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
ƒ F. Laue et al. (KaoS Coll.), PRL 82 (1999), 1640.
ƒ C. Sturm et al. (Kaos Coll.), PRL 86 (2001), 39.
ƒ C. Fuchs, Prog. Part. Nucl. Phys. 56 (2006), 1.
ƒ 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
[email protected]: 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 )
Scarica

File pdf