In-medium hadronsand chiral symmetry

G. Chanfray, IPN Lyon, IN2P3/CNRS, Université Lyon I

The Physics of High Baryon DensityIPHC Strasbourg, september 19, 2006

In-mediumhadrons

Chiraldynamic

s

Many-bodyproblem

-Chiral restoration

-Nucleon structure/ confinement

-Lattice QCD

-Renormalization group

Intermediate energy Machines (1 GeV)

Relativistic heavy ioncollisions

Chiral symmetry breaking Pions (kaons): Goldstone bosons Quark condensate : order parameter (magnétisation)

Modifications of QCD vacuumHadrons =elementary excitations also modified

HADRONIC SPECTRAL FUNCTIONS

Chiral symmetry restoration

Equation of state at finite T and

),,(ln),,( BB TVZTTV

Hadron spectral function and chiral dynamics

Hadron spectral function Current-current correlator

In the medium: Spectral functions of chiral partners should converge: Chiral dynamics?

Fluctuation currents Hadrons

THERMAL SUSCEPTIBILITY

Chiral restoration and hadron structure

In-medium mass splitting generated by chiral dynamics

Pions

Generated by chiral dynamics, linked to condensate evolution

Light quark q fluctuating around a heavy color source: sensitive to the quark condensate (QCD sum rules):

Open charm )(/)( cqDqcD

MeVm )/(50 0

- Increase of D Dbar

DD'-Opening of Channels

- Mechanism for the suppression of the /(J

Production

ApExpériences PANDA/GSI

QCD susceptibilities: fluctuations of the quark condensate

Compare susceptibilities associated with chiral partners

Scalar (sigma) : Pseudoscalar (pion) :

PSEUDOSCALAR

SCALAR

Scalar susceptibility : from the scalar correlator i.e. the correlator of the scalar quark density fluctuations

-Meson in Normal Nuclear Matter

New Data for A → X→ 0 X : [CBELSA/TAPS ‘05]

subtract

• dropping -mass! (m)med ≈ 720MeV, ()med ≈ 60MeV• consistent with (some) hadronic models• connection to baryon-no./chiral susceptibility? (- mixing)

[Klingl etal ’97]

Chiral effective theory

The chiral invariant s field governs the evolution of the masses : we identify it with the sigma field of nuclear physics (M. Ericson, P. Guichon, G.C)

Matter stability: include the scalar response of the nucleon (confinement)Interplay between nuclear structure, chiral dynamics and nucleon structure. Insight from lattice QCD

Msigma=800 MeV Gv=7.3 C=1+ Density dependence

DENSITY

E / A

Mean field (s + omega)

Total

Fock

MASSES

NucleonSigma

Sigma + chiral dropping

SUSCEPTIBILITIES

PSEUDO SCALAR

SCALAR

Higher densities ?Phase transition to quark matter ?

The sigma mass remains stable

Fixing the parameters (nucleon susceptibility) using lattice data

To study phase transition to quark matter: chiral theory Incorporating confinement at the quark level

Attempt (Lawley, Bentz, Thomas): NJL model including diquark interactionand (kind of) confinement

-Low T, : Spontaneous chiral symmetry breaking : quark condensate

-Nucleon : Quark + diquark bound state, confinement generates a scalar susceptibility

-Stable nuclear matter

-High pairing and diquark condensate: color superconducting phase

Phases of matter in equilibrium

Neutron star

Towards High baryonic densites

HEAVY IONS : 10- 40 A.GeV

FAIR/CBM

ISSUES - Chiral symmetry restoration and deconfinement - (Tri)critical point? - Hadrons near phase transition ?

SIGNATURES - Bulk thermodynamic variables - In-medium hadron spectral functions - Charm, dileptons

THEORETICAL TOOLS - Lattice QCD at finite - Effective theories - Renormalization group

Theoretical approaches

• Density expansion• Many-body approaches• Transport codes• QCD sum rules• Weinberg sum rules• ………• Renormalization group

Dilepton production

Current current correlatorIn the vector channel

Dominance

Vector and axialvector spectral functions

Chiral restoration means : vector and axialvector correlation functions become identical

Associated with chiral partners - a1(1260)

An illustration : Weinberg sum rule

)Im(Ims

dsf AV

2 0 at chiral restoration

Axialvector / Vector in Vacuum

pQCDcontinuum

)T(fMqdxd

dN Bee23

2

44 Imem ~ [ImD+ImD/10+ImD/5]

• Low-Mass Dilepton Rate:-mesondominated!

• Axialvector Channel: ± invariant mass-spectra ~ Im Da1(M) ?!

Axialvector / Vector near Tc

Axialvector / Vector at finite density

Axial =Vector + 1 pion from the medium

meson melts in dense matter

Baryon density more important than temperature(40A. GeV vs 158A. GeV)

Hades data/ Futur GSI: CBM (~ 30A.GeV)

Top SPS Energy Lower SPS Energy

→ Evolve dilepton rates over thermal fireball QGP+Mix+HG (Rapp et al):

QGP contribution small

Medium effects on meson

Pb-Au collisions at CERN/SPS : CERES/NA45

NA60 has    extracted  the rho meson spectral function

In-In collisions at CERN/SPS: dimuons from NA60

Free spectral function ruled out Meson gas insufficient

Consistent with the modification(broadening) of the rho meson spectral function(Rapp-Wambach/Chanfray )

Simplistic dropping mass ruled out

0

2

11

B

c

B CTT

m

),T(mvac

HADES data

Perspectives

Strong constraints on effective theories( EFT)

Lattice data at finite

One particular Model exemple(HLS)

gauge boson of a hidden local symmetry

Matching of the correlators at :

Renormalization group equations

Brown-Rho scaling near phase transition ?

Renormalization groupMatching of EFT to QCD

Fate of VDM at finite T and

Conclusions

Chiral invariant scalar mode = amplitude fluctuation of the condensate - Sigma mass stabilized by confinement effect in hadronic phase

Dilepton production : broadening of the rho meson dominated by baryonic effects but - Fate of vector dominance ? - Dropping of the rho mass ? - Through its coupling to the condensate: from the dropping of the sigma mass near the critical point (Shuryak)

3.5.3 NA60 Data: Other -Spectral Functions

Switch off medium modifications

• free spectral function ruled out• meson gas insufficient either

• simplistic dropping mass disfavored:

• vector manifest. of -symmetry? vector dominance?[Harada+Yamawaki, Brown+Rho ‘04]

0

2

11

B

c

B CTT

m

),T(mvac

Chiral Virial Approach

[Dusling,Teaney+Zahed ‘06]• lacks broadening

-Meson in Normal Nuclear Matter

New Data for A → X→ 0 X : [CBELSA/TAPS ‘05]

subtract

• dropping -mass! (m)med ≈ 720MeV, ()med ≈ 60MeV• consistent with (some) hadronic models• connection to baryon-no./chiral susceptibility? (- mixing)

[Klingl etal ’97]

In-medium mass splitting generated by chiral dynamics

Pions

Pattern of symmetry breaking generated by chiral dynamics

Axial-vector mixing at finite temperature