introduzione: l’equazione di stato (eos)
DESCRIPTION
Produzione di particelle come osservabile per l’equazione di stato ad alta densità barionica. Graziella Ferini INFN-LNS, Catania. Introduzione: l’equazione di stato (EoS) Particelle prodotte in collisioni ad energie relativistiche (1-2 AGeV) Pioni e kaoni come osservabili per l’EoS - PowerPoint PPT PresentationTRANSCRIPT
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Introduzione: l’equazione di stato (EoS) 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
Produzione di particelle come osservabile per l’equazione di stato ad alta densità
barionica
Graziella FeriniINFN-LNS, Catania
Otranto, 29 Maggio-3 Giugno 2006
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……iso-scalar sectoriso-scalar sector……iso-vector sectoriso-vector sector
The Nuclear EOS Uncertainties
• Particle multiplicity• Nucleon collective flows (sideward, elliptic)
• Neutron-proton differential flow• Isospin equilibration• Pion flow• Isospin ratios (/+, K0/K+)
0|9 2
220
B
B
EK
Slope parameter Curvature parameter
E sym
M
eV)
1 2 30
Asy-stiff
Asy-soft
Finite nucleiHeavy Ion Collisions
??
hard (MeV
)
soft (MeV
)
sat
??
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K mesons probe the high density phase
K(100)
Pion and kaon production at GeV energies
pions freeze out late (at low density) kaons freeze out early
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Produzione di kaoni
Metodo perturbativo: i kaoni non influenzano la dinamica del sistema
Conservazione di stranezza
• Produzione associata K + Y• Ethresh~1.56 AGeV• No riassorbimento per i K• k~7 fm
BB BYK (BN,)B YK (Y ,)
BK BK
“emissione diretta”
Produzione sotto soglia: moto di Fermi + processi “multi-step”
BB K BB X
0.8-2AGeV BB K < 1 mb!
usd
0
u sK+
K prodotti ad alta densità
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yield does NOT constrain the (isoscalar) EoS
(Isoscalar) EoS from pion and kaon production
KAON data ONLY compatible with a SOFT 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.
Kaon data only compatible with a soft EoS,even varying:
N cross section
KN potential
lifetime
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Effects of the symmetry energy
Vector self energy more repulsive for neutrons (-) and more attractive for protons (+)
a) Neutrons pushed out from the high density stage of the reaction
b) Neutrons converted into protons during the high density stage of the reaction
nn
n0
n- p-
p+ n++
n+ p+
pp
p-
K0, , K+
Baryon current
KK 0
Consequences on
???and/or
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Au+Au 1AGeV: density and isospin of the Kaon source
n,p at High density
n/p at High density
Drop:Competition of fast neutron emission andInelastic channels: n→p transformation
Time interval of Kaon production
“central”density
NL→ DDF→NLρ→NLρ : more neutron escape and more n→p transformation (less asymmetry in the source)
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Au+Au@1AGeV: time evolution of the total number of nucleons
Free nucleons
Large n→p transformation at early times:Less asymmetry in the Kaon source
Check:π-/π+, n/p, K0/K+ vs emission time (P_t)
fρ increasing sequenceNL<DDF<NLρ<NLρδ
Different behavior at lower energies, reduced inelastic competition
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Au+Au central: and K yield ratios vs. beam energy
Pions: less sensitivity ~10%, but larger yields
No sensitive to the KN potential
Kaons:~15% difference betweenDDF and NLρδ
Inclusive multiplicities
132Sn+124Sn
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Conclusions
Isoscalar sector: • Nucleon flow data and K+ multiplicities give indication of a SOFT EoS
Isovector sector:
• Esym reduces the asymmetry in the high density phase of the reaction• A stiffer Esym (i.e. with greater f) favours the neutron to proton conversion through inelastic collisions • /+ 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
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Produzione di K in prossimità della soglia Esperimenti
FOPI GSI
197Au+197Au, 40Ca+40Ca, 96Ru(Zr)+96Ru(Zr)
KaoS197Au+197Au, 12C+12C, 56Ni+56Ni
0.8<Ebeam(AGeV)<2
• Molteplicità K+
• Flussi collettivi K+, • K+/ K0 per (=0.08, 0.16)96Ru+96Ru @1.5 [email protected] AGeV
• Molteplicità K+ • Flussi collettivi K+, • Rapporto molteplicità K+ (197Au+197Au)/(12C+12C)
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System size dependence
N/A NK/A 40Ca+40Ca 0.17 1.410 4 132Sn+124Sn 0.14 2.310 4 197Au+197Au 0.13 3.210 4
Heavy systems• More collisions• More stopping• Higher density
Pions more easily reabsorbed Kaons more easily produced
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Elliptic flow
Sideward + elliptic flows data rule out supersoft (K=167 MeV) and hard (K>300 MeV) EoS
Soft Eos (K200 MeV)
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I kaoni: generalità
u s K+
u s K-
+
++
––––
K0 è una combinazione di coppie e e può decadere in 2 modi: sd sd
0s
0s
(91011 s)
0L–
0L
(5108 s)
mk+=mk– 494 MeV/c2mk0 498 MeV/c2 massa
(1108 s)
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Il potenziale e gli effetti del mezzo sui kaoniEffetti osservabili: Approcci
:CPT (Chiral Perturbation Theory)BEM (Boson Exchange Model)
Relazioni di dispersione: 0
2120
22
0
2120
22
VgVgmgkm
VgVgmgkm
KKKKKK
KKKKKK
Massa efficace:
VVf
mm sKN
kk 22*
,
jf
V 283
Distribuzione azimutaleFlusso trasversoSoglia di produzione
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soft
soft
soft
stiff
stiff
stiff
fluctuations
IBUU : not covariant symmetry term132Sn+124Sn at 0.4AGeV
π(-)/π(+) always decreasing with the iso-stiffness?
Bao-An Li PRC 71 (2005) 014608
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F15
Fa3
ρ/ρ0
UrQMD : not covariant symmetry term
208Pb+208Pb at 0.4AGeV
Inelastic channels less importantbut still crossing at high p_t
softstiff
Q.Li et al. PRC 72 (2005) 034613
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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
Kaons behave like high energy pions
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X
Z
22
22
2 )(Vyx
yxt pp
ppp
Bounce-off
(in-plane flow)
Squeeze-out
(elliptic flow)
iixi
np ypyN
yF )()(
1)( )(V)(V)(V n2
p2
n-p2 ttt ppp
i
xix ypyN
yp )()(
1)(
Isospin
Differenze tra NL e NL(V. Greco et al., PLB 562 (2003), 215)