS. Ko&Li, JPG22( 96) But: Many things have changed! 10 2 pp >ΛK new cross sections πb-channel included momentum dep. forces in-medium potential precise data new conclusions? σ [µb] Sibirtsev Randrup&Ko COSY s s o [GeV] Christian Fuchs - Uni Tübingen p.18/28
38 K + Excitation Function Au+Au*10 1 In-medium K + potential shifts threshold: σ(k+) [mb] 10 0 C+C BB BΛK + sbb ω B + ω Λ + ω K E lab [GeV] soft EOS, w/o pot hard EOS, w/o pot soft EOS, with pot hard EOS, with pot KaoS (exp) Christian Fuchs - Uni Tübingen p.19/28
39 K + Excitation Function Au+Au*10 1 In-medium K + potential shifts threshold: σ(k+) [mb] 10 0 C+C BB BΛK + sbb ω B + ω Λ + ω K E lab [GeV] soft EOS, w/o pot hard EOS, w/o pot soft EOS, with pot hard EOS, with pot KaoS (exp) Data support in-medium kaon potential! Christian Fuchs - Uni Tübingen p.19/28
40 Subthreshold K + production and nuclear EOS (M K+ /A) Au+Au / (M K+ /A) C+C E/A [MeV] E lab [GeV/c] hard soft ρ/ρ 0 E thr Consider ratio large/small system: (Au+Au)/(C+C) Far subthreshold: highly sensitive to collective effects soft EOS, with pot hard EOS, with pot Kaos, Sturm et al., PRL 86 (2001) Christian Fuchs - Uni Tübingen p.20/28
41 Subthreshold K + production and nuclear EOS (M K+ /A) Au+Au / (M K+ /A) C+C E/A [MeV] E lab [GeV/c] soft EOS, with pot hard EOS, with pot Kaos, Sturm et al., PRL 86 (2001) 0 hard soft ρ/ρ 0 E thr Consider ratio large/small system: (Au+Au)/(C+C) Far subthreshold: highly sensitive to collective effects KaoS data = soft EOS! C.F. et al., PRL 86 (2001) 1974 Christian Fuchs - Uni Tübingen p.20/28
42 Interplay EOS K + potential (M K+ /A) Au+Au / (M K+ /A) C+C central collisions (b=0 fm) soft EOS, w/o kaon pot hard EOS, w/o kaon pot soft EOS, witk kaon pot hard EOS, with kaon pot E lab [GeV] compression: yield ρ 2 kaon potential: yield ρ soft EOS: < ρ/ρ 0 >= 1.53 < s >= 2.64 hard EOS: < ρ/ρ 0 >= 1.41 < s >= 2.54 = < U > = 6 MeV = < s > = 100 MeV Christian Fuchs - Uni Tübingen p.21/28
43 Interplay EOS K + potential (M K+ /A) Au+Au / (M K+ /A) C+C central collisions (b=0 fm) soft EOS, w/o kaon pot hard EOS, w/o kaon pot soft EOS, witk kaon pot hard EOS, with kaon pot E lab [GeV] compression: yield ρ 2 kaon potential: yield ρ soft EOS: < ρ/ρ 0 >= 1.53 < s >= 2.64 hard EOS: < ρ/ρ 0 >= 1.41 < s >= 2.54 = < U > = 6 MeV = < s > = 100 MeV = compression wins against repulsive K + potential Christian Fuchs - Uni Tübingen p.21/28
44 Nuclear density at K + production d(m K + /A)/dρ [fm 3 ] 10 4 Au+Au C+C soft EOS hard EOS central 0.8 AGeV: density distribution at K + creation: dm K + dρ B = N K + i dp i dρ B (x i, t i ) ρ/ρ sat Christian Fuchs - Uni Tübingen p.22/28
45 Nuclear density at K + production d(m K + /A)/dρ [fm 3 ] 10 4 Au+Au C+C soft EOS hard EOS central 0.8 AGeV: density distribution at K + creation: dm K + dρ B = N K + i dp i dρ B (x i, t i ) ρ/ρ sat C+C can be used as an EOS independent reference frame! Christian Fuchs - Uni Tübingen p.22/28
46 Centrality dependence 0,0 0,2 0,4 0,6 0,8 1,0 A part / A max 0,0 2, , , , , , M(K + ) / A Au+Au, soft EOS Au+Au, hard EOS C+C, soft EOS C+C, hard EOS E=1.0 AGeV Apart Christian Fuchs - Uni Tübingen p.23/28
47 Centrality dependence 0,0 0,2 0,4 0,6 0,8 1,0 A part / A max 0,0 2, , , , , , M(K + ) / A Au+Au, soft EOS Au+Au, hard EOS C+C, soft EOS C+C, hard EOS E=1.0 AGeV Apart EOS effect most pronounced in central reactions C+C again independent! Christian Fuchs - Uni Tübingen p.23/28
48 Stability of EOS dependence? Workshop on transport models Trento, May 2003: = comparison of independent codes RBUU: Bratkovskaya & Cassing, IQMD: Hartnack & Aichelin, QMD: Tübingen,... NN, N, NΛ(Σ)K + ; Nπ, π Λ(Σ)K + : not all channels are measured! Christian Fuchs - Uni Tübingen p.24/28
49 Stability of EOS dependence? Workshop on transport models Trento, May 2003: = comparison of independent codes different cross sections, independent code (Nantes): RBUU: Bratkovskaya & Cassing, IQMD: Hartnack & Aichelin, QMD: Tübingen,... NN, N, NΛ(Σ)K + 7 ; Nπ, π Λ(Σ)K + : not all channels are measured! (M K+ /A) Au+Au / (M K+ /A) C+C soft EOS, pot ChPT hard EOS, pot ChPT soft EOS, IQMD, pot RMF hard EOS, IQMD, pot RMF soft EOS, IQMD, Giessen cs hard EOS, IQMD, Giessen cs KaoS E lab [GeV] Christian Fuchs - Uni Tübingen p.24/28
50 Stability of EOS dependence? Workshop on transport models Trento, May 2003: = comparison of independent codes different cross sections, independent code (Nantes): RBUU: Bratkovskaya & Cassing, IQMD: Hartnack & Aichelin, QMD: Tübingen,... NN, N, NΛ(Σ)K + 7 ; Nπ, π Λ(Σ)K + : not all channels are measured! (M K+ /A) Au+Au / (M K+ /A) C+C soft EOS, pot ChPT hard EOS, pot ChPT soft EOS, IQMD, pot RMF hard EOS, IQMD, pot RMF soft EOS, IQMD, Giessen cs hard EOS, IQMD, Giessen cs KaoS E lab [GeV] = EOS dependence of ratio is stable! Christian Fuchs - Uni Tübingen p.24/28
51 Information from p + A no pot. a only Coul. Consider ratio of K + production in (p + Au)/(p + C) reactions: Coulomb+Pot. shift: R(Au/C) Coul+pot b p min = 2m K (V Coul + V 0 (ρ)) = V 0 (ρ 0 ) 20 MeV COSY-ANKE, PLB 540 (2002) p K (MeV/c) transport: W. Cassing Christian Fuchs - Uni Tübingen p.25/28
52 Information from p + A no pot. a only Coul. Consider ratio of K + production in (p + Au)/(p + C) reactions: Coulomb+Pot. shift: R(Au/C) p K (MeV/c) transport: W. Cassing Coul+pot b p min = 2m K (V Coul + V 0 (ρ)) = V 0 (ρ 0 ) 20 MeV COSY-ANKE, PLB 540 (2002) 207 p+a consistent with A+A = repulsive K + potential Christian Fuchs - Uni Tübingen p.25/28
53 Is a soft EOS consistent with information from other sources? Consistent with many-body theory (DBHF) Christian Fuchs - Uni Tübingen p.26/28
54 Is a soft EOS consistent with information from other sources? Consistent with many-body theory (DBHF) Consistent with nucleon flow in HICs: Christian Fuchs - Uni Tübingen p.26/28
55 Is a soft EOS consistent with information from other sources? Consistent with many-body theory (DBHF) Consistent with nucleon flow in HICs: E/A [MeV] nuclear matter EOS DBHF Bonn A, K=230 DBHF Bonn B, K=150? Skyrme soft, K=200 Skyrme hard, K=380 SIS ρ/ρ 0 Christian Fuchs - Uni Tübingen p.26/28
56 Is a soft EOS consistent with information from other sources? Consistent with many-body theory (DBHF) Consistent with nucleon flow in HICs: E/A [MeV] nuclear matter EOS DBHF Bonn A, K=230 DBHF Bonn B, K=150? Skyrme soft, K=200 Skyrme hard, K=380 SIS ρ/ρ 0 Constraints from nucleon flow: P. Danielewicz Christian Fuchs - Uni Tübingen p.26/28
57 Summary Christian Fuchs - Uni Tübingen p.27/28
58 Summary Strong evidence for repulsive K + potential Christian Fuchs - Uni Tübingen p.27/28
59 Summary Strong evidence for repulsive K + potential yields, in-plane-, out-of-plane flow Christian Fuchs - Uni Tübingen p.27/28
60 Summary Strong evidence for repulsive K + potential yields, in-plane-, out-of-plane flow A+A, p+a reactions Christian Fuchs - Uni Tübingen p.27/28
61 Summary Strong evidence for repulsive K + potential yields, in-plane-, out-of-plane flow A+A, p+a reactions = partial restoration of chiral symmetry Christian Fuchs - Uni Tübingen p.27/28
62 Summary Strong evidence for repulsive K + potential yields, in-plane-, out-of-plane flow A+A, p+a reactions = partial restoration of chiral symmetry K + as a probe for the nuclear EOS Christian Fuchs - Uni Tübingen p.27/28
63 Summary Strong evidence for repulsive K + potential yields, in-plane-, out-of-plane flow A+A, p+a reactions = partial restoration of chiral symmetry K + as a probe for the nuclear EOS subthreshold = sensitiv to collective effects Christian Fuchs - Uni Tübingen p.27/28
64 Summary Strong evidence for repulsive K + potential yields, in-plane-, out-of-plane flow A+A, p+a reactions = partial restoration of chiral symmetry K + as a probe for the nuclear EOS subthreshold = sensitiv to collective effects ratio large/small system is robust Christian Fuchs - Uni Tübingen p.27/28
65 Summary Strong evidence for repulsive K + potential yields, in-plane-, out-of-plane flow A+A, p+a reactions = partial restoration of chiral symmetry K + as a probe for the nuclear EOS subthreshold = sensitiv to collective effects ratio large/small system is robust = soft EOS Christian Fuchs - Uni Tübingen p.27/28
66 Summary Strong evidence for repulsive K + potential yields, in-plane-, out-of-plane flow A+A, p+a reactions = partial restoration of chiral symmetry K + as a probe for the nuclear EOS subthreshold = sensitiv to collective effects ratio large/small system is robust = soft EOS consistent with many-body theory Christian Fuchs - Uni Tübingen p.27/28
67 Summary Strong evidence for repulsive K + potential yields, in-plane-, out-of-plane flow A+A, p+a reactions = partial restoration of chiral symmetry K + as a probe for the nuclear EOS subthreshold = sensitiv to collective effects ratio large/small system is robust = soft EOS consistent with many-body theory consistent with nucleon flow Christian Fuchs - Uni Tübingen p.27/28
68 Acknowledgements Amand Faessler Thomas Gross-Boelting Zhisong Wang Eugene Zabrodin Yu-Ming Zheng Christian Fuchs - Uni Tübingen p.28/28
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