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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
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
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
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