Study of in-medium effects Study of in-medium effects within transport approacheswithin transport approaches

EElenalena Bratkovskaya Bratkovskaya

25.06.2008 , Workshop ‚Hadrons@FAIR‘FIAS, Uni. Frankfurt, Frankfurt am Main

2

Changes of the particle properties in the hot and dense Changes of the particle properties in the hot and dense baryonic mediumbaryonic medium

How to treat in-medium effects in transport approaches?

In-medium models:

chiral perturbation theory chiral perturbation theory

chiral SU(3) model chiral SU(3) model

coupled-channel G-matrix approachcoupled-channel G-matrix approach

chiral coupled-channel effective field chiral coupled-channel effective field theory theory

predict changes of the particle predict changes of the particle properties in the hot and dense medium, properties in the hot and dense medium, e.g. e.g. broadening of the spectral function broadening of the spectral function

meson spectral functionmeson spectral function

0

2

4

6

8

10

20

1.50

0

0.50

A(s

) [M

eV-1]

p=0 MeV/c

A(s

) [M

eV-1]

20

1.50

0

0.50

p=150 MeV/c

0.2 0.4 0.6 0.80

2

4

6

8

10

20

1.50

0

0.50

s1/2

[GeV]

p=300 MeV/c

s1/2

[GeV]

0.2 0.4 0.6 0.8

20

1.50

0

0.50

p=500 MeV/c

L. Tolos et al., NPA 690 (2001) 547L. Tolos et al., NPA 690 (2001) 547

3

Dynamics of heavy-ion collisions –> Dynamics of heavy-ion collisions –> complicated many-body problem!complicated many-body problem!

Correct wayCorrect way to solve the many-body problem including all quantum to solve the many-body problem including all quantum mechanical features mechanical features

Kadanoff-Baym equationsKadanoff-Baym equations for Green functions S for Green functions S<< (from 1962)(from 1962)

Greens functions S / self-energies Greens functions S / self-energies : :

e.g. for bosons

do Wigner transformation do Wigner transformation

retarded (ret), advanced (adv) (anti-)causal (a,c )

consider only contribution up toconsider only contribution up to first order in the gradientsfirst order in the gradients = a= a standard approximationstandard approximation of kinetic theory which is justified if the gradients in of kinetic theory which is justified if the gradients in the mean spacial coordinate X are smallthe mean spacial coordinate X are small

4

From Kadanoff-Baym equations to transport equationsFrom Kadanoff-Baym equations to transport equations

drift termdrift term Vlasov termVlasov term

collision term =collision term = ‚loss‘ term -‚loss‘ term -‚gain‘ term‚gain‘ term

Operator <> - 4-dimentional generalizaton of Operator <> - 4-dimentional generalizaton of the Poisson-bracketthe Poisson-bracketbackflow termbackflow term

Generalized transport equations =Generalized transport equations = first order gradient expansion of the Wigner first order gradient expansion of the Wigner transformed Kadanoff-Baym equations:transformed Kadanoff-Baym equations:

The imaginary part of the retarded propagator is given by the normalized The imaginary part of the retarded propagator is given by the normalized spectral function:spectral function:

For bosons in first order gradient expansion:For bosons in first order gradient expansion:XPXP – width of spectral function = – width of spectral function = reaction rate of particle (at phase-reaction rate of particle (at phase-space position XP)space position XP)

W. Cassing et al., NPA 665 (2000) 377; 672 (2000) 417; 677 (2000) 445W. Cassing et al., NPA 665 (2000) 377; 672 (2000) 417; 677 (2000) 445

Backflow termBackflow term incorporates the incorporates the off-shell behavioroff-shell behavior in in the particle propagationthe particle propagation !! vanishes in the quasiparticle limit vanishes in the quasiparticle limit

Greens function SGreens function S< < characterizes the characterizes the number of particles (N) and their number of particles (N) and their properties (A – spectral function )properties (A – spectral function )

5

General testparticle off-shell equations of motion General testparticle off-shell equations of motion

Employ Employ testparticle Ansatztestparticle Ansatz for the real valued quantity for the real valued quantity ii S S<<XP XP --

insert in generalized transport equationsinsert in generalized transport equations and determine equations of motion ! and determine equations of motion !

General testparticle off-shell equations of motion:General testparticle off-shell equations of motion:

with

Note:Note: the common factor 1/(1-Cthe common factor 1/(1-C(i)(i)) can be absorbed in an ‚eigentime‘ of particle (i) !) can be absorbed in an ‚eigentime‘ of particle (i) !

W. Cassing , S. Juchem, NPA 665 (2000) 377; 672 (2000) 417; 677 (2000) 445W. Cassing , S. Juchem, NPA 665 (2000) 377; 672 (2000) 417; 677 (2000) 445

6

On-shell limitOn-shell limit

2) Γ(X,P) such that X=0 and P=0

E.g.: Γ = const

=Γ=Γvacuumvacuum (M)(M)

‚Vacuum‘ spectral function with constant or mass dependent width :spectral function AXP does NOT change the shape (and pole position) during propagation through the medium (backflow term vanishes also!)(backflow term vanishes also!)

1) Γ(X,P) 0

quasiparticle approximation quasiparticle approximation : : A(X,P) = 2 A(X,P) = 2 (P(P22-M-M22))

||||Hamiltons equation of motionHamiltons equation of motion - -

independent on Γ !independent on Γ !Backflow termBackflow term - - which which incorporates the off-shell incorporates the off-shell behavior in the particle behavior in the particle propagation - propagation - vanishes in vanishes in the quasiparticle limit !the quasiparticle limit !

Hamiltons equation of motion - Hamiltons equation of motion - independent on Γ !independent on Γ !

7

• for each particle species for each particle species ii ( (i i = = NN, , RR, , YY, , , , , K, …) the phase-space density f, K, …) the phase-space density fi i followsfollows

the the transport equations transport equations

with collision termswith collision terms IIcoll coll describing elastic and inelastic describing elastic and inelastic hadronic reactions: hadronic reactions:

baryon-baryon, meson-baryon, meson-meson, formation and decay of baryon-baryon, meson-baryon, meson-meson, formation and decay of baryonic and mesonicbaryonic and mesonic resonances, stringresonances, string formation and decay formation and decay (for inclusive particle production:(for inclusive particle production:

BB BB X , mB X , mB X, X =many particles)X, X =many particles)

with with propagationpropagation of particles in self-generated of particles in self-generated mean-field potential mean-field potential U(p,U(p,)~Re()~Re(retret)/2p)/2p00

•Numerical realization – solution of classical equations of motion + Numerical realization – solution of classical equations of motion + Monte-Carlo Monte-Carlo simulationssimulations for test-particle interactions for test-particle interactions

‚‚On-shell‘ transport modelsOn-shell‘ transport models

)f,...,f,(fIt),p,r(fUUt M21colliprrp

Basic concept of the ‚on-shell‘ transport modelsBasic concept of the ‚on-shell‘ transport models (VUU, BUU, QMD etc. ): (VUU, BUU, QMD etc. ):

1)1) Transport equations Transport equations = first order gradient expansion of the Wigner = first order gradient expansion of the Wigner transformed Kadanoff-Baym equations transformed Kadanoff-Baym equations

2)2) Quasiparticle approximation Quasiparticle approximation or/andor/and vacuum spectral functions vacuum spectral functions : : A(X,P) = 2 A(X,P) = 2 (p(p22-M-M22) A) Avacuumvacuum(M) (M)

8

Short-lived resonances in semi-classical transport modelsShort-lived resonances in semi-classical transport models

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.610-3

10-2

10-1

100

101

102

103

/=5

M [GeV/c2]

spectral function

A(M

)

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.610-3

10-2

10-1

100

101

102

103

/=0

M [GeV/c2]

spectral function

A(M

)

In-mediumIn-medium

Vacuum Vacuum ((narrow narrow

statesstates

In-medium:In-medium:production of broad statesproduction of broad states

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.110-2

10-1

100

101

M [GeV]

bare mass coll. broadening

E=1.5 GeV

208Pb X e+e- Xd/

dM

[b

/GeV

]

BUU: M. Effenberger et al, PRC60 (1999)BUU: M. Effenberger et al, PRC60 (1999)

,

ρ)p,(M,MΓ)ReΣM(M

ρ)p,(M,ΓM

π

2ρ)p,A(M 2

totret2

02

tot2

, widthwidthIm Im retret

Spectral function:Spectral function:

Example : Example : -meson propagation through the medium -meson propagation through the medium within the on-shell BUU modelwithin the on-shell BUU model broad in-medium spectral function does not broad in-medium spectral function does not become on-shell in vacuum in ‚on-shell‘ become on-shell in vacuum in ‚on-shell‘ transport models!transport models!

9

Off-shell vs. on-shell transport dynamicsOff-shell vs. on-shell transport dynamics

010

2030

40

0.2

0.4

0.6

0.8

1.0

0.00.2

0.40.6

0.81.0

010

2030

40

0.2

0.4

0.6

0.8

1.0

0.00.2

0.40.6

0.81.0

010

2030

40

0.2

0.4

0.6

0.8

1.0

1.2

0.00.2

0.40.6

0.81.0

010

2030

40

0.2

0.4

0.6

0.8

1.0

1.2

0.00.2

0.40.6

0.81.0

C+C, 2.0 A GeV, b=1 fmdropp. mass + coll. broad.

dN/d

M [

a.u.

]

M [GeV/c2 ]

time [fm/c]

-meson off-shell

-meson on-shell

dN/d

M [

a.u.

]

M [GeV/c2 ]

time [fm/c]

-meson on-shell

dN/d

M [

a.u.

]

M [GeV/c2 ]

time [fm/c]

-meson off-shell

dN/d

M [

a.u.

]

M [GeV/c2 ]

time [fm/c]

The off-shell spectral function becomes on-shell in the vacuum dynamically The off-shell spectral function becomes on-shell in the vacuum dynamically by propagation through the medium!by propagation through the medium!

Time evolution of the mass distribution of Time evolution of the mass distribution of andandmesons for central C+C mesons for central C+C collisions (b=1 fm) at 2 A GeV for collisions (b=1 fm) at 2 A GeV for dropping mass + collisional broadening scenariodropping mass + collisional broadening scenario

E.L.B. &W. Cassing, NPA 807 (2008) 214E.L.B. &W. Cassing, NPA 807 (2008) 214

On-shell model:On-shell model:low mass low mass

andandmesons live mesons live forever and shine forever and shine

dileptons!dileptons!

10

Collision term in off-shell transport modelsCollision term in off-shell transport models

Collision termCollision term for reaction 1+2->3+4: for reaction 1+2->3+4:

withwith

The trace over particles 2,3,4 reads explicitly The trace over particles 2,3,4 reads explicitly for fermionsfor fermions for bosonsfor bosons

The transport approach and the particle spectral functions are fully The transport approach and the particle spectral functions are fully determined once the determined once the in-medium transition amplitudes Gin-medium transition amplitudes G are known are known

in their in their off-shell dependenceoff-shell dependence!!

additional integrationadditional integration

11

Study of in-medium KStudy of in-medium K++ and K and K-- properties in heavy-ion collisions properties in heavy-ion collisions within dynamical transport models within dynamical transport models

Theory Theory (status: last millenium < 2000)(status: last millenium < 2000) : :

Implementation of in-medium KImplementation of in-medium K++ and K and K-- scenarios (= scenarios (= ‚dropping‘ of K‚dropping‘ of K--

mass and mass and ‚enhancement‘of K‚enhancement‘of K++ mass) in mass) in on-shellon-shell transport models:transport models:

BUU (Texas) (1994), HSD (or RBUU) (1997), QMD (Tübingen) (1998), BUU (Texas) (1994), HSD (or RBUU) (1997), QMD (Tübingen) (1998), IQMD (Nantes) (2000), ...IQMD (Nantes) (2000), ...

Strangeness production at low energyStrangeness production at low energy

• Baryon-Baryon collisions:

KBBYB

KKBBBB

KYBBB

• meson-Baryon collisions:meson-Baryon collisions:

KBYπ

KKBBπ

KYBπ

• meson-meson collisions:

)(ΛY

Δ,...)(N,B

)K,(KK

)K(K,K0

0

,

KKππ Dominant channel for low Dominant channel for low

energy Kenergy K-- production!production!

12

Need to knowNeed to know in-medium transition amplitudes G and their off-shell in-medium transition amplitudes G and their off-shell dependencedependence

Coupled channel G-matrix approachCoupled channel G-matrix approach

Transition probability :Transition probability :

with G(p,with G(p,,T) - ,T) - G-matrixG-matrix from the from the solution of solution of coupled-channel equationscoupled-channel equations

with pion dressingwith pion dressing, i.e. including , i.e. including the pion self-energy in the the pion self-energy in the intermediate intermediate states states

without pion dressingwithout pion dressing

W. Cassing, L. Tolos, E.L.B., A. Ramos, W. Cassing, L. Tolos, E.L.B., A. Ramos, NPA 727 (2003) 59NPA 727 (2003) 59

L. Tolos et al., L. Tolos et al.,

NPA 690 (2001) 547NPA 690 (2001) 547

Off-shell transport => In-medium transition rates: Off-shell transport => In-medium transition rates: G-matrix approachG-matrix approach

13

KK- - production in A+A within the off-shell transport approachproduction in A+A within the off-shell transport approach

0.0 0.1 0.2 0.3 0.410

-4

10-3

10-2

10-1

100

K free

K in-medium (without pion dressing)

K in-medium (with pion dressing)

C+C -> K+X, 1.8 A GeV

KaoS Collab., cm

=(90 + 10)o

E d

3 /d3 p

[ m

b G

eV -2

c3 s

r-1]

Ecm

kin [GeV]

0.0 0.1 0.2 0.3 0.410

-2

10-1

100

101

102

K free

K in-medium (without pion dressing)

K in-medium (with pion dressing)

Au+Au -> K+X, 1.5 A GeV

KaoS Collab., cm

=(90+10)0

E d

3 /d3 p

[ m

b G

eV -2

c3 s

r-1]

Ecm

kin [GeV]

• Au+Au (and Ni+Ni) Au+Au (and Ni+Ni) data at 1.5 data at 1.5 (1.93) A GeV are consistent with the (1.93) A GeV are consistent with the ‚pion dressing‘ scenario, whereas ‚pion dressing‘ scenario, whereas C+C C+C at 1.8 A GeV are at 1.8 A GeV are underestimated even without pion underestimated even without pion dressing dressing

W. Cassing, L. Tolos, E.L.B., A. Ramos, NPA 727 (2003) 59W. Cassing, L. Tolos, E.L.B., A. Ramos, NPA 727 (2003) 59

0.0 0.1 0.2 0.3 0.410-2

10-1

100

101

102

K+: no; K: no

K+: yes; K: yes G-matrix with dress. G-matrix without dress.

Ni+Ni -> K+X, 1.93 A GeV

KaoS Collab., c.m.

=(90+10)0

E d

3 /d

3 p [

mb

GeV

-2 c

3 sr-1

]

Ec.m.

kin [GeV]

Updated plot‘07Updated plot‘07

14

KK--/K/K++ ratio in Au+Au at 1.5 A GeV within the off-shell ratio in Au+Au at 1.5 A GeV within the off-shell transport approachtransport approach

• Data are consistent with the ‚pion dressing‘ scenario

50 100 150 200 250 300 350 4000.00

0.01

0.02

0.03

0.04

0.05

KaoS Collab., lab

=(40+4)o

(preliminary)

Apart

p>0.35 GeV/c

K free

K in-med. (without pion dressing)

K in-med. (with pion dressing)

Au+Au, 1.5 A GeV

Rat

io K

/K

W. Cassing, L. Tolos, E.L.B., A. Ramos, NPA 727 (2003) 59W. Cassing, L. Tolos, E.L.B., A. Ramos, NPA 727 (2003) 59

15

Dileptons from transport modelsDileptons from transport models

Theory Theory (status: last millenium < 2000)(status: last millenium < 2000) : : Implementation of in-medium vector mesons (Implementation of in-medium vector mesons () scenarios (= ) scenarios (= ‚dropping‘ ‚dropping‘

mass and mass and ‚collisional broadening‘‚collisional broadening‘) in ) in on-shellon-shell transport models:transport models:

BUU/AMPT (Texas) ( > 1995)BUU/AMPT (Texas) ( > 1995)

HSD ( > 1995)HSD ( > 1995)

UrQMD v. 1.3 (1998)UrQMD v. 1.3 (1998)

RQMD (Tübingen) (2003), RQMD (Tübingen) (2003), but NO explicit propagation of vector mesonsbut NO explicit propagation of vector mesons

IQMD (Nantes) (2007), IQMD (Nantes) (2007), but NO explicit propagation of vector mesonsbut NO explicit propagation of vector mesons

Theory Theory (status: this millenium > 2000) :(status: this millenium > 2000) :

Implementation of in-medium vector mesons (Implementation of in-medium vector mesons () scenarios (= ) scenarios (= ‚dropping‘ ‚dropping‘

mass and mass and ‚collisional broadening‘‚collisional broadening‘) in ) in off-shelloff-shell transport models:transport models: HSD (>2000)HSD (>2000)

BRoBUU (Rossendorf) (2006) BRoBUU (Rossendorf) (2006)

16

Modelling of in-medium spectral functions for Modelling of in-medium spectral functions for vector mesonsvector mesons

In-medium scenarios:In-medium scenarios:

dropping mass collisional broadening dropping mass + coll. dropping mass collisional broadening dropping mass + coll. broad.broad.

m*=mm*=m00(1-(1-) ) (M,(M,)=)=vacvac(M)+(M)+CBCB(M,(M,) m* & ) m* & CBCB(M,(M,Collisional widthCollisional widthCBCB(M,(M,) = ) = VNVNtottot

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.010-2

10-1

100

101

102

/ 0 1 2 3 5

M [GeV/c2]

dropping mass

A(M

)

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.010-3

10-2

10-1

100

101

102

/ 0 1 2 3 5

M [GeV/c2]

collisional broadeningA

(M)

meson spectral function:meson spectral function:

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.010-3

10-2

10-1

100

101

102

M [GeV/c2]

/ 0 1 2 3 5

dropping mass + collisional broadening

A(M

)

• Note:Note: for a consistent off-shell transportfor a consistent off-shell transport one one needsneeds not only in-medium not only in-medium spectral functions but also spectral functions but also in-medium transition ratesin-medium transition rates for all channels with for all channels with vector mesons, i.e. the full knowledge of the vector mesons, i.e. the full knowledge of the in-medium off-shell cross in-medium off-shell cross sections sections (s,(s,))

E.L.B., NPA 686 (2001), E.L.B. &W. Cassing, NPA 807 (2008) 214E.L.B., NPA 686 (2001), E.L.B. &W. Cassing, NPA 807 (2008) 214

0.0 0.2 0.4 0.6 0.810-8

10-7

10-6

10-5

10-4

10-3

10-2

0.0 0.2 0.4 0.6 0.810-8

10-7

10-6

10-5

10-4

10-3

10-2

HADES

HSD: Dalitz Dalitz Dalitz Dalitz Brems. NN Brems. N All

C+C, 1.0 A GeVno medium effects

1/N

dN/d

M [

1/G

eV /c

2 ]

HSD: Dalitz Dalitz Dalitz Dalitz Brems. NN Brems. N All

M [GeV/c2]

HADES

C+C, 1.0 A GeVin-medium effects: CB+DM

1/N

dN/d

M [

1/G

eV /c

2 ]

HSD: Dileptons from C+C at 1 and 2 A GeV - HADESHSD: Dileptons from C+C at 1 and 2 A GeV - HADES

• HADES data show exponentially decreasing mass spectra HADES data show exponentially decreasing mass spectra • Data are Data are better described by in-medium scenarios with collisional broadening better described by in-medium scenarios with collisional broadening • In-medium effects are more pronounced for In-medium effects are more pronounced for heavy systemsheavy systems such as Au+Au such as Au+Au

0.0 0.2 0.4 0.6 0.8 1.010-8

10-7

10-6

10-5

10-4

10-3

10-2

0.0 0.2 0.4 0.6 0.8 1.010-8

10-7

10-6

10-5

10-4

10-3

10-2

HADES

HSD: Dalitz Dalitz Dalitz Dalitz Brems. NN Brems. N All

C+C, 2.0 A GeVno medium effects

1/N

dN/d

M [

1/G

eV /c

2 ]

HSD: Dalitz Dalitz Dalitz Dalitz Brems. NN Brems. N All

M [GeV/c2]

HADES

C+C, 2.0 A GeVin-medium effects: CB+DM

1/N

dN/d

M [

1/G

eV /c

2 ]

HSD: Dileptons from A+A at 1 A GeV - DLSHSD: Dileptons from A+A at 1 A GeV - DLS

• bremsstrahlungbremsstrahlung and and -Dalitz are the dominant contributions -Dalitz are the dominant contributions in A+A for 0.15 < M < 0.55 GeV at 1 A GeV !in A+A for 0.15 < M < 0.55 GeV at 1 A GeV !

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

10-3

10-2

10-1

100

101

102

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

10-3

10-2

10-1

100

101

102

Brems. NN Brems. N All

DLS Dalitz Dalitz Dalitz Dalitz

C+C, 1.04 A GeVin-medium effects: CB+DM

d/d

M [b

/(G

eV c

2 )]

M [GeV/c2]

Brems. NN Brems. N All

DLS Dalitz Dalitz Dalitz Dalitz

C+C, 1.04 A GeVno medium effects

d/d

M [b

/(G

eV c

2 )]

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.010-3

10-2

10-1

100

101

102

103

104

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.010-3

10-2

10-1

100

101

102

103

104

Brems. NN Brems. N All

DLS Dalitz Dalitz Dalitz Dalitz

Ca+Ca, 1.04 A GeVin-medium effects: CB+DM

d/d

M [b

/(G

eV c

2 )]

M [GeV/c2]

Brems. NN Brems. N All

DLS Dalitz Dalitz Dalitz Dalitz

Ca+Ca, 1.04 A GeVno medium effects

d/d

M [b

/(G

eV c

2 )]

19

Dileptons at SPSDileptons at SPS

0.0 0.2 0.4 0.6 0.8 1.0 1.210-9

10-8

10-7

10-6

10-5

10-4

0.0 0.2 0.4 0.6 0.8 1.0 1.210-9

10-8

10-7

10-6

10-5

10-4

HSD: free s.f. coll. broad.

CERES:7% (2008 data)30% (95/96 data)

pT> 200 MeV/c

e+e-> 35 mrad

2.1 < < 2.65

<dN

e+ e- /dM

> / <

Nch

> [(

100

MeV

/c2 )

-1]

M [GeV/c2]

Pb+Au, 160 A GeV, 7%

CERES HSD:

free s.f. coll. broad.

pT> 200 MeV/c

e+e-> 35 mrad

2.11 < < 2.64

<dN

e+ e- /dM

> / <

Nch

> [(

100

MeV

/c2 )

-1] Pb+Au, 40 A GeV, 30%

0.2 0.4 0.6 0.8 1.0 1.20

100

200

300

400

500

600

700

800

0.2 0.4 0.6 0.8 1.0 1.20

500

1000

1500

2000

2500

0.2 0.4 0.6 0.8 1.0 1.20

500

1000

1500

2000

2500

3000

0.2 0.4 0.6 0.8 1.0 1.20

200

400

600

800

1000

1200

1400

1600

1800

In+In, 160 A GeV, all pTPeripheral

dN/d

M p

er 2

0 M

eV

Semi-Peripheral

NA60

Semi-Central

M [GeV/c2]

dN/d

M p

er 2

0 M

eV

HSD: free s. f. coll. broad.

Central

M [GeV/c2]

NA60NA60CERESCERES

• NA60 and CERS data are better described byNA60 and CERS data are better described by in-medium scenario with in-medium scenario with collisional broadening collisional broadening

20

Dileptons at RHICDileptons at RHIC

PHENIX: Au+AuPHENIX: Au+AuPHENIX: ppPHENIX: pp

• HSD provides a HSD provides a good description of pp datagood description of pp data • Standard in-medium effects of vector Standard in-medium effects of vector mesons -- compatible with the NA60 and mesons -- compatible with the NA60 and CERES data at SPS – CERES data at SPS – do not explain the do not explain the large enhancement observed by PHENIXlarge enhancement observed by PHENIX in in the invariant mass from 0.2 to 0.5 GeV in the invariant mass from 0.2 to 0.5 GeV in Au+Au collisions at s Au+Au collisions at s 1/21/2=200 GeV (relative to =200 GeV (relative to pp collisions)pp collisions)

0.0 0.2 0.4 0.6 0.8 1.0 1.210-8

10-7

10-6

10-5

10-4

10-3

PHENIX HSD: sum

0 ' c+c e++e (PYTHIA)

M [GeV/c2]

p+p, s1/2=200 GeV

1/N

evt d

N/d

M [

1/(G

eV/c

2 )]

0.0 0.2 0.4 0.6 0.8 1.0 1.2

10-5

10-4

10-3

10-2

10-1

0.0 0.2 0.4 0.6 0.8 1.0 1.210-6

10-5

10-4

10-3

10-2

10-1

HSD: free spectral functions collisional broadening dropp. mass + coll. broad.

PHENIX

min. bias Au+Au, s1/2=200 GeV

M [GeV/c2]

1/N

evt d

N/d

M [

1/(G

eV/c

2 )]

HSD (free spectral functions): sum

0 ' c + c e++e (PYTHIA)

PHENIX

min. bias Au+Au, s1/2=200 GeV

M [GeV/c2]

1/N

evt d

N/d

M [

1/(G

eV/c

2 )]

21

SummarySummary

• Accounting ofAccounting of in-medium effects in-medium effects with medium dependent spectral with medium dependent spectral functionsfunctions requires off-shell requires off-shell transport models !transport models !

• Coupled-channel G-matrix Coupled-channel G-matrix ++ off-shell transport off-shell transport approach is the approach is the most consistent waymost consistent way to investigate to investigate in-medium effects in-medium effects

0

2

4

6

8

10

20

1.50

0

0.50

A(s

) [M

eV-1]

p=0 MeV/c

A(s

) [M

eV-1]

20

1.50

0

0.50

p=150 MeV/c

0.2 0.4 0.6 0.80

2

4

6

8

10

20

1.50

0

0.50

s1/2

[GeV]

p=300 MeV/c

s1/2

[GeV]

0.2 0.4 0.6 0.8

20

1.50

0

0.50

p=500 MeV/c

22

Thanks toThanks to

Laura TolosLaura Tolos

Olena LinnykOlena Linnyk

Wolfgang CassingWolfgang Cassing