In-medium hadrons and chiral symmetry G. Chanfray, IPN Lyon, IN2P3/CNRS, Université Lyon I The Physics of High Baryon Density IPHC Strasbourg, september 19, 2006 In-medium hadrons Chiral dynamics Many-body problem -Chiral restoration -Nucleon structure/ confinement -Lattice QCD -Renormalization group Intermediate energy Machines (1 GeV) Relativistic heavy ion collisions

Chiral symmetry breaking Pions (kaons): Goldstone bosons Quark condensate : order parameter (magnétisation ) Modifications of QCD vacuum Hadrons =elementary excitations also modified HADRONIC SPECTRAL FUNCTIONS Chiral symmetry restoration Equation of state at finite T and  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 - Increase of D Dbar -Opening of Channels - Mechanism for the suppression of the Production Expériences 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 Nucleon Sigma 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 interaction and (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 : 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 correlator In 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 0 at chiral restoration

Axialvector / Vector in Vacuum pQCD continuum Im  em ~ [ImD  +ImD  /10+ImD  /5] Low-Mass Dilepton Rate:  - meson dominated! Axialvector Channel:  ±  invariant mass-spectra ~ Im D a1 (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 EnergyLower 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

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 group Matching 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] 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