QCD Phase Diagram and Finite Energy Sum Rules
Alejandro AyalaInstituto de Ciencias Nucleares, UNAM
(In collaboration with A. Bashir, C. Domínguez, E. Gutiérrez, M. Loewe, and A. Raya, )
Outline
• Status of QCD phase diagram
• Resonance threshold energy as phenomenological tool to study deconfinement
• QCD sum rules at finite temperature/chemical potential
• Non-perturbative quark propagator
Lattice at B=0
Deconfinement and chiral symmetry restoration
Driven by same effect:
• 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)
Possible scenarios for QCD phase diagram
Zooming in: Heavy ion experiments
Lattice quark condensate and Polyakov loop
Critical end point
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 values for endpoint chemical potential/temperature 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
Quark – hadron duality
Operator product expansion
Finite energy sum rules
Dispersion relations
s
s0
Dispersion relations
Imaginary parts at finite T and
Imaginary parts at finite T and
Annihilation term
Dispersion term
Pion pole
Threshold s0 at finite T and
GMOR
N=1, C2<O2> = 0
Need quark condensate at finite T and
• At T==0, general structure:
Parametrize S-D solution in terms of “free-like” propagators
Parameters fixed by requiring S-D conditions on the above functions
T0, Lorentz covariant is lost
Strategy: Add an extra “free-like” propagator
Find extra parameters fitting, for example,
to quark condensate and pressure at T0
+
quark condensate T, 0
Poisson summation formula
quark condensate
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 s0as 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.
• Results… stay tuned!