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ISOSPIN EFFECTS on PHASE TRANSITIONS of HADRONIC
to QUARK MATTER
M.Colonna, V.Baran, M.Di Toro, V. Greco, Liu
Bo, S. Plumari
LNS-INFN and Phys.Astron.Dept. Catania, IHEP
Beijing, Univ.of Bucharest .and with the
contribution of a very lively Etna mountain!
From the Etna Melting Pot
From the Phys.Dept. Jan.2002
Etna Double-Face, Aug.07
Oct.12, 2008
NICA-Round Table, Dubna, September09,
ditoro_at_lns.infn.it
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Tentative Plan of the Talk
1. Homework Symmetry Energy
The problem at High Baryon Density
2. Quantum-Hadro-Dynamics EoS Fully
Covariant Transport, Essential Mean Field
Effects Elliptic Isospin Flows, Meson
Production
3. Transition to a Mixed Phase at High Baryon
and Isospin density
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HOMEWORK Hadron-Quark EoS at High Baryon Density
Hadron STANDARD EoS (with Symmetry Term)
Quark STANDARD MIT-Bag Model
ISOSPIN EFFECTS on the MIXED PHASE
Zero Temperature two pages with a pencil.
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EoS of Symmetric/Neutron Matter Hadron (NL?) vs
MIT-Bag ? Crossings
T0, Gluon as0
Symmetry energies
hadron
Quark Fermi only
symmetric
neutron
Gluon as?0 ? Softer quark EoS
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Symmetry Energy
E/A (?) E(?) Esym(?)I²
I(N-Z)/A
Symmetric ? Asymmetric
Fermi (T0)
x x x x
eF/3 ?2/3
kF
o o o o
N
N
Z
Z
Two-body ? , many-body
correlations?
Interaction (nucleon sector)
? search for ?? but ? can be density
dependent ? momentum dependence?
neutron/proton mass splitting
a4 term (30MeV) of the Weiszäcker Mass Formula
at saturation Esym(Fermi)
Esym(Interaction)
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EOS of Symmetric and Neutron Matter
AFDMC V83body Fantoni et al 0807.5043
symmetric
Consensus on a Stiff Symmetry Term at high
density?
Dirac-Brueckner Variational3-body(non-rel.) RMF(N
L3) Density-Dependent couplings Chiral
Perturbative
Ch.Fuchs, H.H.Wolter, WCI Final Report
EPJA 30 (2006) 5-21
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Quantum Hadrodynamics (QHD) ? Relativistic
Transport Equation (RMF)
OBE
NN scattering nuclear interaction
from meson exchange
main channels (plus correlations)
s(0,0) w(1-,0)
d(0,1) r(1-,1)
Scalar
Vector
Scalar
Vector
Isoscalar
Isovector
Nuclear interaction by Effective Field Theory as
a covariant Density Functional Approach
Relativistic structure also in isospin space !
Esym kin. (r-vector) ( d-scalar)
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RMF Symmetry Energy the d - mechanism
No d fr 1.5 frFREE
fd 2.5 fm2 fr 5f
rFREE
DBHF DHF
a4Esym (r0) fixes (fr , fd)
fd 2.0 2.5 fm2
NL?d
NL?
NL
Constant Coupling Expectations
Liu Bo et al., PRC65(2002)045201
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Self-Energies kinetic momenta and (Dirac)
effective masses
Upper sign n
Dirac dispersion relation single particle
energies
n-rich - Neutrons see a more repulsive vector
field, increasing with f? and isospin density -
m(n)ltm(p)
QHD ? Relativistic Mean Field Transport Equation
Covariance is essential ? Inelastic Processes
? Lorentz
Force
Phys.Rep.410(2005)335-466
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RMF (RBUU) transport equation
Relativistic Vlasov Equation Collision
Term
Wigner transform n Dirac Fields Equation
mean field
drift
Non-relativistic Boltzmann-Nordheim-Vlasov
Lorentz Force? Vector Fields pure
relativistic term
Collision term
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AuAu 1AGeV central Phase Space Evolution in a
CM cell
Testing EoS ?CBM
K production
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Evidences of a STIFF Symmetry term at high baryon
density
Collective Flows v2 Flow Large Squeeze-Out for
n-rich clusters (e.g. t vs 3He at high pT)

• Meson Production
• p-/p increase above the threshold
• K 0/K yield ratio
• (no pT selection)

FOPI data (W.Reisdorf, ECT May 2009) at SIS
energies, More to come from the
LAND-CHIMERA-ALADIN Proposal at GSI
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ISOSPIN IN RELATIVISTIC HEAVY ION COLLISIONS
- Earlier Deconfinement at High Baryon Density
- Is the Critical End-Point affected?

M.Di Toro, V.Greco, B.Liu, S.Plumari, NICA White
Paper Contribution (2009)
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In a C.M. cell
,
Exotic matter over 10 fm/c ?
NPA775(2006)102-126
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Testing deconfinement with RIBs?
Mixed Phase ?
Hadron-RMF
B1/4 150 MeV
(T,rB,r3) binodal surface
Quark- Bag model (two flavors)
NL?
NL?d
GM3
1 AGeV
rtrans onset of the mixed phase
? decreases with asymmetry
300 AMeV
132Sn124Sn, semicentral
DiToro,Drago,Gaitanos,Greco,Lavagno,
NPA775(2006)102-126
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Mixed Phase Boundary Shifts at Low Temperature
NL
NL?
NL?d
Isospin asymmetry
Lower Boundary much affected by the
Symmetry Energy
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mumd5.5MeV
Critical End-Point for Symmetric Matter?
NL?,
NL,
NL?d
?0.0
?1.0

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Symmetric to Asymmetric (not Exotic) Matter
Upper ?1.0
NL?
Lower ?0.0
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Inside the Mixed Phase (asymmetry a0.2)
NL?
lower
upper
Dependence on the High Density Hadron EoS
?0.5
?0.2
NL?d
NL?d more repulsive high density Symmetry
Energy in the hadron phase
lower
upper
?0.5
?0.2
Long way to reach 20 quark matter, but
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1. Isospin Densities in the Two Phases
Isospin Asymmetry in the Quark Phase large
Isospin Distillation near the Lower Border?
0.2
lower
upper
?
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Signatures? Neutron migration to the quark
clusters (instead of a fast emission)
? Symmetry Energy in the Quark Phase?
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2. Baryon Densities in the Two Phases
?0.2
?0.2
NL?
?0.5
?0.5

NL?d
?0.2
?0.2
Larger Baryon Density in the Quark
Phase
?0.5
?0.5
? Signatures?

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NJL Effective Lagrangian (two flavors) non
perturbative ground state
with
q-qbar condensation
Gap Equation
? 1
? 1/2
? 0
? 1/2
0
Large µ
or
Large T
Chiral restoration
M.Buballa, Phys.Rep. 407 (2005)
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NJL Phase Diagram
?B0
T0
mu,d0.0
mu,d5.5MeV
Parameters ?p, G, m vs. Mp, fp,
ltqqbargt (estimation)
? µq
M.Buballa, Phys.Rep. 407 (2005)
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Standard Parameters
? Coexistence ? Spinodal
S.Plumari, Thesis 2009
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Quark Dynamics at High Baryon Density
Isospin Extension of the NJL Effective Lagrangian
(two flavors)
Mass (Gap) Equation with two condensates
a flavor mixing parameter ? a ½ , NJL,
MuMd
a ? 0 , small mixing, favored ?
physical ? mass
a ? 1 , large mixing
M.Buballa, Phys.Rep. 407 (2005)
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Neutron-rich matter at high baryon density ?d
decreases more rapidly due to the larger ?d
? (?u ?d) lt 0
a in the range 0.15 to 0.25
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Iso-NJL
Very n-rich matter I(N-Z)/A0.4 Masses in the
Chiral Phase
Solutions of the Iso-Gap Equation
S.Plumari, Thesis 2009
a 0.2
m 6MeV ? 590MeV G0?22.435 ? Mvac400MeV ltqbar
qgt(-241.5MeV)3 mp140.2MeV fp92.6MeV
a 1
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(No Transcript)
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Symmetry Energy in the Chiral Phase something is
missing
.only kinetic contribution
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Conclusions for the Physics at NICA
Experiments
Isospin dependence of the Mixed Phase
Signatures ( reduced v2 at high pT, nq-scaling
break down. )

• Isospin Trapping
• Reduction of n-rich cluster emission
• Anomalous production of Isospin-rich hadrons at
  high pT
• u-d mass splitting (mu gtmd)

Larger Baryon Density in the Quark Phase -
Large Yield of Isospin-rich Baryons at high pT
Theory
Isospin effects on the spinodal decomposition
Isovector Interaction in Effective QCD Lagrangians
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Nuclear Matter Phase Diagram.NICA updated
our journey is around here
Conclusion
Every Complex Problem has a Simple Solution
.most of the time Wrong (Umberto Eco)
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Back-up Slides
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Bag-Model EoS Relativistic Fermi Gas (two
flavors)
Energy density
Pressure
Number density
q, qbar Fermi Distributions
only kinetic symmetry energy
Baryon/Isospin Densities and Chemical Potentials
34
N-STARS Present status with observation
constraints
N
AAAAAA
D.Page, S.Reddy, astro-ph/0608360,
Ann.Rev.Nucl.Part.Sci. 56 (2006) 327
The broad range of predicted radii for nucleon
EOS will be narrowed in the near future owing
to neutron-skin thickness and probably also to
heavy-ion experiments
General Relativity
Softer EOS?smaller R (larger ?-central), smaller
maximum Mass
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Fast cooling Direct URCA process
Fermi momenta matching
Proton fraction, yZ/A, fixed by Esym(?) at high
baryon density
Charge neutrality, ?e?py?
ß-equilibrium
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Neutron Star (npeµ) properties
NL?d
Direct URCA threshold
NL?
DD-F
- Transition to quark matter? - Faster Cooling
for Heavier NS?
NL?
DD-F
NL?d
Mass/Radius relation
compact stars heavy ion data T.Klaehn et al.
PRC 74 (2006) 035802
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DIRAC OPTICAL POTENTIAL
Dispersion relation
RMF
Schrödinger mass
50 MeV
Dirac mass
upper signs neutron
Asymmetric Matter
Phys.Rep.410(2005)335-466, MSU-RIA05
nucl-th/0505013 AIP Conf. 791(2005)70-82
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BEYOND RMF k-dependence of the Self-Energies
DBHF
Schroedinger mass
High momentum saturation of the optical potential
High momentum increase of the Dirac Mass
Asymmetric Matter
Problem still open ..sensitive observables
Phys.Rep.410(2005)335-466, MSU-RIA05
nucl-th/0505013 AIP Conf. 791(2005)70-82
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Relativistic Landau Vlasov Propagation
C. Fuchs, H.H. Wolter, Nucl. Phys. A589 (1995) 732
Discretization of f(x,p)? Test particles
represented by covariant
Gaussians in xp-space
? Relativistic Equations of motion for xm and pm
for centroids of Gaussians
Test-particle 4-velocity ? Relativity -
momentum dependence always included

due to the Lorentz term
- E/M
boosting of the vector contributions
Collision Term local Montecarlo Algorithm
imposing an average Mean Free Path plus Pauli
Blocking
? in medium reduced Cross Sections
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Isospin Flows at Relativistic Energies
Esym(?) Sensitivity to the Covariant Structure
Enhancement of the Isovector-vector contribution
via the
Lorentz Force
High p_t selections source at higher density
? Symmetry Energy at 3-4?0
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AuAu 800 A MeV elliptic flows, semicentral
v2(n), v2(p) vs. p_t
v2(n)
v2(p)
Rapidity selections
All rapidities
v2(p)
v2(n)
Low p_t spectator contributions
y lt 0.5
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Elliptic flow Difference
132Sn132Sn, 1.5AGeV, b6fm NL-r NL-(r d)
rd
High pt neutrons are emitted earlier
r
Equilibrium (?,d) dynamically broken Importance
of the covariant structure
0.3ltY/Yprojlt0.8
approximations
Dynamical boosting of the vector contribution
V.Greco et al., PLB562(2003)215
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Hunting isospin with v2 the mass 3 pair
W.Reisdorf, ECT May 09 FOPI 3H-3He V2 Results
AuAu with increasing beam energy
High pt selection
A small gradual change in The difference 3H-3He
when Raising the beam energy for AuAu (N/Z 1.5)
Relativistic Lorentz effect?
CHIMERA-LAND-ALADIN Proposal at SIS-GSI
andR3B(FAIR)
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Meson Production at Relativistic Energies ? -/?
, K 0/K
Esym(?) Sensitivity to the Covariant Structure
Self-energy rearrangement in the inelastic
vertices with different isospin structure ? large
effects around the thresholds
High p_t selections source at higher density
? Symmetry Energy at 3-4?0
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PION PRODUCTION
G.Ferini et al., NPA 762 (2005) 147, NM Box
PRL 97 (2006) 202301, HIC
Main mechanism
nn
pp
p?
p?-
n?0
n?
p?-
n?-
n?
p?
n?p transformation
Vector self energy more repulsive for neutrons
and more attractive for protons
1. C.M. energy available threshold effect
p(-) enhanced p() reduced
Some compensation in open systems, HIC, but
threshold effect more effective, in particular
at low energies
2. Fast neutron emission mean field effect
No evidence of Chemical Equilibrium!!
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The Threshold Effect nn?p?- vs pp?n?
The Threshold Effect nn?p?- vs pp?n?
nn?p?-
pp?n?
Compensation of Isospin Effects
Almost same thresholds ? the sin(NN) rules the
relative yields
? very important at low energies
increase near threshold
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Pion/Kaon production in open system AuAu
1AGeV, central
Increasing Esym
Increasing Esym

• Kaons
• early production high density phase
• isovector channel effects ?
• but mostly coming from second step collisions
• ? reduced asymmetry of the source

Pions large freeze-out, compensation
G.Ferini et al.,PRL 97 (2006) 202301
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Kaon production in open system AuAu 1AGeV,
central Main
Channels
NN ? BYK --------- N? ? BY ?? ? BYK ?N ? YK
?? ? YK
K0 vs Kopposite contribution of the
d-coupling.but second steps
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AuAu central Pi and K yield ratios vs. beam
energy
Kaons 15 difference between DDF and NL?d
132Sn124Sn
K-potentials similar effects on K0, K
Inclusive multiplicities
Pions less sensitivity 10, but larger yields
G.Ferini et al.,PRL 97 (2006) 202301
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Equilibrium Pion Production Nuclear Matter Box
Results ? Chemical Equilibrium
Dynamics 1.
Density and temperature like in AuAu 1AGeV at
max.compression (?2?0, T50MeV)
vs. asymmetry
NPA762(2005) 147
Larger isospin effects - no neutron escape -
?s in chemical equilibrium, less n-p
transformation
5 (NL?) to 10 (NL?d)
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AuAu 1AGeV density and isospin of the Kaon
source
Dynamics 2.
central density
Time interval of Kaon production
n/p at High density
n,p at High density
Drop Contribution of fast neutron emission
and Inelastic channels
n?p transformation
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Kaon ratios comparison with experiment
G. Ferini, et al., NPA 762 (2005) and PRL 97
(2006)
equilibrium (box) calculations
finite nucleus calculations

• sensitivity reduced in collisions of finite
  nuclei
• single ratios more sensitive
• enhanced in larger systems
• larger asymmetries
• more exclusive data

Data (Fopi) X. Lopez, et al. (FOPI), PRC 75 (2007)
H.Wolter, ECT May 09
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Nuclear Matter Box Results
NPA762(2005) 147
Density and temperature like in AuAu 1AGeV at
max.compression
vs. asymmetry
Larger isospin effects - no neutron escape
- ?s in
chemical equilibrium?less n-p transformation
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Phases of Nuclear Matter
Plasma of Quarks and Gluons
Isospin ?
20 200 MeV
Mixed Phase In terrestrial Labs.?
Temperature
1 nuclei
5?
Density r/r0
Philippe Chomaz artistic view
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Lower Boundary of the Binodal Surface vs. NM
Asymmetry
symmetric
vs. Bag-constant choice
Proton-fraction
a 1-2 Z/A
NPA775(2006)102-126