QCD Phase Diagram from Finite Energy Sum Rules
Alejandro AyalaInstituto de Ciencias Nucleares, UNAM
(In collaboration with A. Bashir, C. Domínguez, E. Gutiérrez, M. Loewe, and A. Raya)
arXiv:1106.5155 [hep-ph]
Outline
• Deconfinement and chiral symmetry restoration
• Resonance threshold energy as phenomenological tool to study deconfinement
• QCD sum rules at finite temperature/chemical potential
• Results
Deconfinement and chiral symmetry restoration
Driven by same effect:
• With increasing density, confining interaction gets screened and eventually becomes less effective (Deconfinement)
• Inside a hadron, quark mass generated by confining interaction. When deconfinement occurres, generated mass is lost (chiral transition)
Critical end point?
Lattice quark condensate and Polyakov loop
A. Bazavov et al., Phys. Rev. D 90, 014504 (2009)
Status of phase diagram• =0: Physical quark masses, deconfinement and chiral
symmetry restoration coincide. Smooth crossover for 170 MeV < Tc < 200 MeV
• Analysis tools: – Lattice (not applicable at finite ) – Models (Polyakov loop, quark condesate)
• Lattice vs. Models: – Lattices gives: smaller/larger
chemical potential/temperature values for endpoint than models
• Critical end point might not even exist!
Alternative signature: Melting of resonances
s
Im
s0pole
For increasing T and/or B the energy threshold for the continuum goes to 0
Correlator of axial currents
Quark – hadron duality
Operator product expansion
Finite energy sum rules
Non-pert part: dispersion relations
Pert part: imaginary parts at finite T and
Two contributions:
1)Annihilation channel (available also at T==0)2)Dispersion channel (Landau damping)
Imaginary parts at finite T and Annihilation term
Dispersion term
Pion pole
Threshold s0 at finite T and
GMOR
N=1, C2<O2> = 0
2
Need quark condensate at finite T and
quark condensate T, 0
Poisson summation formula
quark condensate
Parameters fixed by requiring S-D conditions and description of lattice data
Lose of Lorentz covariance means that
Parametrize S-D solution in terms of “free-like” propagators
A. Bazavov et al., Phys. Rev. D 90, 014504 (2009)
Representation makes it easy to carry out integration
28 _
Susceptibilities
QCD Phase Diagram
Summary and conclusions
• QCD phase diagram rich in structure: critical end point?• Polyakov loop, quark condensate analysis can be
supplemented with other signals: look at threshold s0 as function of T and
• Finite energy QCD sum rules provide ideal framework. Need calculation of quark condesnate. Use S-D quark propagator parametrized with “free-like” structures.
• Transition temperatures coincide, method not accurate enough to find critical point, stay tuned.
