Search for Simmetry Energy Search for Simmetry Energy at high densityat high density

V. Greco on Behalf of the Theory V. Greco on Behalf of the Theory

Group of CataniaGroup of Catania

University of CataniaUniversity of Catania

INFN-LNSINFN-LNS

OutlineOutline Symmetry energy at high density, E≥400 AMeV:Symmetry energy at high density, E≥400 AMeV:

relativistic structure of Esym

n/p, 3H/3He ratio & flows (impact of m*n,p)

particle production (, K0/K+)

Dependence of QGP transition on isospinDependence of QGP transition on isospin

Strong isospin fractionation Strong isospin fractionation (large asymmetry in the quark (large asymmetry in the quark

phase)phase)

- implementation in the transport codes -> signatures- implementation in the transport codes -> signatures

...)()()(),( 42 OEEE BsymBBpn

pn

0

2

2

2

1

EEsym

pairICsv AZNaAZZaAaAaZAE /)()1(),( 23/13/2

Symmetry EnergySymmetry Energy

High density/energy High density/energy ProbesProbes

• n/p and LCP ratios

• p/n differential flow

• pions flow and ratios

• kaon ratios

• neutron stars

• ….

Liquid drop model

How the value depends on density, .i.e. -> EOS for any n,p content

Theoretical predictionsTheoretical predictions

Only Stiff- Soft is not predicted!Only Stiff- Soft is not predicted!

V. Greco et al., PRC63(01)-RMF-HF

model Only kinetic contribution to Esym

Charged mesons :

,B

F

Fsym f

E

kE 2

1

6

12*

2

(scalar isovector) (vector-isovector)

323

320

:

:

ssnsp

np

m

g

m

gb

0: 33

0

30

0

0

gΦgMbgVgiN SV

Splitting n & p M*

Relativistic structure alsoRelativistic structure alsoin isospin space !in isospin space !

EEsymsym= cin. + (= cin. + (vectorvector) – () – (scalarscalar))

VVmWWΦmΦΦΦgMVgiL VSSV

ˆˆ2

1ˆˆ4

1ˆˆˆ2

1ˆˆ 222

Isospin degrees of freedom in QHD

BF

Fsym E

Mff

E

kE

2

*

*

2*

2

2

1

6

1

QHD-IIQHD-II

QHD-IQHD-I

The Dirac equation becomes:

meson-like fields exchange model

a4=Esym fixes (ff)

Similar structure in DBHF, DHF, DDC, PC-RMF, …Similar structure in DBHF, DHF, DDC, PC-RMF, …consistent with large fields observed in lQCDconsistent with large fields observed in lQCD

f2.0 2.5 fm2

*

BF

Fsym E

Mff

E

kE

2

*

*

2*

2

2

1

6

1 No f 1.5 fFREE 15 MeV

f2.5 fm2 f 5f

FREE (50-35) MeV

F. Hoffmann et al., PRC64 (2001) 034314V. Greco et al., PRC63(2001)035202

Symmetry Energy in RMFT (~DBHF)

Balance of isospin Balance of isospin fields of fields of ~ 100 MeV~ 100 MeV

B.Liu, PRC65(01)045201

Lane potential

)()( 21

protneutrILane UUkU

1

2

*

1

k

U

k

m

m

m qq

Important for: nucleon emission,Important for: nucleon emission,

flow, particle production flow, particle production

data

m*n < m*p

m*n > m*p

Momentum Momentum dependencedependence

Gives a different contribution at equilibrium but in HIC Esym

pot(r,k)-> m*p, ≠ m*n

RMFT-SkLya oppositebehavior, but there are several sources of MD…

Mean Field Symmetry energy

1

..

1*

psnr U

dk

d

kmm

sD mm *

Non-relativistic massParametrize non-locality in space & time

Dirac mass (for Rel.Mod.)

C. Fuchs, H.H. Wolter, EPJA 30(2006)5

Effective masses: different definitions

The real issue with RMFT is not the The real issue with RMFT is not the Dirac or the non-relativistic, but the Dirac or the non-relativistic, but the zero range approximation that zero range approximation that means an explicit MD contribution is means an explicit MD contribution is missedmissed

Diffence in proton/neutron effective masses

Dirac-RMFT

ISOSPIN EMISSION & COLLECTIVE FLOWS:ISOSPIN EMISSION & COLLECTIVE FLOWS:

- Checking the n,p splitting of effective masses

High pT selections: - source at higher density - squeeze-out

asy-stiff

asy-soft

Light isobar 3H/3He yields

Mass splitting: N/Z of Fast Nucleon Emission

Observable very sensitive at high pObservable very sensitive at high pTT

to the mass splitting and not to the asy-to the mass splitting and not to the asy-stiffnessstiffness

197Au+197Au 600 AMeV

b=5 fm, y(0)0.3

(squeeze-out)

• m*n>m*p

• m*n<m*p

V.Giordano, ECT* May 09

asy-stiff

asy-soft

Crossing of the symmetry potentials fora matter at ρ≈1.7ρ0

n/p ratio yields

m*n<m*p : larger neutron squeeze out at mid-rapidity- Larger neutron repulsion for asy-stiff

Mass splitting impact on Elliptic Flow

m*n < m*p

m*n > m*p

197Au+197Au, 400 AMeV, b=5 fm, y(0)0.5

v2 vs rapidity for 3H and 3He:Larger flow but less isospin effects

v2 vs pT

V.Giordano, ECT* May 09

Increasing relevance of

isospin effects for m*n<m*p

m*n>m*p

m*n<m*p

v2 vs Y/Y0

Quantum Hadrodynamics (QHD) → Relativistic Transport Equation (RMF)

Covariant Mean Field Dynamics

Phys.Rep.410(2005)335-466

Relativistic Energies

RBUU transport equation

Elastic Collision

term

collprr IfUfm

p

t

f

Wigner transform ∩ Dirac + Fields Equation Relativistic Vlasov Equation + Collision Term…

Non-relativistic BNV

isi

iii

Mm

kk

,*

*

F

“Lorentz Force”→ Vector Fields pure relativistic term

3

3

),(

)(),(

jfjfpn

ffpn sss

Upper sign: n

richnBnBpB ,03

2*20iii mk

Single particle energiesSingle particle energies n-rich:- Neutrons see a more repulsive vector field, increasing with fρ and isospin density- m*n<m*p

Dynamical Effect of Relativistic Structure

approximations

potsym

F

EE

Mff

Bρ

42

0.3<Y/Yproj<0.8

132Sn+132Sn, 1.5AGeV, b=6fm

Dynamical boosting of theDynamical boosting of theIsopin effect that is Isopin effect that is

larger when flarger when f is larger is larger

V.Greco et al., PLB562(2003)215

Equilibrium (ρ,δ) dynamically broken:Importance of the covariant structure

f, f determined from

p-n v2 flow

V. Greco et al. PLB562 (2003)

A small gradual change inThe difference 3H-3He whenRaising the beam energy forAu+Au (N/Z = 1.5)

W.Reisdorf, ECT* May 09: FOPI 3H-3He V2 Results Au+Au with increasing beam energy

Relativistic Lorentz effect?The vector part of the isovectorgets dynamically enhanced at E~1.5 AGeV (V. Greco et al. PLB562 (2003))

Hunting isospin with v2 : the mass 3 pair

PARTICLE PRODUCTION with different PARTICLE PRODUCTION with different ISOSPIN:ISOSPIN:

- -/+ vs K-/K0 - Circumstantial reasons to be careful - more theorethical efforts …

Pion vs Kaon as a measure of EOSIn the 80’s there was the idea of using pions to infer the EOSC.M. Ko & J. Aichelin, PRL55(85)2661 pointed out that kaons provide a more sensitive and more clean probe of high density EOS. No conclusion on EOS from pion productionC. Fuchs, Prog.Part. Nucl. Phys. 56 (06)

- Pions produced and absorbed during the entire evolution of HIC

- Kaons are closer to threshold -> come only from high density- Kaons have large mean free path -> no rescattering & absorption- Kaons small width -> on-shell

Bao An Li and L.W. Chen groupshows that the situation is less drammatic that the envisaged one for Esym

~20 years after

Kaons:- direct early production: high density phase- isovector channel effects

Au+Au@1AGeV

/K production in “open” system: Au+Au 1AGeV, central

Production stopped at the maximum of the ’s production ~15 fm/c,K’s purely coming from maximum densityNot affected by rescatterng absorption

ISOSPIN EFFECTS ON PION PRODUCTIONMain mechanism NNN

YKN

NLNLNLdecreaseY

Y

p

n

:)(

)(,

,0

1. Fast neutron emission: “mean field effect” (Bao-An)

2. C.M. energy available: “threshold effect” (Di Toro)

Vector self energy + for n and - for pVector self energy + for n and - for p

n→p “transformation”

.1

nn

n0

n- p-

p+n++

n+ p+

pp

p-

3*,, BBpnpn ffE

NLsNLsNLs

NLsNLsNLs

pppppp

nnnnnn

thin ss

NYKDominant close to sub-threshold

NLNLincrease

3. Isospin -hole exicitations: “spectral function effect” (Ko)

NLNLincrease

This should depend alsoon momentum dependence

Larger effects at lower energies“Threshold effect”

Kaons ratio still a bit more sensitive probe:~15% difference betweenDDF and NLρδ small but perhaps measurable!

132Sn+124Sn

G.Ferini et al.,PRL 97 (2006) 202301

Au+Au, 1 AGeV, central

From Soft to Stiff from From Soft to Stiff from upper to lower curves upper to lower curves

Au+Au central: π and K yield ratios vs. beam energy energy

Softer larger ratio!Opposite to mean field effect(IBUU04)!

Inclusive multiplicities

Comparing calculations & experimentsComparing calculations & experiments

Ferini, NPA762(2005) 147

disagreement in magnitude,particularly at low energies,

Threshold effect too strongOthers have the opposite problem

W.Reisdorf et al. NPA781 (2007) 459

Rapidity selection important

central Au+Au

Zhigang Xiao et al.Zhigang Xiao et al.PRL 102, 062502 (2009)PRL 102, 062502 (2009)Circumstantial evidences Circumstantial evidences forforvery soft high very soft high E Esymsym

Note when there is no ENote when there is no Esymsym

we are much closer among uswe are much closer among usand with data!!!and with data!!!

pp→nΔ++

nn→pΔ-

2020* 44 nnnin pEs

200 )()()()( sspth mppms

200 )()()()( ssnth mnnms

2020* 44 pppin pEs Compensation of Isospin Effects in sCompensation of Isospin Effects in sthth

due to simple assumption for due to simple assumption for

Same thresholds → the sin(NN) rules the relative yields → very important at low energies symEwith

The Threshold Effect: nn→pΔ- vs pp→nΔ++

If you have one inelastic collision how do you conserve the energy?At threshold this is really fundamental! For elatic collision the issue is not there!

What is conserved is not the effective E*,p* momentum-energy but the canonical one.

thin ss

Increasing with momentum

Criticism to the present approachProblems with threshold effect calculation:

1) self-energy for are assumed: no self consistency

2) spectral function important close to threshold reduce the effect

3) Collision integral 3) Collision integral cannot becannot be the simple extension of the elastic one the simple extension of the elastic one

4) mistakes…

It would be important that other transport formulation join the effort

Botermans, Malfliet, Phys. Rep. 198(90) “Quantum transport Theory”

For elastic but with spin interaction, a step before the code approximation

Conservation of Canonical momenta

= 1

One recoversBUU collision

integral

ISOSPIN IN RELATIVISTIC HEAVY ION COLLISIONS:ISOSPIN IN RELATIVISTIC HEAVY ION COLLISIONS:

- Earlier Deconfinement at High Baryon Density - Is the Critical Point affected?

AGeVUU 1,238238 fmb 7

Exotic matter over 10 Exotic matter over 10 fm/c? fm/c?

In a C.M. cell

NPA775(2006)102-126

EoS of Symmetric/Neutron Matter: Hadron (NLρ) vs MIT-Bag → Crossings

Symmetry energies

hadron

Quark:Fermi only

symmetricneutron

(T,) binodal surface

Hadron-RMF

Quark-Bag model

(two flavors)

trans onset of the mixed phase → decreases with asymmetry

Signatures?Signatures?DiToro,Drago,Gaitanos,Greco,Lavagno, NPA775(2006)102-126

),,(),,(

(....)(....)

),,(),,(

33

33

33

TPTP

TT

QQB

QHHB

H

QH

QQB

QB

HHB

HB

QH

QB

HBB

333 )1(

)1(

Mixed Phase →

NLρ

NLρδGM3

1 AGeV

300 AMeV

132Sn+124Sn, semicentral

B1/4 =150 MeV

Testing deconfinement with RIB’s?Gibbs Conditions

Liu Bo, M.D.T., V.Greco May 09

Mixed Phase: Boundary Shifts with asymmetry

Lower Boundary muchaffected by the Esym

T dependence

No potential Esym

Lower Boundary significantly decrease with T

Upper bound

Quark Phase: large Isospin Distillation near the Lower Border?Quark Phase: large Isospin Distillation near the Lower Border?

Signatures? Neutron migration to the quark clusters (instead of a fast emission)Large modification of isopsin particle ratio at high pT

A theorethical issue : Potential Symmetry Energy in the Quark Phase?

upper

upper quark fractionlower

In-In-ConclusionConclusionWhile the EOS of symmetric NM is fairly well determined, the

density (and momentum) dependence of the Esym is still rather uncertain.

Can it be done like for the symmetric part? Particle production

• Ratios and + are sensitive probe to high density Esym

- kaon signal is a sharp signal from high density

• Competing effect in isospin particle ratio production: - self-energies revert the dependence respect to the n/p

emission

- a more careful treatment of the collision integral respect to - a more careful treatment of the collision integral respect to the elastic one is essential !the elastic one is essential !

• EE≥ 1.5 A GeV can have a transient quark phase highly ≥ 1.5 A GeV can have a transient quark phase highly

asymmetricasymmetric

- signatures and effective field theories to be developed- signatures and effective field theories to be developed

Lower=0.0

Upper=1.0

Symmetric to Asymmetric (not Exotic) Matter

region explored ~ 1AGeV

No pion excitationsincluded

central Au+Au

analysis of π-/π+ ratios in Au+AuZhigang Xiao et al.PRL 102, 062502 (2009)FOPI data, W. Reisdorf et al.NPA 781 (2007)

Circumstantial evidence for very soft symmetry energyCircumstantial evidence for very soft symmetry energy

NJL Effective Lagrangian (two flavors): non perturbative ground state with q-qbar condensation

M.Buballa, Phys.Rep. 407 (2005)

0)]2([

;)]2([ 2

qGmi

LagrangeEuler

qqGqGmiqLNJL

1

1

03

3

]1/)[exp(),(

]1/)[exp(),(

)],(),(1[)2(

4

TETn

TETn

TnTnE

MpdNNmM

pp

pp

ppp

cf

p

Gap Equation

→ 1

→ 0

→ 1/2

→ 1/2

Large μ Large T 0or

Chiral restoration

Au+Au 1AGeV central: Phase Space Evolution in a CM cellAu+Au 1AGeV central: Phase Space Evolution in a CM cell

Testing EoS→CBM

K production

G. Ferini, et al., NPA762(2005) 147 and nucl-th/0607005

Data (Fopi)

X. Lopez, et al. (FOPI), PRC 75 (2007)

Comparision to FOPI data

(Ru+Ru)/(Zr+Zr)

equilibrium (box) calculations

finite nucleus calculations

• sensitivity reduced in collisions of finite nuclei

• single ratios more sensitive

• enhanced in larger systems

Kaon ratios: comparison with experimentKaon ratios: comparison with experiment

Au+Au 1AGeV: density and isospin of the Kaon source

n,p at High density

n/p at High density

Drop:Contribution of fast neutron emission andInelastic channels: n→p transformation

Time interval of Kaon production

“central”density

Dynamics 2.

Comparing with experiments

Ferini, NPA762(2005) 147

disagreement in magnitude,

particularly at low energies,

(also in other calc.),

but better at midrapidity

(high density), where Kaons

are produced.

W.Reisdorf et al. NPA781 (2007) 459

Rapidity selection

In-medium Klein-Gordon eq. for K propagation:

Two models for medium effects tested:

1.Chiral perturbation (Kaplan, Nelson, et al.) (ChPT)

2.One-boson-exch. (Schaffner-Bielich, et al.,) (OBE)

density and isospin dependent

ChPT

OBEIn-Medium K energy (k=0)

Splitting for K0,+

and NLand NL

Test of kaon potentials models

Absolute yields: Ni+Ni, E=1.93 AGeV, b<4 fm, rapidity distrib.

In-medium Kaon potenial Isospin dep. part

good description od FOPI data: OBE and eff

ChPT

Ratios to minimze influence of eff kaon potentials

robust relative to K-potential, but dep.on isospin-dep part