Produzione di particelle come osservabile per l’equazione di stato ad alta densità barionica Graziella Ferini INFN-LNS, Catania 9 Introduzione: l’equazione di stato (EoS) 9 9 9 9 Particelle prodotte in collisioni ad energie relativistiche (1-2 AGeV) Pioni e kaoni come osservabili per l’EoS La fase di alta densità in una reazione ad energie del GeV Conclusioni Otranto, 29 Maggio-3 Giugno 2006 The Nuclear EOS Uncertainties …iso-vector sector …iso-scalar sector Esym (ρΒ) (MeV) i cle Asy soft ff ? nu ρsat ite ? i -st y As n Fi hard (κ≈380 MeV) -s o f t Heavy Ion Collisions (κ≈200 MeV) 0 1 ρΒ/ρ0 2 3 ∂2E K = 9 ρ 2 | ρ B= ρ 0 ∂ρ B 2 0 Slope parameter • Particle multiplicity • Nucleon collective flows (sideward, elliptic) Curvature parameter • Neutron-proton differential flow • Isospin equilibration • Pion flow • Isospin ratios (π−/π+, K0/K+) Pion and kaon production at GeV energies ∆ π K(×100) 9 pions freeze out late (at low density) 9 kaons freeze out early K mesons probe the high density phase Produzione di kaoni Conservazione di stranezza u s K+ u d s BB → BYK (B≡N,∆) • Produzione associata K + Y πB → YK • Ethresh~1.56 AGeV • No riassorbimento per i K Λ 0 • λk~7 fm Produzione sotto soglia: moto di Fermi + processi “multi-step” K prodotti ad alta densità σBB → K h σBB → X Metodo perturbativo: i kaoni non influenzano la dinamica del sistema (Y ≡Λ,Σ) BK → BK “emissione diretta” 0.8-2AGeV σBB → K < 1 mb! (Isoscalar) EoS from pion and kaon production KAON dataonly ONLY compatible Kaon data compatible with a soft EoS, with SOFT EoS even avarying: N∆ cross section π yield does NOT constrain the KN potential (isoscalar) EoS F. Laue et al. (KaoS Coll.), PRL 82 (1999), 1640. C. Sturm et al. (Kaos Coll.), PRL 86 (2001), 39. C. Fuchs, Prog. Part. Nucl. Phys. 56 (2006), 1. Ch. Hartnack et al., PRL 96 (2006), 012302. ∆ lifetime Effects of the symmetry energy Vector self energy more repulsive for neutrons (-) and more attractive for protons (+) Baryon current b) Neutrons converted into protons during the high density stage of the reaction a) Neutrons pushed out from the high density stage of the reaction nn p∆nπ- Consequences on π− π+ and/or K0 K+ ??? pp n∆0 p∆+ pπ- nπ+ K0, K+ n∆++ pπ+ Au+Au 1AGeV: density and isospin of the Kaon source “central” density Time interval of Kaon production NL→ DDF→NLρ→NLρδ : more neutron escape and more n→p n,p at High density transformation (less asymmetry in the source) n/p at High density Drop: Competition of fast neutron emission and Inelastic channels: n→p transformation Au+Au@1AGeV: time evolution of the total number of nucleons Large n→p transformation at early times: Less asymmetry in the Kaon source fρ increasing sequence NL<DDF<NLρ<NLρδ Check: π-/π+, n/p, K0/K+ vs emission time (P_t) Free nucleons Different behavior at lower energies, reduced inelastic competition Au+Au central: π and K yield ratios vs. beam energy Kaons: ~15% difference between DDF and NLρδ 132Sn+124Sn No sensitive to the KN potential Pions: less sensitivity ~10%, but larger yields Inclusive multiplicities Conclusions ¾ Isoscalar sector: • Nucleon flow data and K+ multiplicities give indication of a SOFT EoS ¾ Isovector sector: • Esym reduces the asymmetry in the high density phase of the reaction • A stiffer Esym (i.e. with greater fρ) favours the neutron to proton conversion through inelastic collisions • π−/π+ and K0/K+ ratios are affected by Esym • In the 1-2 AGeV range K0/K+ ratio is more sensitive to Esym, in terms of the strength of the isovector channel • The effect is enhanced in colliding systems with large asymmetry Produzione di K in prossimità della soglia Esperimenti GSI FOPI KaoS 197Au+197Au, 40Ca+40Ca, 96Ru(Zr)+96Ru(Zr) • Molteplicità K+ • Flussi collettivi K+, Λ • K+/ K0 per (α=0.08, 0.16) 96Ru+96Ru @1.5 AGeV [email protected] AGeV 0.8<Ebeam(AGeV)<2 197Au+197Au, 12C+12C, 56Ni+56Ni • Molteplicità K+ • Flussi collettivi K+, Λ • Rapporto molteplicità K+ (197Au+197Au)/(12C+12C) System size dependence Nπ/A 40 Ca+40Ca NK/A 0.17 1.4×10−4 132 0.14 2.3×10−4 197 0.13 3.2×10−4 Sn+124Sn Au+197Au Heavy systems • More collisions • More stopping • Higher density 9 Pions more easily reabsorbed 9 Kaons more easily produced Elliptic flow Sideward + elliptic flows data rule out supersoft (K=167 MeV) and hard (K>300 MeV) EoS Soft Eos (K≈200 MeV) I kaoni: generalità u u K+ s K- s Κ+ → µ+ + νµ , Κ+ → π+ + π0 Κ–→ µ– + νµ , Κ – → π – + π0 (τ∼1×10−8 s) K0 è una combinazione di coppie ds e d s e può decadere in 2 modi: Κ0 s Κ0 L π+ + π− π+ + π – + π0 massa Κ0 s Κ0 L π0 + π0 π0 + π0 + π0 mk+=mk– ≈ 494 MeV/c2 mk0 ≈ 498 MeV/c2 (τ∼9×10−11 s) (τ∼5×10−8 s) Il potenziale e gli effetti del mezzo sui kaoni Effetti osservabili: Approcci: 9Distribuzione azimutale 9CPT (Chiral Perturbation Theory) 9Flusso trasverso 9BEM (Boson Exchange Model) 9Soglia di produzione Relazioni di dispersione: [ = [m ] V )] ω K = mK2 + k 2 − gσK mK φ + (gωKV0 )2 + ωK − 2 K + k 2 − gσK mK φ + ( gωK 0 Massa efficace: Σ mk*+ , − = mk2 − KN2 ρ s + VµV µ fπ 3 Vµ = jµ 8 fπ2 12 + gωKV0 2 12 − gωKV0 IBUU : not covariant symmetry term 132Sn+124Sn at 0.4AGeV soft stiff stiff soft fluctuations π(-)/π(+) always decreasing with the iso-stiffness? soft stiff Bao-An Li PRC 71 (2005) 014608 UrQMD : not covariant symmetry term 208Pb+208Pb at 0.4AGeV F15 Fa3 ρ/ρ0 soft stiff Inelastic channels less important but still crossing at high p_t Q.Li et al. PRC 72 (2005) 034613 Kaons behave like high energy pions P. Senger, H. Stroebele,J. Phys. G 25 (1999) R59 D Best et al, Fopi , NPA 625 (1997), 307 Bass et al, PRC 51 (1995), 3343 Wagner et al, kaos, PLB 420 (1998), 20 Wagner et al., kaos, PRL 85 (2000), 18 〈 px ( y )〉 = 1 ∑ pxi ( y ) N ( y) i Bounce-off (in-plane flow) X Z V2 ( pt ) = F p −n ( y ) = px2 − p y2 px2 + p 2y Squeeze-out (elliptic flow) 1 ∑ pxi ( y )τ i N ( y) i Isospin Differenze tra NLρ e NLρδ (V. Greco et al., PLB 562 (2003), 215) V2p-n ( pt ) = V2p ( pt ) − V2n ( pt )
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