The High-Density Symmetry Energy in Heavy Ion Collisions

The High-Density Symmetry Energy in Heavy Ion Collisions

Int. School on Nuclear Physics: Probing the Extremes of Matter with Heavy Ions, Erice, Sept. 16-24 2012

Hermann WolterLudwig-Maximilians-Universität München (LMU)

The High-Density Symmetry Energy in Heavy Ion Collisions

The High-Density Symmetry Energy in Heavy Ion Collisions

Int. School on Nuclear Physics: Probing the Extremes of Matter with Heavy Ions, Erice, Sept. 16-24 2012

Hermann WolterLudwig-Maximilians-Universität München (LMU)

Massimo Di Toro, Maria Colonna, V. Greco, G. Ferini, (LNS Catania), Theodoros Gaitanos, (Giessen),

Vaia Prassa, (Thessaloniki)

Schematic Phase Diagram of Strongly Interacting Matter

Liquid-gas coexistence

Quark-hadron coexistence

Z/N

1

0

SIS18

neutron starsSupernovae IIa

Isospin degree of freedom

1. Density dependence of the Symmetry energy in the hadronic sector2. Investigation via heavy ion collisions3. Observables in the above-saturation density regime:

difference flows, meson ratios

SIS300

...)(O)(E)(EA/),(E 42BsymBnmB

pn

pn

Equation-of-State and Symmetry Energy

pair22

s3/4

C3/1

sv )ZN/()ZN(aA)1Z(ZaAaaA/)Z,A(E BW mass formula

density-asymmetry dep. of nucl.matt.

)(Ea 0symS

stiff

soft

saturation point

Fairly well fixed! Soft!

EOS of symmetric nuclear matter

symmetry energy

asymmetry density

Symmetry energy: neutron - symm matter, rather unknown,e.g. Skyrme-like param.,B.A.Li

asy-

stiff

asy-soft

neutron matter EOS

Esympot() often parametrized as

)/(C 0

)(E)/()(E potsym

3/20F3

1sym

2

0

0sym

0

0sym 18

K

3

LJ)(E

Parametrizations around 0 :

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

matt.nuclmatt.neutrsym EEE

The Nuclear Symmetry Energy (SE) in „realistic“ models

The EOS of symmetric and pure neutron matter in different many-body aproaches

)UU(U

n,pq;k

U

k

m1

m

m

pn21

Lane

1

q

2

*q

SE ist also momentum dependent p/n effective mass splitting

Lane potential; mom. dep.

Why is symmetry energy so uncertain?? ->In-medium mass, and short range isovector tensor correlations (B.A. Li, PRC81 (2010));

use HIC to investigate in the laboratory and neutron star observations

Rel, BruecknerNonrel. BruecknerVariationalRel. Mean fieldChiral perturb.

SE

nuclear matter

neutron matter

Esy

m

M

eV)

1 2 30

Asy-stiff

Asy-soft

Importance of Nuclear Symmetry Energy

Bayesian analysis of mass-radius relation;A. Steiner, et al., arXiv 1205.6871

neutron starsSupernovae, very dilute matter,Cluster correlations

Constraints on the Slope of SE from Structure and low-energy HIC

MeV2560L

Nat

ow

itz

et a

l., P

RL

104

(20

10)

,fIfUfm

p

t

fcollp

2-body collisions

)1)(1()1)(1(

)()2(

1

432432

43213412

1243223

ffffffff

ppppd

dvdpdpdp

loss term gain term

11 1

12

3 4

non-relativistic: BUU

Vlasov eq.; mean field

EOSisoscalar and isovector

isospin dependent, pp,nn,pn

1) Approximation to a much more complicated non-equilibrium quantum transport equation (Kadanoff-Baym) by neglecting finite width of particles (quasi-particle approximation)

2) Relativistic equivalent available; RMF or EFT models for EOS

3) Consistency between EOS and in-medium cross sections: e.g. (Dirac) Brueckner approach

4) Isovecor effects are small relative to isoscalar quantities; differences or ratios of observables to become independent of isoscalar uncertainties

5) Collision termdissipation, NO fluctuation termBoltzmann-Langevin eq.

Învestigation of the symmetry energy in heavy ion collisions

Transport theory

Heavy Ion Collisions at Relativistic Energies: “Flow“

Global Global momentum momentum spacespace

Fourier analysis of momentum tensor : „flow“

v2: elliptic flowv1: directed flow

..)2cos)b,y(vcos)b,y(v1(N)b,y,(N 210

p

nasystiffasysoft

asystiff

Proton-neutron differential flow

)neutron(protonfor)1(1w

,)wp()y(p

i

)y(N

1ii

xi)y(N

1npx

132132Sn + Sn + 132132Sn @ 1.5 AGeV b=6fmSn @ 1.5 AGeV b=6fm

asysoft

Au+Au, 400AMeV asysoft

m*n>m*p

m*n<m*p

Inversion of elliptic flows with effective mass

<p

x(y)

>

<p

xp-n(y

)>

Sensitivity to SE: asy-stiff more flow of neutrons,

V.Giordano, M.Colonna et al., arXiv 1001.4961, PRC81(2010)

Ell

ipti

c fl

ow

v2

But also to effective mass difference (i.e. momentum dep. of SE):Inversion of n/p potential at higher momentum

First measurement of isospin flow

Each band: soft vs. stiff eos of symmetric matter, (Cozma, 1102.2728) robust probe

Au+Au @ 400 AMeV, FOPI-LAND (Russotto, et al., PLB 697, 471 (11))

directed flow (v1) not very sensitive,

but elliptic flow (v2), originates in compressed zone

determines a rather stiff symmetry energy, i.e.

=0.5=1.5

neutronprotonhydrogen

ASYEOS experiment at GSIMay 2011, being analyzed

also study t/3He flow!

1

1. „direct effects“: difference in proton and neutron (or light cluster) emission and momentum distribution

2. „secondary effects“: production of particles, isospin partners -,+, K0,+

NNK

K

NN N

in-medium in-elastic

K and potential (in-medium mass)

in-medium self-energies and width

potential ,

0,K, p, n

Particle production as probe of symmetry energy

Two limits:1. isobar model

(yield determined by CG-Coeff of ->N

2. chemical equilibrium

-> -/+ should be good probe!

2

2

2

Z

N

NZZ5

NZN5/

T

)(E8exp

T

)(2exp/ sympn

box calculation

Ferini et al.,

B.A.Li et al., PRL102

Therefore consider ratios -/+; K0/K+

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

stiffnessasywithdecrease

)(Y

)(Y

p

n,

,0

1. Mean field effect: Usym more repulsive for neutrons, and more for asystiff pre-equilibrium emission of neutron, reduction of asymmetry of residue

2. Threshold effect, in medium effective masses:

Canonical momenta have to be conserved. To convert to kinetic momenta, the self energies enter

In inelastic collisions, like nn->p-, the self-energies may change. Simple assumption about self energies of

Yield of particles depends on

Detailed analysis gives

Particle production as probe of symmetry energy (2)

Two effects:

stiffnessasywithincrease

)'f1)(f1(ff)f1)(f1(ff

)pppp()2()(vvdvdvdI

2'12121'2'1

'2'1213

inel12'2'12coll

Competing effects!- How taken into account in different calculations? - dynamics may be too simple.

thininel ss

Au+Au@1AGeV G.Ferini et al.,PRL 97 (2006) 202301

Central density

and K: production in high density phase

Pions: low and high density phase

Sensitivity to asy-stiffness

Dynamics of particle production (Dynamics of particle production (,K) in heavy ion collisions,K) in heavy ion collisions

time [fm/c]

Dependence of ratios on asy-stiffness: n/p ratio governs particle ratios

n/p 0,-/+,++

-/+ K0/K+

K0,+ multiplicity

and multiplicity

incr

easi

ng

sti

ffn

ess

Kaons were a decisive observable to determine the symmetric EOS;

perhaps also useful for SE?Kaons are closer to threshold, come only from high density, have large mean free path, small width:

Ratio of K+ yield in (Au+Au)/(C+C)

C. Fuchs et al., PRL 86(01)1974

MDI, x=0, mod. soft Xiao,.. B.A.Li, PRL 102 (09)MDI, x=1, very softNL, stiff Ferini, Gaitanos,.. NPA 762 (05)NLlinear=2, stiff Feng,… PLB 683 (10)SIII, very softsmall dep. on SE J. Hong, P.Danielewicz

FOPI, exp

Pion ratios in comparison to FOPI data (W.Reisdorf et al. NPA781 (2007) 459)

Widely differering results of transport calculations with similar input!

- -dynamics in medium (potential, widths, etc) largely unknown- threshold and mean field effects- pion potential: U=0 in most calculations. OK?- differences in simulations of collision term

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

132Sn+124Sn

Au+Au, 1 AGeV, central

Inclusive multiplicities

132Sn+124Sn

Nuclear matter (box calculation)

K

K 0

single ratios more sensitive

• enhanced in larger systems

- Stiffer asy-EOSlarger ratio! Opposite to mean field effect!- Kaons somewhat more sensitive than pions. esp. at low energies, close to threshold- Sensitivity reduced in finite nuclei due to evolution of asymmetry in collision

Kaon production in HIC

Comparision to FOPI data

(Ru+Ru)/(Zr+Zr)

equilibrium (box) calculations

finite nucleus calculations

Data (Fopi) X. Lopez, et al., PRC 75 (2007)

G. Ferini, et al., NPA762(2005) 147

mo

re a

sy-s

tiff

nes

s

+/- ratioB.A. Li, et al.

+/- ratio,Feng, et al.

Fermi Energy HIC, various observables, compilation MSU

Present constraints on the symmetry energy

Moving towards a determination of the symmetry energy in HIC

but at higher densitynon-consistent results of simulations for pion observables.

Au+Au, elliptic flow, FOPI

Limits on the EOS in -equilibrium,Including constraints from neutron stars and microscopic calc.

A. Steiner, J. Lattimer, E.F.Brown, arXiv 1205.6871

Combined methods move towards stronger constraints

Summary and Outlook

• EOS of symmetric NM is now fairly well determined, but density (and momentum) dependence of the Symmetry Energy rather uncertain, but important for exotic nuclei, neutron stars and supernovae.

• Constraints from HIC both at sub-saturation (Fermi energy regime) and supra-saturation densities (relativistic collisions), and increasingly from neutron star observables.

• At subsaturation densities increasingly stringent (~1, L~60 MeV), but constraints are largely lacking at supra-saturation densities.

• Observables for the supra-saturation symmetry energy

N/Z of pre-equilibrium light clusters (MSU, FOPI),difference flows, (first hints -> ASYEOS)

part. production rations -/+ , K0/K+ (FOPI,HADES)

• More work to do, esp. In theory (consistency of transport codes, dynamics)

• Symmery energy important in the partonic phase or for the phase transition to the partonic phase? What is the SE in the partonic phase.

Thank you

Backup

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

In-Medium K energy (k=0)

Test of kaon potentials models

ChPT

Ratios to minimze influence of eff kaon potentials

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

ChPT

OBE

Splitting for K0,+

and NLand NL

Strangeness ratio : Infinite Nuclear Matter vs. HIC

Au≈0.2Au≈0.2

Au+Au@1AGeV (HIC)Au+Au@1AGeV (HIC)Au≈1.5Au≈1.5

NL→ DDF→NLρ→NLρδ : more neutron escape and more n→p transformation(less asymmetry in the source)

Density & asymmetry of the K-sourceDensity & asymmetry of the K-source

Inf. NM

G. Ferini, et al., NPA762(2005) 147

Pre-equilibrium emission (mainly of neutrons) reduced asymmetry of source for kaon production reduces sensitivity relative to equilibrium (box) calculation

asy-stiff

asy-soft

Light isobar 3H/3He yields

Observable very sensitive at high pObservable very sensitive at high pTT

to the mass splitting and to the mass splitting and notnot to the asy-stiffness to the asy-stiffness

197Au+197Au 600 AMeV

b=5 fm, y(0)0.3

• m*n>m*p

• m*n<m*p

V.Giordano, M.Colonna et al., PRC 81(2010)

asy-stiff

asy-soft

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

n/p ratio yields

Pre-equilibrium nucleon and light cluster emission at higher energy

Differential elliptic flow

asystiff asysoft

m*n>m*p

m*n<m*p

Inversion of elliptic flows because of inversion of potentials with effective mass

W. Reisdorf, ECT*, May 09

Indication of experimental effect

Au+Au, 400 AMeV

t-3He pair similar but weaker

Au+Au, 600 AMeV

Elliptic flow more sensitive, since determined by particles that are emitted perp to the beam direction

V.Giordano, M.Colonna et al., arXiv 1001.4961, PRC81(2010)

Pion ratios in comparison to FOPI data (W.Reisdorf et al. NPA781 (2007) 459)

Many attempts to understand behaviour:

Double ratio of Sn+Sn systems

Yong, et al.,PRC73,034603(06)

Sensitivity=Y(x=1)/Y(x=0)

Zhang, et al., PRC80,034616(09)

Possible causes:

- Pion are created via ‘s. dynamics in medium (potential, width, etc) largely unknown.

- Threshold and mean field effects

- Pion potential: U=0 in most calculations. OK?

- differences in simulations, esp. collision term

- Urgent problem to solve!!!

Transverse Pion Flows

FOPI: W.Reisdorf et al. NPA781 (2007) 459

Antiflow: decoupling of the pion/nucleon flowsOK general trend. but:- smaller flow for both - and +-not much dependent on Iso-EoS

IQMD softMD FOPI IQMD stiffMD

Au+Au

General behaviour (centrality dep.)

+

-

-

+

--

+

+

Simulations: V.Prassa, PhD Sept.07

Rapidity dependence

stiff

soft

asy-stiff

asy-soft

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

matt.nuclmatt.neutrsym EEE

Rel, BruecknerNonrel. BruecknerVariationalRel. Mean fieldChiral perturb.

The Nuclear Symmetry Energy in different „realistic“ models

The EOS of symmetric and pure neutron matter in different many-body aproaches

SE

asy-soft at0

(asystiff very similar)

n,pq

;k

U

k

m1

m

m1

q

2

*q

Isovector (Lane) potential: momentum dependence

)UU()k(U pn21

Lane

SE ist also momentum dependent p/n effective mass splitting

Why is symmetry energy so uncertain?? ->In-medium mass, and short range tensor correlations (B.A. Li, PRC81 (2010));

Neutron stars: a laboratory for the high-density symmetry energy

A normal NS (n,p,e)

… or exotic NS ??

Typical neutron stars

Neutron star mass dep. on Symmetry Energy

pro

ton

fra

ctio

n x

Onset of direct URCA (x>1/9)

Fast cooling of NS: direct URCA process

enep

Klähn, Blaschke, Typel, Faessler, Fuchs, Gaitanos,Gregorian, Trümper, Weber, Wolter, Phys. Rev. C74 (2006) 035802

Neutron star cooling: a test of the symmetry energy

A given symmetry energy behavior leads to a distribution of NS masses:

Comparison to mass distribution from population synthesis models (Popov et al., A&A 448 (2006)

plus other neutron star observables;consistency far from obvious

e.g. for DBHF EOS)

D. Blaschke, Compstar workshop, Caen, 10

Limits on the EoS from a Bayesian analysis of NS mass-Radius observationsA. Steiner, J. Lattimer, E.F.Brown, arXiv 1205.6871

Comparison to models

many Skyrme models eliminated

Limits on the EOS in -equilibrium Limits on SE powerlaw

Lattimer, Lim, arxiv 1203.4286

Synthesis of constraints

..but measurement in very different density ranges!

Astrophysics: Supernovae and neutron stars

A normal NS (n,p,e)

or exotic NS?PSR J1614-2730

typical neutron stars

heaviest neutron star

Onset of direct URCA: Yp>.11;Too fast cooling

central density

Comparison to models

many Skyrme models eliminated

Limits on the EoS from a Bayesian analysis of NS mass-Radius observationsA. Steiner, J. Lattimer, E.F.Brown, arXiv 1205.6871

Deconfinement Transition with Large Asymmetry

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

DiToro,et al.,, NPA775(2006)102-126

Quark:Fermi only

symmetricneutron

NLρ

NLρδGM3

1 AGeV

300 AMeV

132Sn+124Sn, semicentral

B1/4 =150 MeVHadronSymmetry energy